#pragma once

#include "OwnerWorldLoader.h"
#include "StandaloneResearchTunnels.h"
#include "VoxelCaveMorphology.h"
#include "VoxelNoise.h"
#include "VoxelStrateManager.h"
#include "VoxelDensityPrimitives.h"
#include "VoxelForgeCore/VoxelForgeCore.h"
#include "VoxelForgeFieldShared.h"

#include <algorithm>
#include <array>
#include <atomic>
#include <bit>
#include <chrono>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <limits>
#include <memory>
#include <mutex>
#include <immintrin.h>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <variant>
#include <vector>

// Standalone-only world compiler. It compiles the runtime room/tunnel/passages into
// axis-line intervals, composes rock/cave signs into packed Z-column words, then displaces
// only the conservative surface band. The copied Unreal generator remains the A/B reference.
class FStandaloneShapeWorld
{
public:
    const VoxelForgeCore::ResolvedLayoutSnapshotV3* ResolvedLayout=nullptr;
    struct FResolvedStratumBounds
    {
        double BottomZ=0.0;
        double TopZ=0.0;
        double SealThickness=0.0;
    };

    // Immutable adapters share densityAt(x,y,z,out) without a virtual call in the sample
    // loop. The variant is selected once per resolved strate; callers retain concrete access
    // to fixed-point and interval operations where the legacy arithmetic requires them.
    struct FSurfaceWorldFieldAdapter
    {
        VoxelForgeCore::Heightfield2D Evaluator;
        FSurfaceWorldFieldAdapter(const VoxelForgeCore::WorldAssemblyRecipeV1& Recipe,
            const VoxelForgeCore::WorldAssemblyStratumPlanV1& Plan) noexcept
            :Evaluator(Recipe,Plan){}

        bool densityAt(float X,float Y,float Z,float& OutDensity) const noexcept
        {
            if(!std::isfinite(X)||!std::isfinite(Y)||!std::isfinite(Z))return false;
            constexpr double Scale=static_cast<double>(
                VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
            const double MaxVoxel=static_cast<double>(std::numeric_limits<int64>::max())/Scale;
            if(std::abs(static_cast<double>(X))>MaxVoxel
                ||std::abs(static_cast<double>(Y))>MaxVoxel
                ||std::abs(static_cast<double>(Z))>MaxVoxel)return false;
            const auto ToFixed=[](float Value)
            {return static_cast<int64>(std::llround(static_cast<double>(Value)
                *VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel));};
            if(!Evaluator.isValid())return false;
            OutDensity=static_cast<float>(Evaluator.point(ToFixed(X),ToFixed(Y),ToFixed(Z))
                .densitySubvoxels/Scale);
            return true;
        }
    };

    struct FFloatingIslandFieldAdapter
    {
        VoxelForgeCore::FloatingIslandFieldV1 Evaluator;
        int32 BottomChunkZ=0;
        std::vector<FFloatingIslandParams> LegacyBoundaryParams;

        FFloatingIslandFieldAdapter(const VoxelForgeCore::FloatingIslandRecipeV1& Recipe,
            const VoxelForgeCore::FloatingIslandPlanV1& Plan,int32 InBottomChunkZ,
            int32 InTopChunkZ,const UVoxelStrateManager* Manager)
            :Evaluator(Recipe,Plan),BottomChunkZ(InBottomChunkZ)
        {
            if(Manager&&Recipe.geometryVersion<4&&InTopChunkZ>=InBottomChunkZ)
            {
                LegacyBoundaryParams.reserve(static_cast<std::size_t>(
                    static_cast<int64>(InTopChunkZ)-InBottomChunkZ+1));
                for(int32 ChunkZ=InBottomChunkZ;ChunkZ<=InTopChunkZ;++ChunkZ)
                    LegacyBoundaryParams.push_back(Manager->GetFloatingIslandParamsForChunk(
                        FIntVector(0,0,ChunkZ)));
            }
        }

        std::int64_t densitySubvoxelsAt(std::int64_t X,std::int64_t Y,
            std::int64_t Z) const noexcept
        {return Evaluator.densitySubvoxels(X,Y,Z);}

        const FFloatingIslandParams* legacyBoundaryParamsAt(int32 ChunkZ) const noexcept
        {
            const int64 Index=static_cast<int64>(ChunkZ)-BottomChunkZ;
            return Index>=0&&static_cast<std::size_t>(Index)<LegacyBoundaryParams.size()
                ?&LegacyBoundaryParams[static_cast<std::size_t>(Index)]:nullptr;
        }

        bool densityAt(float X,float Y,float Z,float& OutDensity) const noexcept
        {
            if(!Evaluator.isValid()||!std::isfinite(X)||!std::isfinite(Y)
                ||!std::isfinite(Z))return false;
            constexpr double Scale=static_cast<double>(
                VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
            constexpr double Maximum=1000000000000.0/Scale;
            if(std::abs(static_cast<double>(X))>Maximum
                ||std::abs(static_cast<double>(Y))>Maximum
                ||std::abs(static_cast<double>(Z))>Maximum)return false;
            const auto ToFixed=[](float Value)
            {return static_cast<int64>(std::llround(static_cast<double>(Value)
                *VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel));};
            OutDensity=static_cast<float>(static_cast<double>(densitySubvoxelsAt(
                ToFixed(X),ToFixed(Y),ToFixed(Z)))/Scale);
            return std::isfinite(OutDensity);
        }
    };

    struct FLegacyGeneratorFieldAdapter
    {
        const UVoxelGenerator* Generator=nullptr;
        bool densityAt(float X,float Y,float Z,float& OutDensity) const
        {
            if(!Generator)return false;
            OutDensity=Generator->GetDensityAt(X,Y,Z);
            return std::isfinite(OutDensity);
        }
    };

    using FGeneratorFieldAdapterV1=std::variant<std::monostate,
        FSurfaceWorldFieldAdapter,FFloatingIslandFieldAdapter,
        FLegacyGeneratorFieldAdapter>;

    struct FBoundStratumField
    {
        enum class EKind : uint8 { Legacy, SurfaceWorld, FloatingIslands };
        const VoxelForgeCore::ResolvedLayoutStratumV2* Resolved=nullptr;
        const VoxelForgeCore::WorldAssemblyStratumPlanV1* SurfacePlan=nullptr;
        const VoxelForgeCore::WorldAssemblyFloatingIslandPlanV1* IslandPlan=nullptr;
        FGeneratorFieldAdapterV1 Evaluator;
        int32 StrateIndex=-1;
        int32 BottomChunkZ=0;
        int32 TopChunkZ=-1;
        EKind Kind=EKind::Legacy;
    };

    const std::vector<FStandalonePassageVoidCrossing>& GetPassageVoidCrossings() const
    {return PassageVoidCrossings;}

    class FScopedPassageTileQueries
    {
    public:
        FScopedPassageTileQueries(const FStandaloneShapeWorld& shape,
            const std::array<std::int64_t,3>& minimumSubvoxels,
            const std::array<std::int64_t,3>& maximumSubvoxels)
            :shape_(&shape),minimumSubvoxels_(minimumSubvoxels),
             maximumSubvoxels_(maximumSubvoxels),previous_(ActivePassageTileQueries)
        {
            mayContainResolvedBoundaryBand_=shape.ResolvedBoundaryBandsIntersectSubvoxelRange(
                minimumSubvoxels_[2],maximumSubvoxels_[2]);
            mayContainTransitionPassageFade_=shape.ResolvedTransitionPassageFadeIntersectsTileXY(
                minimumSubvoxels_,maximumSubvoxels_);
            featureIndices_=shape.BuildPassageFeatureTileList(
                minimumSubvoxels_,maximumSubvoxels_);
            stampIndices_=shape.BuildStampTileList(minimumSubvoxels_,maximumSubvoxels_);
            cavernFeatureIndices_=shape.BuildCavernFeatureTileList(
                minimumSubvoxels_,maximumSubvoxels_);
            passageRoutes_.assign(shape.ResolvedLayout?shape.ResolvedLayout->passages.size():0,0);
            passageColumns_=passageRoutes_;
            passageMouthSupports_=passageRoutes_;
            for(const auto& crossing:shape.PassageVoidCrossings)
                if(crossing.needsColumn
                    &&crossing.bottomZSubvoxels<=maximumSubvoxels_[2]
                    &&crossing.topZSubvoxels>=minimumSubvoxels_[2])
                    columnZOverlap_=true;
            for(const std::uint32_t featureIndex:featureIndices_)
            {
                if(featureIndex>=shape.PassageTileFeatures.size())continue;
                const auto& feature=shape.PassageTileFeatures[featureIndex];
                if(feature.passageIndex>=passageRoutes_.size())continue;
                if(feature.bColumn)passageColumns_[feature.passageIndex]=1;
                else if(feature.bMouthSupport)passageMouthSupports_[feature.passageIndex]=1;
                else
                {
                    passageRoutes_[feature.passageIndex]=1;
                    routeFeatureOverlap_=true;
                }
            }
            ActivePassageTileQueries=this;
        }
        ~FScopedPassageTileQueries(){ActivePassageTileQueries=previous_;}
        FScopedPassageTileQueries(const FScopedPassageTileQueries&)=delete;
        FScopedPassageTileQueries& operator=(const FScopedPassageTileQueries&)=delete;

        bool matches(const FStandaloneShapeWorld& shape) const{return shape_==&shape;}
        bool hasFeature(std::size_t passageIndex,bool columnFeature) const
        {
            const auto& candidates=columnFeature?passageColumns_:passageRoutes_;
            return passageIndex<candidates.size()&&candidates[passageIndex]!=0;
        }
        bool hasMouthSupport(std::size_t passageIndex) const
        {return passageIndex<passageMouthSupports_.size()&&passageMouthSupports_[passageIndex]!=0;}
        bool hasAnyMouthSupport() const
        {return std::any_of(passageMouthSupports_.begin(),passageMouthSupports_.end(),
            [](std::uint8_t value){return value!=0;});}
        bool hasRouteFeatureOverlap() const{return routeFeatureOverlap_;}
        bool hasColumnZOverlap() const{return columnZOverlap_;}
        bool mayContainResolvedBoundaryBand() const{return mayContainResolvedBoundaryBand_;}
        bool mayContainTransitionPassageFade() const{return mayContainTransitionPassageFade_;}
        bool mayContainResolvedBoundaryBandAtZ(double zMicrometres) const
        {
            return mayContainResolvedBoundaryBand_
                &&shape_->ResolvedBoundaryBandMayAffectAtZMicrometres(zMicrometres);
        }
        std::size_t featureCount() const{return featureIndices_.size();}
        bool hasStampCandidates() const{return !stampIndices_.empty();}
        const std::vector<std::uint32_t>& stampCandidates() const{return stampIndices_;}
        bool hasCavernCandidates() const{return !cavernFeatureIndices_.empty();}
        const std::vector<std::uint32_t>& cavernFeatureCandidates() const
        {return cavernFeatureIndices_;}

    private:
        const FStandaloneShapeWorld* shape_;
        std::array<std::int64_t,3> minimumSubvoxels_,maximumSubvoxels_;
        std::vector<std::uint32_t> featureIndices_;
        std::vector<std::uint32_t> stampIndices_;
        std::vector<std::uint32_t> cavernFeatureIndices_;
        std::vector<std::uint8_t> passageRoutes_,passageColumns_,passageMouthSupports_;
        bool routeFeatureOverlap_=false,columnZOverlap_=false;
        bool mayContainResolvedBoundaryBand_=true;
        bool mayContainTransitionPassageFade_=true;
        const FScopedPassageTileQueries* previous_;
    };

    bool IsResolvedPassageColumnSample(std::size_t PassageIndex,std::size_t SegmentIndex,
        const VoxelForgeCore::Vec3d& Position) const
    {
        (void)SegmentIndex;
        for(const auto& range:PassageVoidCrossings)
        {
            if(!range.needsColumn||range.passageIndex!=PassageIndex)continue;
            if(PassageColumnSignedDistance(range,static_cast<float>(Position.x),
                static_cast<float>(Position.y),static_cast<float>(Position.z))<=0.0)return true;
        }
        return false;
    }

    bool IsResolvedPassageShortSpanSample(std::size_t PassageIndex,std::size_t SegmentIndex,
        const VoxelForgeCore::Vec3d& Position) const
    {
        return IsPassageShortSpanSegment(PassageIndex,SegmentIndex)
            &&PassageBridgeSignedDistance(PassageIndex,SegmentIndex,
                static_cast<float>(Position.x),static_cast<float>(Position.y),
                static_cast<float>(Position.z))<=0.0;
    }

    double GetCoreVoxelSizeCm() const
    {
        return Owner == nullptr || Owner->CoreVoxelSizeMicrons == 0
            ? static_cast<double>(VOXEL_SIZE)
            : static_cast<double>(Owner->CoreVoxelSizeMicrons) / 10000.0;
    }

    double GetResolvedLayoutChunkWidthVoxels() const
    {
        return ResolvedLayout&&ResolvedLayout->strateLayoutChunkWidthSubvoxels>0
            ?static_cast<double>(ResolvedLayout->strateLayoutChunkWidthSubvoxels)
                /VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel
            :Owner?static_cast<double>(Owner->StrateLayoutChunkWidthSubvoxels)
                /VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel:0.0;
    }

    const VoxelForgeCore::ResolvedLayoutStratumV2* FindResolvedLayoutStratum(int32 StrateIndex) const
    {
        if(!ResolvedLayout)return nullptr;
        if(StrateIndex>=0&&static_cast<std::size_t>(StrateIndex)<ResolvedLayout->strates.size())
        {
            const auto& direct=ResolvedLayout->strates[static_cast<std::size_t>(StrateIndex)];
            if(direct.strateIndex==StrateIndex)return &direct;
        }
        const auto it=std::find_if(ResolvedLayout->strates.begin(),ResolvedLayout->strates.end(),
            [StrateIndex](const auto& item){return item.strateIndex==StrateIndex;});
        return it==ResolvedLayout->strates.end()?nullptr:&*it;
    }

    void BindResolvedStratumFields()
    {
        BoundStratumFields.clear();
        BoundManagerLayoutChunkWidthVoxels=Owner&&Owner->Manager
            ?Owner->Manager->GetStrateLayoutChunkWidthVoxels():0.0f;
        if(!ResolvedLayout||ResolvedLayout->strateLayoutChunkSizeMicrometres<=0)return;
        const int64 ChunkWidthMicrometres=ResolvedLayout->strateLayoutChunkSizeMicrometres;
        const auto FloorDiv64=[](int64 Value,int64 Divisor)
        {
            const int64 Quotient=Value/Divisor;
            const int64 Remainder=Value%Divisor;
            return Remainder<0?Quotient-1:Quotient;
        };
        BoundStratumFields.reserve(ResolvedLayout->strates.size());
        for(const auto& Stratum:ResolvedLayout->strates)
        {
            if(Stratum.strateIndex<0
                ||Stratum.interiorTopMicrometres<=Stratum.interiorBottomMicrometres)
                continue;
            const int64 Bottom=FloorDiv64(Stratum.interiorBottomMicrometres,
                ChunkWidthMicrometres);
            const int64 Top=FloorDiv64(Stratum.interiorTopMicrometres-1,
                ChunkWidthMicrometres);
            if(Bottom<std::numeric_limits<int32>::min()
                ||Bottom>std::numeric_limits<int32>::max()
                ||Top<std::numeric_limits<int32>::min()
                ||Top>std::numeric_limits<int32>::max()||Top<Bottom)continue;

            FBoundStratumField Bound;
            Bound.Resolved=&Stratum;
            Bound.StrateIndex=Stratum.strateIndex;
            Bound.BottomChunkZ=static_cast<int32>(Bottom);
            Bound.TopChunkZ=static_cast<int32>(Top);
            if(Stratum.generatorKind=="SurfaceWorld")
            {
                Bound.Kind=FBoundStratumField::EKind::SurfaceWorld;
                if(WorldAssembly)
                {
                    const auto Plan=std::find_if(WorldAssembly->plan.strates.begin(),
                        WorldAssembly->plan.strates.end(),[&](const auto& Candidate)
                        {return Candidate.strateIndex==Bound.StrateIndex
                            &&Candidate.bottomChunkZ==Bound.BottomChunkZ
                            &&Candidate.topChunkZ==Bound.TopChunkZ;});
                    if(Plan!=WorldAssembly->plan.strates.end())
                    {
                        Bound.SurfacePlan=&*Plan;
                        FSurfaceWorldFieldAdapter Adapter(WorldAssembly->recipe,*Plan);
                        if(Adapter.Evaluator.isValid())
                            Bound.Evaluator.emplace<FSurfaceWorldFieldAdapter>(
                                std::move(Adapter));
                    }
                }
            }
            else if(Stratum.generatorKind=="FloatingIslands")
            {
                Bound.Kind=FBoundStratumField::EKind::FloatingIslands;
                if(WorldAssembly)
                {
                    const auto Plan=std::find_if(WorldAssembly->floatingIslands.begin(),
                        WorldAssembly->floatingIslands.end(),[&](const auto& Candidate)
                        {return Candidate.strateIndex==Bound.StrateIndex
                            &&Candidate.bottomChunkZ==Bound.BottomChunkZ
                            &&Candidate.topChunkZ==Bound.TopChunkZ;});
                    if(Plan!=WorldAssembly->floatingIslands.end())
                    {
                        Bound.IslandPlan=&*Plan;
                        Bound.Evaluator.emplace<FFloatingIslandFieldAdapter>(
                            Plan->manifest.recipe,Plan->manifest.plan,
                            Bound.BottomChunkZ,Bound.TopChunkZ,
                            Owner?Owner->Manager.get():nullptr);
                    }
                }
            }
            if(std::holds_alternative<std::monostate>(Bound.Evaluator))
                Bound.Evaluator.emplace<FLegacyGeneratorFieldAdapter>(
                    FLegacyGeneratorFieldAdapter{Owner?Owner->Generator.get():nullptr});
            BoundStratumFields.push_back(std::move(Bound));
        }
        std::sort(BoundStratumFields.begin(),BoundStratumFields.end(),
            [](const auto& A,const auto& B){return A.BottomChunkZ<B.BottomChunkZ;});
    }

    const FBoundStratumField* FindBoundStratumForChunk(int32 ChunkZ) const
    {
        const auto Upper=std::upper_bound(BoundStratumFields.begin(),
            BoundStratumFields.end(),ChunkZ,[](int32 Z,const auto& Field)
                {return Z<Field.BottomChunkZ;});
        if(Upper==BoundStratumFields.begin())return nullptr;
        const auto& Candidate=*std::prev(Upper);
        return ChunkZ<=Candidate.TopChunkZ?&Candidate:nullptr;
    }

    const FBoundStratumField* FindBoundStratumForZ(float Z) const
    {
        if(!std::isfinite(Z))return nullptr;
        const float LayoutWidth=static_cast<float>(GetResolvedLayoutChunkWidthVoxels());
        if(!(LayoutWidth>0.0f))return nullptr;
        return FindBoundStratumForChunk(FMath::FloorToInt(Z/LayoutWidth));
    }

    const FBoundStratumField* FindBoundStratumForManagerZ(float Z) const
    {
        if(!std::isfinite(Z)||!Owner||!(BoundManagerLayoutChunkWidthVoxels>0.0f))
            return nullptr;
        const float WorldZCentimetres=static_cast<float>(
            static_cast<double>(Z)*GetCoreVoxelSizeCm());
        const int32 ChunkZ=FMath::FloorToInt((WorldZCentimetres/VOXEL_SIZE)
            /BoundManagerLayoutChunkWidthVoxels);
        return FindBoundStratumForChunk(ChunkZ);
    }

    const VoxelForgeCore::ResolvedLayoutStratumV2* FindResolvedLayoutStratumByOrder(int32 Order) const
    {
        if(!ResolvedLayout||Order<0)return nullptr;
        if(static_cast<std::size_t>(Order)<ResolvedLayout->strates.size())
        {
            const auto& direct=ResolvedLayout->strates[static_cast<std::size_t>(Order)];
            if(direct.order==Order)return &direct;
        }
        const auto it=std::find_if(ResolvedLayout->strates.begin(),ResolvedLayout->strates.end(),
            [Order](const auto& item){return item.order==Order;});
        return it==ResolvedLayout->strates.end()?nullptr:&*it;
    }

    bool IsResolvedLayoutTransitionActive(const VoxelForgeCore::ResolvedLayoutStratumV2& Upper) const
    {
        return Upper.transitionMode!="Hard"&&!Upper.transitionFallsBackToHard
            &&Upper.transitionWidthMicrometres>0
            &&Upper.transitionHonouredInCore;
    }

    bool ResolvedBoundaryBandsIntersectSubvoxelRange(std::int64_t minimumZSubvoxels,
        std::int64_t maximumZSubvoxels) const
    {
        if(!ResolvedLayout||!Owner||Owner->CoreVoxelSizeMicrons==0
            ||minimumZSubvoxels>maximumZSubvoxels)return false;
        constexpr double Subvoxels=static_cast<double>(
            VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double queryMinimumMicrometres=static_cast<double>(minimumZSubvoxels)
            *Owner->CoreVoxelSizeMicrons/Subvoxels;
        const double queryMaximumMicrometres=static_cast<double>(maximumZSubvoxels)
            *Owner->CoreVoxelSizeMicrons/Subvoxels;
        const double sampleMarginMicrometres=static_cast<double>(Owner->CoreVoxelSizeMicrons);
        for(const auto& interval:ResolvedBoundaryZIntervalsMicrometres)
        {
            if(queryMaximumMicrometres+sampleMarginMicrometres>=interval[0]-1.0
                &&queryMinimumMicrometres-sampleMarginMicrometres<interval[1]+1.0)
                return true;
        }
        return false;
    }

    bool ResolvedBoundaryBandMayAffectAtZMicrometres(double zMicrometres) const
    {
        if(!std::isfinite(zMicrometres)||ResolvedBoundaryZIntervalsMicrometres.empty())return false;
        const auto it=std::upper_bound(ResolvedBoundaryZIntervalsMicrometres.begin(),
            ResolvedBoundaryZIntervalsMicrometres.end(),zMicrometres,
            [](double z,const auto& interval){return z<interval[0];});
        return it!=ResolvedBoundaryZIntervalsMicrometres.begin()
            &&zMicrometres<std::prev(it)->at(1);
    }

    void BuildResolvedBoundaryZIntervals()
    {
        ResolvedBoundaryZIntervalsMicrometres.clear();
        if(!ResolvedLayout)return;
        for(const auto& stratum:ResolvedLayout->strates)
        {
            if(stratum.ceiling.presentInCurrentField
                &&stratum.ceiling.bottomMicrometres<stratum.ceiling.topMicrometres)
                ResolvedBoundaryZIntervalsMicrometres.push_back({
                    static_cast<double>(stratum.ceiling.bottomMicrometres),
                    static_cast<double>(stratum.ceiling.topMicrometres)});
            if(stratum.bedrock.presentInCurrentField
                &&stratum.bedrock.bottomMicrometres<stratum.bedrock.topMicrometres)
                ResolvedBoundaryZIntervalsMicrometres.push_back({
                    static_cast<double>(stratum.bedrock.bottomMicrometres),
                    static_cast<double>(stratum.bedrock.topMicrometres)});
        }
        for(std::int32_t order=0;order+1<static_cast<std::int32_t>(ResolvedLayout->strates.size());
            ++order)
        {
            const auto* upper=FindResolvedLayoutStratumByOrder(order);
            const auto* lower=FindResolvedLayoutStratumByOrder(order+1);
            if(!upper||!lower||!IsResolvedLayoutTransitionActive(*upper))continue;
            const auto displacement=ResolvedTransitionMaximumFaceDisplacementMicrometres(
                *upper,*lower);
            ResolvedBoundaryZIntervalsMicrometres.push_back({
                static_cast<double>(std::min(upper->bedrock.bottomMicrometres,
                    lower->ceiling.bottomMicrometres)-displacement),
                static_cast<double>(std::max(upper->bedrock.topMicrometres,
                    lower->ceiling.topMicrometres)+displacement)});
        }
        std::sort(ResolvedBoundaryZIntervalsMicrometres.begin(),
            ResolvedBoundaryZIntervalsMicrometres.end(),
            [](const auto& a,const auto& b){return a[0]<b[0];});
        std::size_t write=0;
        for(const auto& interval:ResolvedBoundaryZIntervalsMicrometres)
        {
            if(write>0&&interval[0]<=ResolvedBoundaryZIntervalsMicrometres[write-1][1])
                ResolvedBoundaryZIntervalsMicrometres[write-1][1]=std::max(
                    ResolvedBoundaryZIntervalsMicrometres[write-1][1],interval[1]);
            else
                ResolvedBoundaryZIntervalsMicrometres[write++]=interval;
        }
        ResolvedBoundaryZIntervalsMicrometres.resize(write);
    }

    std::int64_t ResolvedTransitionMaximumFaceDisplacementMicrometres(
        const VoxelForgeCore::ResolvedLayoutStratumV2& Upper,
        const VoxelForgeCore::ResolvedLayoutStratumV2& Lower) const
    {
        const std::int64_t width=std::max<std::int64_t>(0,Upper.transitionWidthMicrometres);
        if(Upper.transitionMode=="Gradient")
            return width/8;
        if(Upper.transitionMode!="Interleaved")return 0;
        const std::int64_t upperThickness=std::max<std::int64_t>(0,
            Upper.bedrock.topMicrometres-Upper.bedrock.bottomMicrometres);
        const std::int64_t lowerThickness=std::max<std::int64_t>(0,
            Lower.ceiling.topMicrometres-Lower.ceiling.bottomMicrometres);
        const std::int64_t maximumCrossing=std::min(width,upperThickness+lowerThickness);
        return (maximumCrossing+1)/2;
    }

    bool ResolvedTransitionPassageFadeIntersectsTileXY(
        const std::array<std::int64_t,3>& minimumSubvoxels,
        const std::array<std::int64_t,3>& maximumSubvoxels) const
    {
        if(!Owner||!ResolvedLayout||Owner->CoreVoxelSizeMicrons==0)return true;
        for(std::size_t axis=0;axis<2;++axis)
            if(minimumSubvoxels[axis]>maximumSubvoxels[axis])return true;
        constexpr std::int64_t Subvoxels=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
        constexpr std::int64_t SupportMarginMicrometres=1000000;
        constexpr std::int64_t FadeWidthMicrometres=2000000;
        const double voxelMicrometres=static_cast<double>(Owner->CoreVoxelSizeMicrons);
        const double minimumX=static_cast<double>(minimumSubvoxels[0])*voxelMicrometres
            /Subvoxels-voxelMicrometres;
        const double maximumX=static_cast<double>(maximumSubvoxels[0])*voxelMicrometres
            /Subvoxels+voxelMicrometres;
        const double minimumY=static_cast<double>(minimumSubvoxels[1])*voxelMicrometres
            /Subvoxels-voxelMicrometres;
        const double maximumY=static_cast<double>(maximumSubvoxels[1])*voxelMicrometres
            /Subvoxels+voxelMicrometres;
        for(std::int32_t order=0;order+1<static_cast<std::int32_t>(ResolvedLayout->strates.size());
            ++order)
        {
            const auto* upper=FindResolvedLayoutStratumByOrder(order);
            const auto* lower=FindResolvedLayoutStratumByOrder(order+1);
            if(!upper||!lower||!IsResolvedLayoutTransitionActive(*upper))continue;
            const std::int64_t seam=upper->bedrock.bottomMicrometres;
            for(const auto& passage:ResolvedLayout->passages)
            {
                if(passage.upperStrateIndex!=upper->strateIndex
                    ||passage.lowerStrateIndex!=lower->strateIndex)continue;
                const std::int64_t mouthRadius=std::max<std::int64_t>(0,
                    passage.mouthRadiusSubvoxels*Owner->CoreVoxelSizeMicrons/Subvoxels);
                const std::int64_t protectedRadius=mouthRadius+SupportMarginMicrometres;
                const double fadeEnd=static_cast<double>(protectedRadius+FadeWidthMicrometres);
                for(const auto* mouth:{&passage.upperMouthSubvoxels,&passage.lowerMouthSubvoxels})
                {
                    const std::int64_t mouthZ=mouth->at(2)*Owner->CoreVoxelSizeMicrons/Subvoxels;
                    if(std::abs(mouthZ-seam)
                        >upper->transitionWidthMicrometres/2+mouthRadius)continue;
                    const double mouthX=static_cast<double>(mouth->at(0)
                        *Owner->CoreVoxelSizeMicrons/Subvoxels);
                    const double mouthY=static_cast<double>(mouth->at(1)
                        *Owner->CoreVoxelSizeMicrons/Subvoxels);
                    const double dx=mouthX<minimumX?minimumX-mouthX
                        :mouthX>maximumX?mouthX-maximumX:0.0;
                    const double dy=mouthY<minimumY?minimumY-mouthY
                        :mouthY>maximumY?mouthY-maximumY:0.0;
                    if(dx*dx+dy*dy<fadeEnd*fadeEnd)return true;
                }
            }
        }
        return false;
    }

    std::int64_t ResolvedTransitionPassageWeightQ16(
        const VoxelForgeCore::ResolvedLayoutStratumV2& Upper,
        const VoxelForgeCore::ResolvedLayoutStratumV2& Lower,
        std::int64_t XMicrometres,std::int64_t YMicrometres) const
    {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
        ++ThreadClassificationStats().TransitionPassageFadeCalls;
#endif
        constexpr std::int64_t Q16=1ll<<16;
        constexpr std::int64_t SupportMarginMicrometres=1000000;
        constexpr std::int64_t FadeWidthMicrometres=2000000;
        if(!ResolvedLayout||!Owner||Owner->CoreVoxelSizeMicrons==0)return Q16;
        const std::int64_t seam=Upper.bedrock.bottomMicrometres;
        const std::int64_t coreMicrometres=Owner->CoreVoxelSizeMicrons;
        const std::int64_t subvoxelsPerVoxel=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
        std::int64_t weight=Q16;
        for(const auto& passage:ResolvedLayout->passages)
        {
            if(passage.upperStrateIndex!=Upper.strateIndex
                ||passage.lowerStrateIndex!=Lower.strateIndex)continue;
            const std::int64_t mouthRadiusMicrometres=std::max<std::int64_t>(0,
                passage.mouthRadiusSubvoxels*coreMicrometres/subvoxelsPerVoxel);
            const std::int64_t protectedRadius=mouthRadiusMicrometres
                +SupportMarginMicrometres;
            for(const auto* mouth:{&passage.upperMouthSubvoxels,&passage.lowerMouthSubvoxels})
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().TransitionPassageMouthTests;
#endif
                const std::int64_t mouthZMicrometres=mouth->at(2)*coreMicrometres
                    /subvoxelsPerVoxel;
                if(std::abs(mouthZMicrometres-seam)
                    >Upper.transitionWidthMicrometres/2+mouthRadiusMicrometres)continue;
                const double dx=static_cast<double>(XMicrometres-mouth->at(0)*coreMicrometres
                    /subvoxelsPerVoxel);
                const double dy=static_cast<double>(YMicrometres-mouth->at(1)*coreMicrometres
                    /subvoxelsPerVoxel);
                const std::int64_t fadeEnd=protectedRadius+FadeWidthMicrometres;
                const double distanceSquared=dx*dx+dy*dy;
                if(distanceSquared>=static_cast<double>(fadeEnd)*fadeEnd)continue;
                if(distanceSquared<=static_cast<double>(protectedRadius)*protectedRadius)return 0;
                const double distance=std::sqrt(distanceSquared);
                const double t=static_cast<double>(static_cast<std::int64_t>(distance)
                    -protectedRadius)/FadeWidthMicrometres;
                const double smooth=t*t*(3.0-2.0*t);
                weight=std::min(weight,static_cast<std::int64_t>(std::llround(smooth*Q16)));
            }
        }
        return weight;
    }

    VoxelForgeCore::ResolvedLayoutTransitionBandsV1 ResolvedTransitionBandsAtXY(
        const VoxelForgeCore::ResolvedLayoutStratumV2& Upper,
        const VoxelForgeCore::ResolvedLayoutStratumV2& Lower,
        std::int64_t XMicrometres,std::int64_t YMicrometres,bool SkipPassageFade=false) const
    {
        auto bands=VoxelForgeCore::EvaluateResolvedLayoutTransitionBandsV1(Upper,Lower,
            Owner?Owner->Seed:0,ResolvedLayout?ResolvedLayout->strateLayoutChunkSizeMicrometres:0,
            XMicrometres,YMicrometres);
        constexpr std::int64_t TransitionQ16=1ll<<16;
        const std::int64_t weight=SkipPassageFade?TransitionQ16:
            ResolvedTransitionPassageWeightQ16(Upper,Lower,XMicrometres,YMicrometres);
        if(weight>=TransitionQ16)return bands;
        const std::int64_t seam=Upper.bedrock.bottomMicrometres;
        const std::int64_t upperThickness=Upper.bedrock.topMicrometres-seam;
        const std::int64_t lowerThickness=Lower.ceiling.topMicrometres
            -Lower.ceiling.bottomMicrometres;
        const auto scaled=[&](std::int64_t value){return (value*weight)/TransitionQ16;};
        bands.upperBedrockBottomMicrometres=seam+scaled(
            bands.upperBedrockBottomMicrometres-seam);
        bands.upperBedrockTopMicrometres=bands.upperBedrockBottomMicrometres+upperThickness;
        bands.lowerCeilingTopMicrometres=seam+scaled(
            bands.lowerCeilingTopMicrometres-seam);
        bands.lowerCeilingBottomMicrometres=bands.lowerCeilingTopMicrometres-lowerThickness;
        bands.crossingDepthMicrometres=std::max<std::int64_t>(0,
            bands.lowerCeilingTopMicrometres-bands.upperBedrockBottomMicrometres);
        return bands;
    }

    bool ResolvedBedrockTopAt(const VoxelForgeCore::ResolvedLayoutStratumV2& Upper,
        double X,double Y,double& TopZ) const
    {
        const auto* lower=FindResolvedLayoutStratumByOrder(Upper.order+1);
        if(!lower||!Owner||Owner->CoreVoxelSizeMicrons==0
            ||!IsResolvedLayoutTransitionActive(Upper))return false;
        const auto toMicrometres=[&](double value)
        {return static_cast<std::int64_t>(std::llround(value*Owner->CoreVoxelSizeMicrons));};
        const auto* tileQueries=ActivePassageTileQueries;
        const bool skipPassageFade=tileQueries&&tileQueries->matches(*this)
            &&!tileQueries->mayContainTransitionPassageFade();
        const auto bands=ResolvedTransitionBandsAtXY(Upper,*lower,toMicrometres(X),
            toMicrometres(Y),skipPassageFade);
        TopZ=static_cast<double>(bands.upperBedrockTopMicrometres)
            /Owner->CoreVoxelSizeMicrons;
        return std::isfinite(TopZ);
    }

    bool ResolvedCeilingBottomAt(const VoxelForgeCore::ResolvedLayoutStratumV2& Lower,
        double X,double Y,double& BottomZ) const
    {
        const auto* upper=FindResolvedLayoutStratumByOrder(Lower.order-1);
        if(!upper||!Owner||Owner->CoreVoxelSizeMicrons==0
            ||!IsResolvedLayoutTransitionActive(*upper))return false;
        const auto toMicrometres=[&](double value)
        {return static_cast<std::int64_t>(std::llround(value*Owner->CoreVoxelSizeMicrons));};
        const auto* tileQueries=ActivePassageTileQueries;
        const bool skipPassageFade=tileQueries&&tileQueries->matches(*this)
            &&!tileQueries->mayContainTransitionPassageFade();
        const auto bands=ResolvedTransitionBandsAtXY(*upper,Lower,toMicrometres(X),
            toMicrometres(Y),skipPassageFade);
        BottomZ=static_cast<double>(bands.lowerCeilingBottomMicrometres)
            /Owner->CoreVoxelSizeMicrons;
        return std::isfinite(BottomZ);
    }

    bool IsInsideResolvedStrateBoundaryBand(float Z) const
    {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
        ++ThreadClassificationStats().BoundaryBandCalls;
#endif
        const auto* tileQueries=ActivePassageTileQueries;
        if(tileQueries&&tileQueries->matches(*this))
        {
            if(!tileQueries->mayContainResolvedBoundaryBand())
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().BoundaryTileCullRejects;
#endif
                return false;
            }
            if(Owner&&!tileQueries->mayContainResolvedBoundaryBandAtZ(
                static_cast<double>(Z)*Owner->CoreVoxelSizeMicrons))
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().BoundaryPointCullRejects;
#endif
                return false;
            }
            // This predicate only selects the scalar path for boundary-capable Z
            // samples. The merged intervals are conservative, so a positive is safe.
            return true;
        }
        if(!ResolvedLayout||!Owner||!std::isfinite(Z))return false;
        const FBoundStratumField* bound=FindBoundStratumForManagerZ(Z);
        const auto* stratum=bound?FindResolvedLayoutStratum(bound->StrateIndex):nullptr;
        if(!stratum)return false;
        const double zMicrometres=static_cast<double>(Z)*Owner->CoreVoxelSizeMicrons;
        const auto solidAt=[&](const VoxelForgeCore::ResolvedLayoutBandV2& band)
        {return band.presentInCurrentField&&zMicrometres>=band.bottomMicrometres
            &&zMicrometres<band.topMicrometres;};
        const auto mayTouchTransition=[&](const VoxelForgeCore::ResolvedLayoutStratumV2* Upper,
            const VoxelForgeCore::ResolvedLayoutStratumV2* Lower)
        {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
            ++ThreadClassificationStats().TransitionWindowChecks;
#endif
            if(!Upper||!Lower||!IsResolvedLayoutTransitionActive(*Upper))return false;
            const auto maxDisplacement=ResolvedTransitionMaximumFaceDisplacementMicrometres(
                *Upper,*Lower);
            const double minimum=std::min(Upper->bedrock.bottomMicrometres,
                Lower->ceiling.bottomMicrometres)-maxDisplacement;
            const double maximum=std::max(Upper->bedrock.topMicrometres,
                Lower->ceiling.topMicrometres)+maxDisplacement;
            const bool touches=zMicrometres>=minimum&&zMicrometres<maximum;
#if defined(VF_L30_ENABLE_COST_COUNTERS)
            if(touches)++ThreadClassificationStats().TransitionWindowHits;
#endif
            return touches;
        };
        const auto* lower=FindResolvedLayoutStratumByOrder(stratum->order+1);
        const auto* upper=stratum->order>0?FindResolvedLayoutStratumByOrder(stratum->order-1):nullptr;
        if(mayTouchTransition(stratum,lower)||mayTouchTransition(upper,stratum))return true;
        return solidAt(stratum->ceiling)||solidAt(stratum->bedrock);
    }

    float ApplyResolvedStrateBoundaryBand(float density,float X,float Y,float Z) const
    {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
        ++ThreadClassificationStats().BoundaryBandCalls;
#endif
        (void)X;(void)Y;
        const auto* tileQueries=ActivePassageTileQueries;
        if(tileQueries&&tileQueries->matches(*this))
        {
            if(!tileQueries->mayContainResolvedBoundaryBand())
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().BoundaryTileCullRejects;
#endif
                return density;
            }
            if(Owner&&!tileQueries->mayContainResolvedBoundaryBandAtZ(
                static_cast<double>(Z)*Owner->CoreVoxelSizeMicrons))
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().BoundaryPointCullRejects;
#endif
                return density;
            }
        }
        if(!ResolvedLayout||!Owner||Owner->CoreVoxelSizeMicrons==0
            ||!std::isfinite(Z))return density;
        const double zMicrometres=static_cast<double>(Z)*Owner->CoreVoxelSizeMicrons;
        if(ResolvedLayout->strates.size()==2)
        {
            const auto* transitionUpper=FindResolvedLayoutStratumByOrder(0);
            const auto* transitionLower=FindResolvedLayoutStratumByOrder(1);
            if(transitionUpper&&transitionLower
                &&IsResolvedLayoutTransitionActive(*transitionUpper))
            {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().TransitionWindowChecks;
#endif
                const auto maximumDisplacement=ResolvedTransitionMaximumFaceDisplacementMicrometres(
                    *transitionUpper,*transitionLower);
                const double minimum=std::min(transitionUpper->bedrock.bottomMicrometres,
                    transitionLower->ceiling.bottomMicrometres)-maximumDisplacement;
                const double maximum=std::max(transitionUpper->bedrock.topMicrometres,
                    transitionLower->ceiling.topMicrometres)+maximumDisplacement;
                if(zMicrometres>=minimum&&zMicrometres<maximum)
                {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                    ++ThreadClassificationStats().TransitionWindowHits;
                    ++ThreadClassificationStats().TransitionEvaluatorCalls;
#endif
                    const auto* tileQueries=ActivePassageTileQueries;
                    const bool skipPassageFade=tileQueries&&tileQueries->matches(*this)
                        &&!tileQueries->mayContainTransitionPassageFade();
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                    if(skipPassageFade)
                        ++ThreadClassificationStats().TransitionPassageTileSkips;
#endif
                    const auto xMicrometres=static_cast<std::int64_t>(std::llround(
                        static_cast<double>(X)*Owner->CoreVoxelSizeMicrons));
                    const auto yMicrometres=static_cast<std::int64_t>(std::llround(
                        static_cast<double>(Y)*Owner->CoreVoxelSizeMicrons));
                    const auto bands=ResolvedTransitionBandsAtXY(*transitionUpper,
                        *transitionLower,xMicrometres,yMicrometres,skipPassageFade);
                    const std::int64_t solidBottom=std::min(
                        bands.upperBedrockBottomMicrometres,bands.lowerCeilingBottomMicrometres);
                    const std::int64_t solidTop=std::max(
                        bands.upperBedrockTopMicrometres,bands.lowerCeilingTopMicrometres);
                    const double signedDistanceMicrometres=zMicrometres<solidBottom
                        ?static_cast<double>(solidBottom-zMicrometres)
                        :zMicrometres>solidTop
                            ?static_cast<double>(zMicrometres-solidTop)
                            :-static_cast<double>(std::min(zMicrometres-solidBottom,
                                solidTop-zMicrometres));
                    const std::int64_t seam=transitionUpper->bedrock.bottomMicrometres;
                    const bool floatingIslandAirGap=
                        transitionUpper->lowerInterfaceCapabilities.preserveUpperBedrockAirGap
                        &&bands.upperBedrockTopMicrometres<seam
                        &&zMicrometres>=bands.upperBedrockTopMicrometres
                        &&zMicrometres<seam;
                    if(!(signedDistanceMicrometres>0.0&&density<0.0f
                        &&!floatingIslandAirGap))
                        return static_cast<float>(signedDistanceMicrometres
                            /Owner->CoreVoxelSizeMicrons);
                }
            }
        }
        const FBoundStratumField* bound=FindBoundStratumForManagerZ(Z);
        const auto* stratum=bound?FindResolvedLayoutStratum(bound->StrateIndex):nullptr;
        if(!stratum)return density;
        const auto solidAt=[&](const VoxelForgeCore::ResolvedLayoutBandV2& band)
        {return band.presentInCurrentField&&zMicrometres>=band.bottomMicrometres
            &&zMicrometres<band.topMicrometres;};

        bool bCeilingHandledByTransition=false,bBedrockHandledByTransition=false;
        const auto applyInterface=[&](const VoxelForgeCore::ResolvedLayoutStratumV2* upper,
            const VoxelForgeCore::ResolvedLayoutStratumV2* lower)
        {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
            ++ThreadClassificationStats().TransitionWindowChecks;
#endif
            if(!upper||!lower||!IsResolvedLayoutTransitionActive(*upper))return false;
            const auto maxDisplacement=ResolvedTransitionMaximumFaceDisplacementMicrometres(
                *upper,*lower);
            const double minimum=std::min(upper->bedrock.bottomMicrometres,
                lower->ceiling.bottomMicrometres)-maxDisplacement;
            const double maximum=std::max(upper->bedrock.topMicrometres,
                lower->ceiling.topMicrometres)+maxDisplacement;
            if(zMicrometres<minimum||zMicrometres>=maximum)return false;
#if defined(VF_L30_ENABLE_COST_COUNTERS)
            ++ThreadClassificationStats().TransitionWindowHits;
            ++ThreadClassificationStats().TransitionEvaluatorCalls;
#endif
            if(upper==stratum)bBedrockHandledByTransition=true;
            if(lower==stratum)bCeilingHandledByTransition=true;
            const auto* tileQueries=ActivePassageTileQueries;
            const std::int64_t xMicrometres=static_cast<std::int64_t>(std::llround(
                static_cast<double>(X)*Owner->CoreVoxelSizeMicrons));
            const std::int64_t yMicrometres=static_cast<std::int64_t>(std::llround(
                static_cast<double>(Y)*Owner->CoreVoxelSizeMicrons));
            const bool skipPassageFade=tileQueries&&tileQueries->matches(*this)
                &&!tileQueries->mayContainTransitionPassageFade();
#if defined(VF_L30_ENABLE_COST_COUNTERS)
            if(skipPassageFade)++ThreadClassificationStats().TransitionPassageTileSkips;
#endif
            const auto resolvedBands=ResolvedTransitionBandsAtXY(*upper,*lower,
                xMicrometres,yMicrometres,skipPassageFade);
            // Treat the two authored bands as one continuous solid interval. Its
            // exterior faces remain the lower ceiling bottom and upper bedrock top;
            // measuring signed distance from those faces also clears native generator
            // density on both air sides of the displaced interface.
            const std::int64_t solidBottom=std::min(
                resolvedBands.upperBedrockBottomMicrometres,
                resolvedBands.lowerCeilingBottomMicrometres);
            const std::int64_t solidTop=std::max(
                resolvedBands.upperBedrockTopMicrometres,
                resolvedBands.lowerCeilingTopMicrometres);
            const double signedDistanceMicrometres=zMicrometres<solidBottom
                ?static_cast<double>(solidBottom-zMicrometres)
                :zMicrometres>solidTop
                    ?static_cast<double>(zMicrometres-solidTop)
                    :-static_cast<double>(std::min(zMicrometres-solidBottom,
                        solidTop-zMicrometres));
            const std::int64_t seam=upper->bedrock.bottomMicrometres;
            const bool floatingIslandAirGap=
                upper->lowerInterfaceCapabilities.preserveUpperBedrockAirGap
                &&resolvedBands.upperBedrockTopMicrometres<seam
                &&zMicrometres>=resolvedBands.upperBedrockTopMicrometres
                &&zMicrometres<seam;
            // A native solid may continue beyond either authored face. Keep that
            // connected rock; the FI gap is the explicit exception that must stay open.
            if(signedDistanceMicrometres>0.0&&density<0.0f&&!floatingIslandAirGap)
                return false;
            density=static_cast<float>(signedDistanceMicrometres
                /std::max<std::uint32_t>(1,Owner->CoreVoxelSizeMicrons));
            return true;
        };

        const auto* lower=FindResolvedLayoutStratumByOrder(stratum->order+1);
        const auto* upper=stratum->order>0?FindResolvedLayoutStratumByOrder(stratum->order-1):nullptr;
        if(applyInterface(stratum,lower)||applyInterface(upper,stratum))return density;
        const auto* band=(!bCeilingHandledByTransition&&solidAt(stratum->ceiling))
            ?&stratum->ceiling:(!bBedrockHandledByTransition&&solidAt(stratum->bedrock))
                ?&stratum->bedrock:nullptr;
        if(!band)return density;
        return -std::max(0.05f,static_cast<float>(band->solidDensityQ16)/65536.0f);
    }

    float ApplyResolvedStratePassageCarves(float density,float X,float Y,float Z) const
    {
        if(!ResolvedLayout||ResolvedLayout->passages.empty()||!std::isfinite(X)
            ||!std::isfinite(Y)||!std::isfinite(Z))return density;
        constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double qPerMetre=Q*1000000.0/
            std::max<std::uint32_t>(1,ResolvedLayout->coreVoxelSizeMicrometres);
        const double qx=static_cast<double>(X)*Q,qy=static_cast<double>(Y)*Q,
            qz=static_cast<double>(Z)*Q;
        const auto* passageTileQueries=ActivePassageTileQueries;
        const bool passageTileScopeMatches=passageTileQueries
            &&passageTileQueries->matches(*this);
        bool queryNearUpperMouthSupport=false;
        for(const auto& passage:ResolvedLayout->passages)
        {
            const double dx=qx-static_cast<double>(passage.upperMouthSubvoxels[0]);
            const double dy=qy-static_cast<double>(passage.upperMouthSubvoxels[1]);
            const double dz=qz-static_cast<double>(passage.upperMouthSubvoxels[2]);
            const double reach=15.0*qPerMetre;
            if(dx*dx+dy*dy<=reach*reach&&std::abs(dz)<=8.0*qPerMetre)
            {queryNearUpperMouthSupport=true;break;}
        }
        if(passageTileScopeMatches&&density>=0.0f
            &&!passageTileQueries->hasRouteFeatureOverlap()
            &&!passageTileQueries->hasColumnZOverlap()
            &&!passageTileQueries->hasAnyMouthSupport()
            &&!queryNearUpperMouthSupport)return density;
        const double floorThicknessVoxels=qPerMetre/Q;
        const double playerCenterAboveFloorQ=1.13*qPerMetre;
        float composed=density;
        const auto composeRouteMouthSupport=[&](std::int32_t strateIndex,
            const std::array<std::int64_t,3>& mouth,bool departure)
        {
            // Surface-route treads may reinforce native solid terrain only.
            if(!(density<0.0f))return;
            const double mouthDx=qx-static_cast<double>(mouth[0]);
            const double mouthDy=qy-static_cast<double>(mouth[1]);
            const double routeSupportReach=13.0*qPerMetre;
            if(mouthDx*mouthDx+mouthDy*mouthDy>routeSupportReach*routeSupportReach)return;
            const auto stratum=std::find_if(ResolvedLayout->strates.begin(),
                ResolvedLayout->strates.end(),[strateIndex](const auto& value)
                    {return value.strateIndex==strateIndex;});
            if(stratum==ResolvedLayout->strates.end())return;
            std::array<const VoxelForgeCore::ResolvedLayoutAnchorV2*,5> route{};
            std::size_t routeCount=0;
            for(const auto& anchor:stratum->anchors)
                if(anchor.kind=="route_point"&&anchor.values.size()>=3)
                {
                    if(departure)
                    {
                        if(routeCount<route.size())route[routeCount++]=&anchor;
                        else
                        {
                            std::move(route.begin()+1,route.end(),route.begin());
                            route.back()=&anchor;
                        }
                    }
                    else if(routeCount<route.size())route[routeCount++]=&anchor;
                }
            if(routeCount<2)return;
            const std::size_t lastSegment=routeCount-1;
            constexpr double MouthSupportBlendMetres=0.45;
            const double mouthBlendWidth=MouthSupportBlendMetres*qPerMetre;
            double mouthSupportDistance=std::numeric_limits<double>::infinity();
            for(std::size_t index=0;index<lastSegment;++index)
            {
                const auto& a=*route[index];const auto& b=*route[index+1];
                const double dx=static_cast<double>(b.values[0]-a.values[0]);
                const double dy=static_cast<double>(b.values[1]-a.values[1]);
                const double lengthSq=dx*dx+dy*dy;
                const double t=lengthSq>0.0?std::clamp(((qx-a.values[0])*dx
                    +(qy-a.values[1])*dy)/lengthSq,0.0,1.0):0.0;
                const double centerX=a.values[0]+t*dx,centerY=a.values[1]+t*dy;
                const double centerZ=a.values[2]+t*(static_cast<double>(b.values[2])-a.values[2]);
                const double routeRadius=a.values.size()>=4
                    ?a.values[3]+t*(static_cast<double>(b.values[3])-a.values[3]):0.0;
                const double halfWidth=std::clamp(routeRadius,
                    0.42*qPerMetre,0.56*qPerMetre);
                const double horizontalX=qx-centerX,horizontalY=qy-centerY;
                const double horizontalDistance=DeterministicSqrt(
                    horizontalX*horizontalX+horizontalY*horizontalY);
                const double floorQ=centerZ-(VoxelForgeCore::WorldAssemblyEvaluatorVersion>=184
                    ?playerCenterAboveFloorQ+0.25*qPerMetre:1.20*qPerMetre);
                const double sideDistance=horizontalDistance-halfWidth;
                const double topDistance=qz-floorQ;
                const double bottomDistance=floorQ-qPerMetre-qz;
                const double verticalDistance=std::max(topDistance,bottomDistance);
                if(sideDistance>mouthBlendWidth||verticalDistance>mouthBlendWidth)continue;
                const double outside=DeterministicSqrt(
                    std::max(sideDistance,0.0)*std::max(sideDistance,0.0)
                    +std::max(verticalDistance,0.0)*std::max(verticalDistance,0.0));
                const double inside=std::min(std::max(sideDistance,verticalDistance),0.0);
                mouthSupportDistance=std::min(mouthSupportDistance,outside+inside);
            }
            if(std::isfinite(mouthSupportDistance))
                composed=SmoothMinDistance(composed,
                    static_cast<float>(mouthSupportDistance/Q),
                    static_cast<float>(mouthBlendWidth/Q));
        };
        // The connected passage tread continues the surface route into the tunnel.
        for(std::size_t passageIndex=0;passageIndex<ResolvedLayout->passages.size();++passageIndex)
        {
            const auto& passage=ResolvedLayout->passages[passageIndex];
            if(passage.controlPoints.size()<2)continue;
            const auto supportStratum=[&](std::int32_t strateIndex)
                ->const VoxelForgeCore::ResolvedLayoutStratumV2*
            {
                const auto it=std::find_if(ResolvedLayout->strates.begin(),
                    ResolvedLayout->strates.end(),[strateIndex](const auto& stratum)
                        {return stratum.strateIndex==strateIndex;});
                return it==ResolvedLayout->strates.end()?nullptr:&*it;
            };
            const auto* supportUpper=supportStratum(passage.upperStrateIndex);
            const auto* supportLower=supportStratum(passage.lowerStrateIndex);
            const bool floatingIslandPassage=supportUpper
                &&supportUpper->passageCapabilities.hasFloatingIslandLanding;
            const bool surfaceToTunnelSupport=supportUpper&&supportLower
                &&supportUpper->lowerInterfaceCapabilities.surfaceToTunnelLandingSupport;
            const double firstFloorQ=passage.controlPoints.front().positionSubvoxels[2]
                -passage.controlPoints.front().radiusSubvoxels+playerCenterAboveFloorQ;
            const double lastFloorQ=passage.controlPoints.back().positionSubvoxels[2]
                -passage.controlPoints.back().radiusSubvoxels+playerCenterAboveFloorQ;
            for(const auto& crossing:PassageVoidCrossings)
            {
                if(!crossing.needsColumn||crossing.passageIndex!=passageIndex
                    ||qz>crossing.topZSubvoxels||qz<crossing.bottomZSubvoxels)continue;
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                ++ThreadClassificationStats().ColumnZOverlapCalls;
#endif
                double columnDistance;
                const bool tileProvesColumnExterior=passageTileScopeMatches
                    &&!ActivePassageTileQueries->hasFeature(passageIndex,true);
                if(tileProvesColumnExterior)
                {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                    ++ThreadClassificationStats().ColumnGuardCalls;
#endif
                    if(composed<0.0f)
                    {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                        ++ThreadClassificationStats().ColumnGuardNonpositiveSkips;
#endif
                        continue;
                    }
                    const double dx=qx-crossing.centerXSubvoxels;
                    const double dy=qy-crossing.centerYSubvoxels;
                    const double horizontalSquared=dx*dx+dy*dy;
                    const double maximumRadius=static_cast<double>(crossing.maximumRadiusSubvoxels);
                    const double exteriorLimit=maximumRadius
                        +static_cast<double>(composed)*Q+1.0e-4;
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                    if(horizontalSquared>exteriorLimit*exteriorLimit)
                    {
                        ++ThreadClassificationStats().ColumnGuardRadialRejects;
                        continue;
                    }
                    ++ThreadClassificationStats().ColumnSignedDistanceCalls;
#else
                    if(horizontalSquared>exteriorLimit*exteriorLimit)continue;
#endif
                    columnDistance=PassageColumnSignedDistance(crossing,X,Y,Z);
                }
                else
                {
#if defined(VF_L30_ENABLE_COST_COUNTERS)
                    ++ThreadClassificationStats().ColumnSignedDistanceCalls;
#endif
                    columnDistance=PassageColumnSignedDistance(crossing,X,Y,Z);
                }
                composed=std::min(composed,static_cast<float>(columnDistance/Q));
            }
            const bool tilePassageFree=passageTileScopeMatches
                &&!ActivePassageTileQueries->hasFeature(passageIndex,false);
            if(composed>=0.0f&&tilePassageFree)
            {
                continue;
            }
            if(qz>firstFloorQ+2.0*passage.mouthRadiusSubvoxels
                ||qz<lastFloorQ-2.0*passage.mouthRadiusSubvoxels)
            {
                continue;
            }
            const auto floorProfile=[&](const auto& point)
            {return point.positionSubvoxels[2]-point.radiusSubvoxels+playerCenterAboveFloorQ;};
            const std::ptrdiff_t lastIndex=static_cast<std::ptrdiff_t>(passage.controlPoints.size())-1;
            const std::ptrdiff_t lowerMouthIndex=std::clamp<std::ptrdiff_t>(
                static_cast<std::ptrdiff_t>(passage.lowerMouthControlIndex),1,lastIndex);
            const auto mainEnd=passage.controlPoints.begin()+lowerMouthIndex+1;
            // The tube radius is measured from its centerline, while floorProfile is
            // one player-center offset away. Search the full vertical radius of the SDF;
            // a narrow point window misses earlier turns of a low-pitch helix.
            const double carveSearchMargin=std::max(passage.mouthRadiusSubvoxels,
                passage.midRadiusSubvoxels)+0.25*qPerMetre;
            const auto carveHigh=std::lower_bound(passage.controlPoints.begin(),mainEnd,
                qz+carveSearchMargin,
                [&](const auto& point,double value){return floorProfile(point)>value;});
            const auto carveLow=std::lower_bound(passage.controlPoints.begin(),mainEnd,
                qz-carveSearchMargin,
                [&](const auto& point,double value){return floorProfile(point)>value;});
            const std::ptrdiff_t carveBegin=std::max<std::ptrdiff_t>(0,
                (carveHigh-passage.controlPoints.begin())-1);
            const std::ptrdiff_t carveEnd=std::min<std::ptrdiff_t>(lowerMouthIndex-1,
                (carveLow-passage.controlPoints.begin())+1);
            const std::ptrdiff_t mouthSearchBegin=std::max<std::ptrdiff_t>(0,lowerMouthIndex-8);
            const std::ptrdiff_t mouthSearchEnd=std::min<std::ptrdiff_t>(lastIndex,
                lowerMouthIndex+8);
            if(density<0.0f&&tilePassageFree
                &&!PassageMayAffectDensity(passageIndex,carveBegin,carveEnd,
                    lowerMouthIndex,mouthSearchBegin,mouthSearchEnd,lastIndex,qx,qy,qz,
                    -static_cast<double>(composed)*Q+0.24*qPerMetre))
            {
                continue;
            }
            // For a positive source sample, the tube can only change it within relief reach;
            // the supported column tread is within 2.25 m of its centerline. A short-span
            // bridge's positive exterior SDF is not bounded this way, so keep its full query.
            // Pour un échantillon source positif, le tube ne change le champ qu'à portée du relief ;
            // le plancher du pilier reste à 2,25 m de son axe. Le SDF extérieur d'une courte passerelle
            // n'a pas cette borne, donc sa requête complète est conservée.
            const bool canCullPositiveRoute=passageTileScopeMatches&&density>=0.0f
                &&!PassageHasShortSpanSegments(passageIndex);
            if(canCullPositiveRoute&&!PassageMayAffectDensity(passageIndex,carveBegin,carveEnd,
                lowerMouthIndex,mouthSearchBegin,mouthSearchEnd,lastIndex,qx,qy,qz,
                std::max(2.25*qPerMetre,-static_cast<double>(composed)*Q
                    +0.24*qPerMetre)))continue;
            double bestSignedDistance=std::numeric_limits<double>::infinity();
            double bestPlayerCapsuleSignedDistance=std::numeric_limits<double>::infinity();
            double bestT=0.0;
            std::ptrdiff_t bestIndex=0;
            int bestScanPhase=std::numeric_limits<int>::max();
            std::ptrdiff_t bestScanIndex=std::numeric_limits<std::ptrdiff_t>::max();
            std::ptrdiff_t bestSupportSegmentIndex=0;
            bool hasSupportFloor=false;
            bool bestSupportIsMouthTread=false;
            double bestSupportMouthBlend=1.0;
            double bestSupportDistanceSquared=std::numeric_limits<double>::infinity();
            double bestSupportDensity=std::numeric_limits<double>::infinity();
            double bestSupportNativeBlend=0.0;
            double bestSupportFloorQ=0.0;
            bool bestSupportUsesSignedDistance=false;
            std::ptrdiff_t selectedSupportSegmentIndex=-1;
            const double lowerMouthDx=qx-passage.lowerMouthSubvoxels[0];
            const double lowerMouthDy=qy-passage.lowerMouthSubvoxels[1];
            const double lowerMouthDz=qz-passage.lowerMouthSubvoxels[2];
            const double lowerMouthDistance=DeterministicSqrt(
                lowerMouthDx*lowerMouthDx+lowerMouthDy*lowerMouthDy
                    +lowerMouthDz*lowerMouthDz)/qPerMetre;
            const double lowerMouthT=std::clamp((20.0-lowerMouthDistance)/12.0,0.0,1.0);
            const double lowerMouthBlend=lowerMouthT*lowerMouthT
                *(3.0-2.0*lowerMouthT);
            const auto considerCarveSegment=[&](std::size_t segmentIndex,int scanPhase)
            {
                const std::ptrdiff_t index=static_cast<std::ptrdiff_t>(segmentIndex);
                const auto& a=passage.controlPoints[static_cast<std::size_t>(index)];
                const auto& b=passage.controlPoints[static_cast<std::size_t>(index+1)];
                const double ax=static_cast<double>(a.positionSubvoxels[0]);
                const double ay=static_cast<double>(a.positionSubvoxels[1]);
                const double az=static_cast<double>(a.positionSubvoxels[2]);
                const double dx=static_cast<double>(b.positionSubvoxels[0])-ax;
                const double dy=static_cast<double>(b.positionSubvoxels[1])-ay;
                const double dz=static_cast<double>(b.positionSubvoxels[2])-az;
                const double lengthSq=dx*dx+dy*dy+dz*dz;
                if(lengthSq<=0.0)return;
                const double t=std::clamp(((qx-ax)*dx+(qy-ay)*dy+(qz-az)*dz)/lengthSq,0.0,1.0);
                if(!passageTileScopeMatches)
                {
                    const double horizontalLengthSq=dx*dx+dy*dy;
                    const double playerT=horizontalLengthSq>0.0
                        ?std::clamp(((qx-ax)*dx+(qy-ay)*dy)/horizontalLengthSq,0.0,1.0):t;
                    const double playerDx=qx-(ax+playerT*dx);
                    const double playerDy=qy-(ay+playerT*dy);
                    const double playerRadius=static_cast<double>(a.radiusSubvoxels)
                        +playerT*(b.radiusSubvoxels-a.radiusSubvoxels);
                    const double playerCenterZ=az+playerT*dz-playerRadius+playerCenterAboveFloorQ;
                    const double playerVertical=std::max(0.0,
                        std::abs(qz-playerCenterZ)-0.54*qPerMetre);
                    bestPlayerCapsuleSignedDistance=std::min(bestPlayerCapsuleSignedDistance,
                        DeterministicSqrt(playerDx*playerDx+playerDy*playerDy
                            +playerVertical*playerVertical)-0.34*qPerMetre);
                }
                double cx=ax+t*dx,cy=ay+t*dy,cz=az+t*dz;
                const bool smoothCarveJoin=index>2&&index+12<lastIndex
                    &&DeterministicSqrt(lengthSq)<=8.0*qPerMetre
                    &&!IsPassageShortSpanSegment(passageIndex,segmentIndex-1)
                    &&!IsPassageShortSpanSegment(passageIndex,segmentIndex)
                    &&!IsPassageShortSpanSegment(passageIndex,segmentIndex+1);
                if(smoothCarveJoin)
                {
                    const auto& p0=passage.controlPoints[static_cast<std::size_t>(index-1)];
                    const auto& p3=passage.controlPoints[static_cast<std::size_t>(index+2)];
                    constexpr double SmoothJoinWeight=1.0;
                    const double t2=t*t,t3=t2*t;
                    for(std::size_t axis=0;axis<3;++axis)
                    {
                        const double v0=static_cast<double>(p0.positionSubvoxels[axis]);
                        const double v1=static_cast<double>(a.positionSubvoxels[axis]);
                        const double v2=static_cast<double>(b.positionSubvoxels[axis]);
                        const double v3=static_cast<double>(p3.positionSubvoxels[axis]);
                        const double curve=0.5*((2.0*v1)+(-v0+v2)*t
                            +(2.0*v0-5.0*v1+4.0*v2-v3)*t2
                            +(-v0+3.0*v1-3.0*v2+v3)*t3);
                        const double line=axis==0?cx:axis==1?cy:cz;
                        const double blended=line+(curve-line)*SmoothJoinWeight;
                        if(axis==0)cx=blended;
                        else if(axis==1)cy=blended;
                        else cz=blended;
                    }
                }
                const double ex=qx-cx,ey=qy-cy,ez=qz-cz;
                const double radius=static_cast<double>(a.radiusSubvoxels)
                    +t*(b.radiusSubvoxels-a.radiusSubvoxels);
                const double signedDistance=DeterministicSqrt(ex*ex+ey*ey+ez*ez)-radius;
                if(signedDistance<bestSignedDistance
                    ||(signedDistance==bestSignedDistance
                        &&(scanPhase<bestScanPhase
                            ||(scanPhase==bestScanPhase&&index<bestScanIndex))))
                {
                    bestSignedDistance=signedDistance;bestT=t;bestIndex=index;
                    bestScanPhase=scanPhase;bestScanIndex=index;
                }
            };
            // Alternate styles can bend locally at either mouth, so floorProfile is
            // not monotone over those short endpoint runs. Keep the binary search for
            // the long descent and inspect both endpoint neighborhoods directly.
            // The route-bound landing can rise and fall after the lower mouth. Scan
            // that short tail directly; binary search is only valid on the descent.
            if(passageTileScopeMatches)
            {
                VisitNearestPassageSegmentRange(passageIndex,carveBegin,carveEnd,qx,qy,qz,
                    0,bestSignedDistance,considerCarveSegment);
                VisitNearestPassageSegmentRange(passageIndex,0,
                    std::min<std::ptrdiff_t>(8,lowerMouthIndex)-1,qx,qy,qz,
                    1,bestSignedDistance,considerCarveSegment);
                VisitNearestPassageSegmentRange(passageIndex,mouthSearchBegin,mouthSearchEnd-1,
                    qx,qy,qz,2,bestSignedDistance,considerCarveSegment);
                VisitNearestPassageSegmentRange(passageIndex,lowerMouthIndex,lastIndex-1,
                    qx,qy,qz,3,bestSignedDistance,considerCarveSegment);
            }
            else
            {
                for(std::ptrdiff_t index=carveBegin;index<=carveEnd;++index)
                    considerCarveSegment(static_cast<std::size_t>(index),0);
                for(std::ptrdiff_t index=0;index<std::min<std::ptrdiff_t>(8,lowerMouthIndex);++index)
                    considerCarveSegment(static_cast<std::size_t>(index),1);
                for(std::ptrdiff_t index=mouthSearchBegin;index<mouthSearchEnd;++index)
                    considerCarveSegment(static_cast<std::size_t>(index),2);
                for(std::ptrdiff_t index=lowerMouthIndex;index<lastIndex;++index)
                    considerCarveSegment(static_cast<std::size_t>(index),3);
            }
            if(!std::isfinite(bestSignedDistance))continue;
            const auto& nearestA=passage.controlPoints[static_cast<std::size_t>(bestIndex)];
            const auto& nearestB=passage.controlPoints[static_cast<std::size_t>(bestIndex+1)];
            const double nearestRadius=nearestA.radiusSubvoxels+bestT*(
                static_cast<double>(nearestB.radiusSubvoxels)-nearestA.radiusSubvoxels);
            const double distanceToCenter=std::max(1.0e-9,bestSignedDistance+nearestRadius);
            const double verticalWallAlignment=distanceToCenter>1.0e-9
                ?std::clamp(-(qz-(nearestA.positionSubvoxels[2]+bestT*(
                    static_cast<double>(nearestB.positionSubvoxels[2])-nearestA.positionSubvoxels[2])))
                    /distanceToCenter,0.0,1.0):0.0;
            const float relief=VF_FieldPassageWallRelief(static_cast<float>(X),static_cast<float>(Y),
                static_cast<float>(Z),static_cast<std::uint32_t>(Owner?Owner->Seed:0));
            const float mouthSurfaceRelief=VF_FieldSurfaceRelief(static_cast<float>(X)*1.5f,
                static_cast<float>(Y)*1.5f,static_cast<float>(Z)*1.5f,
                static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x4D4F5554u);
            const float mouthTerrainRelief=VF_FieldSurfaceRelief(static_cast<float>(X)*1.5f,
                static_cast<float>(Y)*1.5f,static_cast<float>(Z)*1.5f,
                static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x4D4F5554u);
            const float mouthTreadFieldRelief=VF_FieldSurfaceRelief(static_cast<float>(X)*0.75f,
                static_cast<float>(Y)*0.75f,static_cast<float>(Z)*0.75f,
                static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x54485244u);
            const auto routeSegmentLengthMetres=[&](std::ptrdiff_t routeIndex)
            {
                const auto& before=passage.controlPoints[static_cast<std::size_t>(routeIndex)];
                const auto& after=passage.controlPoints[static_cast<std::size_t>(routeIndex+1)];
                const double dx=static_cast<double>(after.positionSubvoxels[0])
                    -before.positionSubvoxels[0];
                const double dy=static_cast<double>(after.positionSubvoxels[1])
                    -before.positionSubvoxels[1];
                const double dz=static_cast<double>(after.positionSubvoxels[2])
                    -before.positionSubvoxels[2];
                return DeterministicSqrt(dx*dx+dy*dy+dz*dz)/qPerMetre;
            };
            double distanceFromOpenMouth=std::numeric_limits<double>::infinity();
            if(bestIndex<=2)
            {
                distanceFromOpenMouth=bestT*routeSegmentLengthMetres(bestIndex);
                for(std::ptrdiff_t routeIndex=0;routeIndex<bestIndex;++routeIndex)
                    distanceFromOpenMouth+=routeSegmentLengthMetres(routeIndex);
            }
            else if(bestIndex>=lowerMouthIndex-2&&bestIndex<=lowerMouthIndex+2)
            {
                if(bestIndex<lowerMouthIndex)
                {
                    distanceFromOpenMouth=(1.0-bestT)*routeSegmentLengthMetres(bestIndex);
                    for(std::ptrdiff_t routeIndex=bestIndex+1;
                        routeIndex<lowerMouthIndex;++routeIndex)
                        distanceFromOpenMouth+=routeSegmentLengthMetres(routeIndex);
                }
                else
                {
                    distanceFromOpenMouth=bestT*routeSegmentLengthMetres(bestIndex);
                    for(std::ptrdiff_t routeIndex=lowerMouthIndex;routeIndex<bestIndex;++routeIndex)
                        distanceFromOpenMouth+=routeSegmentLengthMetres(routeIndex);
                }
            }
            double mouthEntryFloorAlignment=0.0;
            double mouthEntryPlanDistance=std::numeric_limits<double>::infinity();
            double mouthEntryFloorQ=0.0;
            bool upperMouthFloorFade=false;
            {
                // The large mouth bore overlaps several inner coils. Its global
                // nearest SDF can belong to a later turn even at the lip, so use the
                // projected entrance path to recover the local floor orientation.
                double prefixMetres=0.0;
                double nearestEntryPlanDistance=std::numeric_limits<double>::infinity();
                double projectedEntryDistance=std::numeric_limits<double>::infinity();
                for(std::ptrdiff_t routeIndex=0;
                    routeIndex<std::min<std::ptrdiff_t>(3,lowerMouthIndex);++routeIndex)
                {
                    const auto& before=passage.controlPoints[static_cast<std::size_t>(routeIndex)];
                    const auto& after=passage.controlPoints[static_cast<std::size_t>(routeIndex+1)];
                    const double ax=static_cast<double>(before.positionSubvoxels[0]);
                    const double ay=static_cast<double>(before.positionSubvoxels[1]);
                    const double az=static_cast<double>(before.positionSubvoxels[2]);
                    const double dx=static_cast<double>(after.positionSubvoxels[0])-ax;
                    const double dy=static_cast<double>(after.positionSubvoxels[1])-ay;
                    const double dz=static_cast<double>(after.positionSubvoxels[2])-az;
                    const double horizontalLengthSq=dx*dx+dy*dy;
                    const double t=horizontalLengthSq>0.0?std::clamp(
                        ((qx-ax)*dx+(qy-ay)*dy)/horizontalLengthSq,0.0,1.0):0.0;
                    double projectedX=ax+t*dx,projectedY=ay+t*dy;
                    const double horizontalLength=DeterministicSqrt(horizontalLengthSq);
                    if(horizontalLength>1.0e-6)
                    {
                        const double pathRelief=std::clamp(static_cast<double>(
                            VF_FieldSurfaceRelief(static_cast<float>(projectedX/qPerMetre*1.5),
                                static_cast<float>(projectedY/qPerMetre*1.5),
                                static_cast<float>((az+t*dz)/qPerMetre*1.5),
                                static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x4D4F5554u)),
                            -1.0,1.0);
                        const double lateralOffset=pathRelief*0.18*qPerMetre;
                        projectedX-=dy/horizontalLength*lateralOffset;
                        projectedY+=dx/horizontalLength*lateralOffset;
                    }
                    const double planDx=qx-projectedX,planDy=qy-projectedY;
                    const double planDistance=DeterministicSqrt(planDx*planDx+planDy*planDy);
                    if(planDistance<nearestEntryPlanDistance)
                    {
                        nearestEntryPlanDistance=planDistance;
                        const double centerZ=az+t*dz;
                        const double radius=before.radiusSubvoxels+t*(
                            static_cast<double>(after.radiusSubvoxels)-before.radiusSubvoxels);
                        mouthEntryFloorQ=centerZ-radius+0.20*qPerMetre;
                        const double centerDistance=DeterministicSqrt(planDx*planDx
                            +planDy*planDy+(qz-centerZ)*(qz-centerZ));
                        mouthEntryFloorAlignment=centerDistance>1.0e-9
                            ?std::clamp(-(qz-centerZ)/centerDistance,0.0,1.0):0.0;
                        projectedEntryDistance=prefixMetres
                            +t*routeSegmentLengthMetres(routeIndex);
                    }
                    prefixMetres+=routeSegmentLengthMetres(routeIndex);
                }
                if(nearestEntryPlanDistance<=2.0*qPerMetre
                    &&projectedEntryDistance<=8.0
                    &&std::abs(qz-mouthEntryFloorQ)<=4.0*qPerMetre)
                {
                    distanceFromOpenMouth=projectedEntryDistance;
                    mouthEntryPlanDistance=nearestEntryPlanDistance/qPerMetre;
                    upperMouthFloorFade=true;
                }
            }
            double mouthFloorBlend=0.0;
            if(std::isfinite(distanceFromOpenMouth))
            {
                const double fade=std::clamp(distanceFromOpenMouth/11.0,0.0,1.0);
                const double smooth=fade*fade*(3.0-2.0*fade);
                mouthFloorBlend=1.0-smooth;
            }
            const double floorReliefT=std::clamp((verticalWallAlignment-0.55)/0.45,0.0,1.0);
            const double floorReliefWeight=floorReliefT*floorReliefT
                *(3.0-2.0*floorReliefT);
            const double floorReliefOffset=std::clamp(
                static_cast<double>(mouthTerrainRelief),-1.0,1.0)
                *0.20*qPerMetre*mouthFloorBlend*floorReliefWeight
                *(upperMouthFloorFade?1.0:0.0);
            const double wallReliefWeight=0.05+0.95*(1.0-verticalWallAlignment);
            const double roughSignedDistance=bestSignedDistance
                +static_cast<double>(std::clamp(relief,-1.0f,1.0f))*0.21*qPerMetre*wallReliefWeight
                +floorReliefOffset;
            if(IsPassageShortSpanSegment(passageIndex,static_cast<std::size_t>(bestIndex)))
            {
                const double bridgeDistance=PassageBridgeSignedDistance(passageIndex,
                    static_cast<std::size_t>(bestIndex),X,Y,Z);
                composed=std::min(composed,static_cast<float>(bridgeDistance/Q));
            }
            // Leave native crater ground at the lip. The bore opens through the walls
            // immediately, while its floor cut eases in along the passage centerline.
            double mouthCarveFade=1.0;
            if(upperMouthFloorFade)
            {
                constexpr double mouthCarveFadeMetres=8.0;
                mouthCarveFade=std::clamp(distanceFromOpenMouth/mouthCarveFadeMetres,
                    0.0,1.0);
                mouthCarveFade=mouthCarveFade*mouthCarveFade*(3.0-2.0*mouthCarveFade);
            }
            const double floorAlignment=std::max(verticalWallAlignment,
                mouthEntryFloorAlignment)*std::max(verticalWallAlignment,
                mouthEntryFloorAlignment);
            double floorBelowWeight=0.0;
            if(upperMouthFloorFade)
            {
                const double belowFloor=(mouthEntryFloorQ-qz)/qPerMetre;
                const double supportRamp=std::clamp(belowFloor/0.15,0.0,1.0);
                const double supportFade=std::clamp((1.0-belowFloor)/0.35,0.0,1.0);
                const double rampSmooth=supportRamp*supportRamp*(3.0-2.0*supportRamp);
                const double fadeSmooth=supportFade*supportFade*(3.0-2.0*supportFade);
                floorBelowWeight=rampSmooth*fadeSmooth;
            }
            // Preserve native terrain only along a capsule-scale worn lane. The
            // former bore-wide alignment feather left a straight platform-width
            // bridge across the FI mouth.
            double mouthWalkLaneT=std::clamp((1.05-mouthEntryPlanDistance)/0.60,0.0,1.0);
            mouthWalkLaneT=mouthWalkLaneT*mouthWalkLaneT*(3.0-2.0*mouthWalkLaneT);
            const double mouthWalkLaneWeight=upperMouthFloorFade?mouthWalkLaneT:0.0;
            const double floorCarveWeight=1.0-(1.0-mouthCarveFade)
                *floorAlignment*floorAlignment*floorBelowWeight*mouthWalkLaneWeight;
            const float fullyCarvedDensity=std::max(composed,
                static_cast<float>(-roughSignedDistance/Q));
            composed=std::lerp(composed,fullyCarvedDensity,
                static_cast<float>(floorCarveWeight));
            const auto considerSupportSegment=[&](std::ptrdiff_t index)
            {
                const auto& segmentA=passage.controlPoints[static_cast<std::size_t>(index)];
                const auto& segmentB=passage.controlPoints[static_cast<std::size_t>(index+1)];
                const double dx=static_cast<double>(segmentB.positionSubvoxels[0])-segmentA.positionSubvoxels[0];
                const double dy=static_cast<double>(segmentB.positionSubvoxels[1])-segmentA.positionSubvoxels[1];
                const double dz=static_cast<double>(segmentB.positionSubvoxels[2])-segmentA.positionSubvoxels[2];
                const double radiusA=segmentA.radiusSubvoxels;
                const double radiusB=segmentB.radiusSubvoxels;
                const bool entryMouthShoulder=index<=2;
                // Keep the tread within the probe band and below the capsule's
                // lowest sampled point.
                const bool bridgeDeck=IsPassageShortSpanSegment(passageIndex,
                    static_cast<std::size_t>(index))
                    ||IsPassageColumnSegment(passageIndex,static_cast<std::size_t>(index));
                // Keep a small capsule margin at regular treads and restore most of
                // the nominal height smoothly as a tread approaches its landing.
                double floorOffset=bridgeDeck
                    ?PassageBridgeDeckOffsetMetres(passageIndex,static_cast<std::size_t>(index))
                    :std::lerp(0.15,0.20,lowerMouthBlend);
                const double horizontalLengthSq=dx*dx+dy*dy;
                const bool overlapSupportJoin=index+12<lastIndex
                    &&!IsPassageShortSpanSegment(passageIndex,static_cast<std::size_t>(index))
                    &&(index==0||(!IsPassageShortSpanSegment(passageIndex,
                        static_cast<std::size_t>(index-1))));
                const bool smoothSupportJoin=index>0&&overlapSupportJoin
                    &&!IsPassageShortSpanSegment(passageIndex,static_cast<std::size_t>(index+1));
                const double projection=horizontalLengthSq>0.0
                    ?((qx-segmentA.positionSubvoxels[0])*dx
                        +(qy-segmentA.positionSubvoxels[1])*dy)/horizontalLengthSq:bestT;
                // Extend tread segments by a fixed distance through route knots. A
                // fractional extension made the support width change with segment length.
                const double overlapFraction=overlapSupportJoin&&horizontalLengthSq>0.0
                ?std::min(0.5,2.0*qPerMetre/DeterministicSqrt(horizontalLengthSq)):0.0;
                const double supportT=horizontalLengthSq>0.0
                    ?std::clamp(projection,-overlapFraction,1.0+overlapFraction):bestT;
                double centerX=segmentA.positionSubvoxels[0]+supportT*dx;
                double centerY=segmentA.positionSubvoxels[1]+supportT*dy;
                double centerZ=segmentA.positionSubvoxels[2]+supportT*(
                    static_cast<double>(segmentB.positionSubvoxels[2])-segmentA.positionSubvoxels[2]);
                double radius=segmentA.radiusSubvoxels+supportT*(
                    static_cast<double>(segmentB.radiusSubvoxels)-segmentA.radiusSubvoxels);
                if(smoothSupportJoin)
                {
                    const auto& p0=passage.controlPoints[static_cast<std::size_t>(index-1)];
                    const auto& p3=passage.controlPoints[static_cast<std::size_t>(index+2)];
                    const double t2=supportT*supportT,t3=t2*supportT;
                    const auto interpolate=[&](double v0,double v1,double v2,double v3)
                    {
                        return 0.5*((2.0*v1)+(-v0+v2)*supportT
                            +(2.0*v0-5.0*v1+4.0*v2-v3)*t2
                            +(-v0+3.0*v1-3.0*v2+v3)*t3);
                    };
                    constexpr double SmoothSupportHeightWeight=0.25;
                    centerZ+=(interpolate(p0.positionSubvoxels[2],segmentA.positionSubvoxels[2],
                        segmentB.positionSubvoxels[2],p3.positionSubvoxels[2])-centerZ)
                        *SmoothSupportHeightWeight;
                    radius+=(interpolate(p0.radiusSubvoxels,segmentA.radiusSubvoxels,
                        segmentB.radiusSubvoxels,p3.radiusSubvoxels)-radius)
                        *SmoothSupportHeightWeight;
                }
                double treadRelief=0.0;
                if(entryMouthShoulder
                    ||(index>=lowerMouthIndex-2&&index<=lowerMouthIndex+2))
                {
                    const double horizontalLength=DeterministicSqrt(horizontalLengthSq);
                    if(horizontalLength>1.0e-6)
                    {
                        const double pathRelief=std::clamp(static_cast<double>(
                            VF_FieldSurfaceRelief(static_cast<float>(centerX/qPerMetre*1.5),
                                static_cast<float>(centerY/qPerMetre*1.5),
                                static_cast<float>(centerZ/qPerMetre*1.5),
                                static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x4D4F5554u)),
                            -1.0,1.0);
                        treadRelief=pathRelief;
                        const double lateralOffset=pathRelief*0.18*qPerMetre;
                        centerX-=dy/horizontalLength*lateralOffset;
                        centerY+=dx/horizontalLength*lateralOffset;
                    }
                }
                const double horizontalX=qx-centerX,horizontalY=qy-centerY;
                const double horizontalDistance=DeterministicSqrt(horizontalX*horizontalX
                    +horizontalY*horizontalY);
                const double supportPlayerCenterZ=centerZ-radius+playerCenterAboveFloorQ;
                const double supportQueryDepth=supportPlayerCenterZ-qz;
                // Support belongs just below the avatar's foot plane. Queries within
                // the capsule body, or a neighbouring coil's overlapping bore, must
                // not turn that tread into a ceiling or mid-air shelf.
                // Sparse authored routes use the full signed distance around the top;
                // dense routes retain the legacy one-sided tread density.
                const double supportSegmentLength=DeterministicSqrt(
                    horizontalLengthSq+dz*dz)/qPerMetre;
                const double sparseRouteThreshold=VoxelForgeCore::WorldAssemblyEvaluatorVersion>=188
                    &&floatingIslandPassage&&passage.style==0?1.0:1.5;
                const bool sparseRouteSupport=supportSegmentLength>sparseRouteThreshold;
                const double minimumSupportQueryDepth=index==selectedSupportSegmentIndex
                    &&sparseRouteSupport?0.65:0.93;
                if(supportQueryDepth<minimumSupportQueryDepth*qPerMetre
                    ||supportQueryDepth>1.30*qPerMetre)return;
                const bool fallbackSupport=qz>=supportPlayerCenterZ-1.50*qPerMetre;
                const double supportThicknessVoxels=fallbackSupport
                    ?qPerMetre/Q:0.5*qPerMetre/Q;
                // Keep the supported ramp to a comfortable walking width. Extending a
                // full bore-radius shelf across overlapping helix coils can block the
                // capsule on the neighbouring turn.
                const bool lowerMouthBodyOverlap=index>=lowerMouthIndex-2
                    &&supportQueryDepth<0.98*qPerMetre;
                // Keep a narrow walk core, but place its top on the native surface
                // so the support remains a worn ramp instead of a route-height slab.
                const bool mouthTread=entryMouthShoulder
                    &&(!floatingIslandPassage||passage.style==0);
                double distanceFromMouthMetres=std::numeric_limits<double>::infinity();
                if(entryMouthShoulder)
                {
                    double prefixMetres=0.0;
                    for(std::ptrdiff_t routeIndex=0;routeIndex<index;++routeIndex)
                    {
                        const auto& before=passage.controlPoints[
                            static_cast<std::size_t>(routeIndex)];
                        const auto& after=passage.controlPoints[
                            static_cast<std::size_t>(routeIndex+1)];
                        const double dx=static_cast<double>(after.positionSubvoxels[0])
                            -before.positionSubvoxels[0];
                        const double dy=static_cast<double>(after.positionSubvoxels[1])
                            -before.positionSubvoxels[1];
                        const double dz=static_cast<double>(after.positionSubvoxels[2])
                            -before.positionSubvoxels[2];
                        prefixMetres+=DeterministicSqrt(dx*dx+dy*dy+dz*dz)/qPerMetre;
                    }
                    distanceFromMouthMetres=std::max(0.0,
                        prefixMetres+supportT*supportSegmentLength);
                }
                else if(lowerMouthBodyOverlap)
                {
                    double suffixMetres=0.0;
                    for(std::ptrdiff_t routeIndex=index+1;
                        routeIndex<lowerMouthIndex;++routeIndex)
                    {
                        const auto& before=passage.controlPoints[
                            static_cast<std::size_t>(routeIndex)];
                        const auto& after=passage.controlPoints[
                            static_cast<std::size_t>(routeIndex+1)];
                        const double dx=static_cast<double>(after.positionSubvoxels[0])
                            -before.positionSubvoxels[0];
                        const double dy=static_cast<double>(after.positionSubvoxels[1])
                            -before.positionSubvoxels[1];
                        const double dz=static_cast<double>(after.positionSubvoxels[2])
                            -before.positionSubvoxels[2];
                        suffixMetres+=DeterministicSqrt(dx*dx+dy*dy+dz*dz)/qPerMetre;
                    }
                    distanceFromMouthMetres=std::max(0.0,
                        suffixMetres+(1.0-supportT)*supportSegmentLength);
                }
                double mouthReliefT=std::clamp(distanceFromMouthMetres/8.0,0.0,1.0);
                mouthReliefT=mouthReliefT*mouthReliefT*(3.0-2.0*mouthReliefT);
                double mouthSupportT=std::clamp((distanceFromMouthMetres-0.25)/4.0,0.0,1.0);
                mouthSupportT=mouthSupportT*mouthSupportT*(3.0-2.0*mouthSupportT);
                const double mouthSupportWidth=std::lerp(0.82,1.00,mouthSupportT);
                const double supportHalfWidthMetres=mouthTread?mouthSupportWidth
                    :lowerMouthBodyOverlap?0.90:1.25;
                double supportHalfWidth=std::min(radius,
                    supportHalfWidthMetres*qPerMetre);
                const double shoulderWarp=mouthTread
                    ?std::clamp(static_cast<double>(mouthSurfaceRelief),-1.0,1.0)
                        *0.12*qPerMetre:0.0;
                supportHalfWidth=mouthTread
                    ?std::clamp(supportHalfWidth+shoulderWarp,
                        std::lerp(0.52,0.62,mouthSupportT)*qPerMetre,
                        std::lerp(0.92,1.10,mouthSupportT)*qPerMetre)
                    :std::max(0.0,supportHalfWidth+shoulderWarp);
                // Keep the walk core within the player footprint, then ease the outer
                // edge into native ground over a long enough shoulder to avoid a berm.
                const double supportEdgeCoreMetres=mouthTread?0.08
                    :entryMouthShoulder?0.60:0.90;
                const double supportEdgeBlendMetres=std::min(
                    mouthTread?1.40:entryMouthShoulder?0.85:0.35,
                    std::max(0.0,supportHalfWidth/qPerMetre-supportEdgeCoreMetres));
                const double supportEdgeT=supportEdgeBlendMetres>1.0e-6
                    ?std::clamp((horizontalDistance
                        -(supportHalfWidth-supportEdgeBlendMetres*qPerMetre))
                        /(supportEdgeBlendMetres*qPerMetre),0.0,1.0):0.0;
                const double supportEdgeSmooth=supportEdgeT*supportEdgeT
                    *(3.0-2.0*supportEdgeT);
                const double mouthSupportThicknessVoxels=std::lerp(
                    0.35*supportThicknessVoxels,supportThicknessVoxels,mouthSupportT);
                const double localSupportThicknessVoxels=entryMouthShoulder
                    ?mouthSupportThicknessVoxels*(1.0-0.72*supportEdgeSmooth)
                    :supportThicknessVoxels;
                double mouthSupportBlend=1.0;
                if(mouthTread&&std::isfinite(distanceFromMouthMetres))
                {
                    const double mouthBlendT=std::clamp(
                        distanceFromMouthMetres/0.75,0.0,1.0);
                    mouthSupportBlend=0.75+0.25*mouthBlendT*mouthBlendT
                        *(3.0-2.0*mouthBlendT);
                }
                const double supportEdgeDepth=mouthTread?0.25:0.35;
                const double mouthFloorOffset=mouthTread
                    ?std::lerp(0.15,0.19,lowerMouthBlend):floorOffset;
                const double baseFloorQ=centerZ-radius+mouthFloorOffset*qPerMetre
                    -supportEdgeSmooth*supportEdgeDepth*qPerMetre;
                const double nativeSurfaceQ=static_cast<double>(qz)
                    -static_cast<double>(density)*Q;
                // Keep support near the route floor; visible mouth preservation below
                // blends the source field directly instead of extending this SDF top.
                const double nativeFieldOffset=std::clamp(nativeSurfaceQ-baseFloorQ,
                    -0.80*qPerMetre,0.80*qPerMetre);
                const double nativeSurfaceBlend=mouthTread?1.0:1.0-mouthReliefT;
                const double nativeTreadOffset=std::clamp(
                    nativeFieldOffset*nativeSurfaceBlend+floorReliefOffset
                        -std::abs(treadRelief)*0.08*qPerMetre
                            *(1.0-0.25*mouthReliefT),
                    -0.80*qPerMetre,0.80*qPerMetre);
                const double floorQ=baseFloorQ
                    +(mouthTread?std::clamp(nativeTreadOffset
                        +std::clamp(static_cast<double>(mouthTreadFieldRelief),-1.0,1.0)
                            *0.40*qPerMetre,-0.80*qPerMetre,0.0):0.0);
                const double floorVoxels=floorQ/Q;
                const bool signedDistanceSupport=sparseRouteSupport||mouthTread;
                const double supportPositiveRangeVoxels=signedDistanceSupport
                    ?0.35*qPerMetre/Q:1.0/Q;
                if(Z<floorVoxels-localSupportThicknessVoxels
                    ||Z>floorVoxels+supportPositiveRangeVoxels)return;
                const double supportQueryHalfWidth=supportHalfWidth
                    +(mouthTread?0.45*qPerMetre:0.0);
                if(horizontalDistance>supportQueryHalfWidth)return;
                const double supportDistanceSquared=horizontalDistance*horizontalDistance
                    +(Z-floorVoxels)*(Z-floorVoxels);
                if(supportDistanceSquared>=bestSupportDistanceSquared)return;
                bestSupportDistanceSquared=supportDistanceSquared;
                hasSupportFloor=true;
                bestSupportSegmentIndex=index;
                bestSupportIsMouthTread=mouthTread;
                if(signedDistanceSupport)
                {
                    // Sparse support profiles need both sides of a signed distance
                    // so the sampled zero crossing stays on the tread top.
                    const double topDistance=qz-floorQ;
                    const double bottomDistance=floorQ-localSupportThicknessVoxels*Q-qz;
                    const double verticalDistance=std::max(topDistance,bottomDistance);
                    const double sideDistance=horizontalDistance-supportHalfWidth;
                    bestSupportDensity=SmoothMaxDistance(
                        static_cast<float>(sideDistance/Q),
                        static_cast<float>(verticalDistance/Q),
                        entryMouthShoulder?0.80f:0.20f);
                }
                else
                {
                    bestSupportDensity=std::clamp(Z-floorVoxels,
                        -localSupportThicknessVoxels,0.0);
                }
                bestSupportFloorQ=floorQ;
                bestSupportUsesSignedDistance=signedDistanceSupport;
                bestSupportMouthBlend=mouthSupportBlend;
                bestSupportNativeBlend=mouthTread
                    ?0.85*mouthSupportBlend*(1.0-supportEdgeSmooth):0.0;
            };
            std::ptrdiff_t supportCenterIndex=bestIndex;
            if(bestIndex<lowerMouthIndex)
            {
                // A helix can have multiple centerlines at one XY. Select the tread
                // whose floor is just below this density query, not the closest wall.
                const double supportProfileOffset=surfaceToTunnelSupport?1.13:0.93;
                const double supportProfileTarget=qz+supportProfileOffset*qPerMetre;
                const auto supportProfile=std::lower_bound(passage.controlPoints.begin(),mainEnd,
                    supportProfileTarget,[&](const auto& point,double value)
                        {return floorProfile(point)>value;});
                const std::ptrdiff_t profileIndex=std::clamp<std::ptrdiff_t>(
                    supportProfile-passage.controlPoints.begin(),0,lowerMouthIndex);
                // At floor height the nearest 3D centerline can belong to the next
                // coil below. The descending floor profile identifies the coil that
                // owns this tread, even when it is more than eight control points away.
                supportCenterIndex=profileIndex;
            }
            const std::ptrdiff_t supportBegin=std::max<std::ptrdiff_t>(0,supportCenterIndex-1);
            const std::ptrdiff_t supportEnd=std::min<std::ptrdiff_t>(lastIndex-1,
                supportCenterIndex+1);
            selectedSupportSegmentIndex=supportCenterIndex>0
                ?supportCenterIndex-1:supportCenterIndex;
            for(std::ptrdiff_t index=supportBegin;index<=supportEnd;++index)
                considerSupportSegment(index);
            // Keep route treads inside the native rock envelope. Carving may reopen the
            // floor above this point, but a support cannot create a new surface in air.
            const bool passageColumnFloorSupport=hasSupportFloor
                &&IsPassageColumnSegment(passageIndex,
                    static_cast<std::size_t>(bestSupportSegmentIndex));
            const bool shortSpanFloorSupport=hasSupportFloor
                &&IsPassageShortSpanSegment(passageIndex,
                    static_cast<std::size_t>(bestSupportSegmentIndex));
            const double capsuleClearanceMetres=bestSupportUsesSignedDistance?0.045:0.05;
            const double capsuleQueryZ=bestSupportUsesSignedDistance?bestSupportFloorQ:qz;
            const bool supportCapsuleProfileAvailable=passageIndex<PassageNearestNodes.size()
                &&!PassageNearestNodes[passageIndex].empty();
            const bool capsuleAllowsSupport=(passageTileScopeMatches
                ||(bestSupportUsesSignedDistance&&supportCapsuleProfileAvailable))
                ?!PassagePlayerCapsuleBlocksSupport(passageIndex,carveBegin,carveEnd,
                    lowerMouthIndex,mouthSearchBegin,mouthSearchEnd,lastIndex,qx,qy,
                    capsuleQueryZ,qPerMetre,capsuleClearanceMetres)
                :bestPlayerCapsuleSignedDistance>=capsuleClearanceMetres*qPerMetre;
            // Outside bridge and short-span segments, add the tread only where the
            // native field already provides a solid envelope; the capsule check keeps
            // that support below the player's walk space.
            if(hasSupportFloor&&(density<0.0f||passageColumnFloorSupport
                ||shortSpanFloorSupport)
                &&(capsuleAllowsSupport||bestSupportDensity>=0.0))
            {
                if(bestSupportIsMouthTread)
                {
                    // Preserve the owner's native ground through the shallow mouth
                    // carve. Blending back the native field keeps its crater curvature
                    // and noise. The capsule test keeps neighbouring coils open.
                    const bool nativeRestoreCapsuleClear=density<0.0f
                        &&bestSupportNativeBlend>0.0&&capsuleAllowsSupport
                        &&!PassagePlayerCapsuleBlocksSupport(passageIndex,carveBegin,
                            carveEnd,lowerMouthIndex,mouthSearchBegin,mouthSearchEnd,
                            lastIndex,qx,qy,qz,qPerMetre,capsuleClearanceMetres);
                    if(nativeRestoreCapsuleClear)
                    {
                        const double nativeSurfaceDetail=std::clamp(
                            static_cast<double>(mouthTerrainRelief),-1.0,1.0)
                            *0.18*qPerMetre/Q;
                        const float nativeGroundWithRelief=static_cast<float>(density
                            -nativeSurfaceDetail);
                        composed=std::lerp(composed,nativeGroundWithRelief,
                            static_cast<float>(bestSupportNativeBlend));
                    }
                }
                else composed=std::min(composed,static_cast<float>(bestSupportDensity));
            }
        }
        // Restore the surface route where the passage cut crossed otherwise solid
        // native ground. The support stays native-solid-only, so it cannot float.
        for(std::size_t passageIndex=0;passageIndex<ResolvedLayout->passages.size();++passageIndex)
        {
            const auto& passage=ResolvedLayout->passages[passageIndex];
            if(passage.controlPoints.size()<2)continue;
            const bool tileHasSupport=passageTileScopeMatches;
            if(!tileHasSupport
                ||ActivePassageTileQueries->hasMouthSupport(passageIndex))
                composeRouteMouthSupport(passage.upperStrateIndex,
                    passage.upperMouthSubvoxels,true);
        }
        return composed;
    }

    float ApplyResolvedStrateComposition(float density,float X,float Y,float Z) const
    {
        const float graphDensity=ApplyResolvedCavernGraph(density,X,Y,Z);
        const float composed=ApplyResolvedStratePassageCarves(
            ApplyResolvedStrateBoundaryBand(graphDensity,X,Y,Z),X,Y,Z);
        const float stamped=StampRuntime.empty()?composed:ApplyResolvedSdfStamps(composed,X,Y,Z);
        // Keep the explicit graph floor cap after smooth unions, relief, passages,
        // and decorative stamps so nothing can reopen the tunnel floor below profile.
        return ApplyResolvedCavernFloorCaps(stamped,X,Y,Z);
    }

    bool ResolvedPassageIntersectsBox(const int32 minimum[3],const int32 maximum[3]) const
    {
        if(!ResolvedLayout||ResolvedLayout->passages.empty())return false;
        if(PassageProofNodes.empty())
        {
            // Native-only readiness tiles have not built the passage BVH. Keep their
            // exact conservative fallback instead of indexing an empty tree.
            constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
            const double voxelsPerMetre=Owner&&Owner->CoreVoxelSizeMicrons>0
                ?1000000.0/Owner->CoreVoxelSizeMicrons:4.0;
            const double bridgeHalfWidthVoxels=3.5*voxelsPerMetre;
            const double bridgeFootDepthVoxels=(5.0-0.13)*voxelsPerMetre;
            const auto overlaps=[&](const double low[3],const double high[3])
            {
                for(int axis=0;axis<3;++axis)
                    if(high[axis]<minimum[axis]||low[axis]>maximum[axis])return false;
                return true;
            };
            for(const auto& passage:ResolvedLayout->passages)
            {
                for(std::size_t i=1;i<passage.controlPoints.size();++i)
                {
                    const auto& a=passage.controlPoints[i-1];const auto& b=passage.controlPoints[i];
                    const double radius=static_cast<double>(std::max(a.radiusSubvoxels,b.radiusSubvoxels))/Q;
                    const double floorThicknessVoxels=voxelsPerMetre;
                    const double horizontalExtent=std::max(radius,bridgeHalfWidthVoxels);
                    const double footDepth=std::max(floorThicknessVoxels,bridgeFootDepthVoxels);
                    const double low[3]={
                        std::min(a.positionSubvoxels[0],b.positionSubvoxels[0])/Q-horizontalExtent,
                        std::min(a.positionSubvoxels[1],b.positionSubvoxels[1])/Q-horizontalExtent,
                        std::min(a.positionSubvoxels[2],b.positionSubvoxels[2])/Q-radius-footDepth};
                    const double high[3]={
                        std::max(a.positionSubvoxels[0],b.positionSubvoxels[0])/Q+horizontalExtent,
                        std::max(a.positionSubvoxels[1],b.positionSubvoxels[1])/Q+horizontalExtent,
                        std::max(a.positionSubvoxels[2],b.positionSubvoxels[2])/Q+radius};
                    if(overlaps(low,high))return true;
                }
                const auto upperStratum=std::find_if(ResolvedLayout->strates.begin(),
                    ResolvedLayout->strates.end(),[&passage](const auto& value)
                        {return value.strateIndex==passage.upperStrateIndex;});
                if(upperStratum!=ResolvedLayout->strates.end())
                {
                    std::array<const VoxelForgeCore::ResolvedLayoutAnchorV2*,5> route{};
                    std::size_t routeCount=0;
                    for(const auto& anchor:upperStratum->anchors)
                        if(anchor.kind=="route_point"&&anchor.values.size()>=3)
                        {
                            if(routeCount<route.size())route[routeCount++]=&anchor;
                            else
                            {
                                std::move(route.begin()+1,route.end(),route.begin());
                                route.back()=&anchor;
                            }
                        }
                    if(routeCount>=2)
                    {
                        const double mouthReach=13.0*voxelsPerMetre*Q;
                        double minimumZ=std::numeric_limits<double>::infinity();
                        double maximumZ=-std::numeric_limits<double>::infinity();
                        for(std::size_t index=0;index<routeCount;++index)
                        {
                            minimumZ=std::min(minimumZ,static_cast<double>(route[index]->values[2]));
                            maximumZ=std::max(maximumZ,static_cast<double>(route[index]->values[2]));
                        }
                        const double mouthX=passage.upperMouthSubvoxels[0];
                        const double mouthY=passage.upperMouthSubvoxels[1];
                        const double low[3]={(mouthX-mouthReach)/Q,(mouthY-mouthReach)/Q,
                            (minimumZ-3.0*voxelsPerMetre*Q)/Q};
                        const double high[3]={(mouthX+mouthReach)/Q,(mouthY+mouthReach)/Q,
                            (maximumZ+3.0*voxelsPerMetre*Q)/Q};
                        if(overlaps(low,high))return true;
                    }
                }
            }
            for(const auto& crossing:PassageVoidCrossings)
            {
                if(!crossing.needsColumn)continue;
                const double radius=static_cast<double>(crossing.maximumRadiusSubvoxels)/Q;
                const double low[3]={crossing.centerXSubvoxels/Q-radius,
                    crossing.centerYSubvoxels/Q-radius,crossing.bottomZSubvoxels/Q};
                const double high[3]={crossing.centerXSubvoxels/Q+radius,
                    crossing.centerYSubvoxels/Q+radius,crossing.topZSubvoxels/Q};
                if(overlaps(low,high))return true;
            }
            return false;
        }
        const double low[3]={static_cast<double>(minimum[0]),static_cast<double>(minimum[1]),
            static_cast<double>(minimum[2])};
        const double high[3]={static_cast<double>(maximum[0]),static_cast<double>(maximum[1]),
            static_cast<double>(maximum[2])};
        return PassageProofBoundsOverlapNode(0,low,high);
    }

    static bool MakeResolvedStratumBounds(double BottomZ,double TopZ,double SealThickness,
        FResolvedStratumBounds& Out)
    {
        if(!std::isfinite(BottomZ)||!std::isfinite(TopZ)||!std::isfinite(SealThickness)
            ||TopZ<=BottomZ||SealThickness<0.0)return false;
        Out={BottomZ,TopZ,SealThickness};
        return true;
    }

    bool GetResolvedStratumBounds(const FStrateSlot& Slot,FResolvedStratumBounds& Out) const
    {
        if(!Owner)return false;
        if(const auto* resolved=FindResolvedLayoutStratum(Slot.StrateIndex))
        {
            const double coreMicrons=std::max<std::uint32_t>(1,Owner->CoreVoxelSizeMicrons);
            const double bottom=static_cast<double>(resolved->interiorBottomMicrometres)/coreMicrons;
            const double top=static_cast<double>(resolved->interiorTopMicrometres)/coreMicrons;
            const double ceiling=static_cast<double>(resolved->ceiling.topMicrometres
                -resolved->ceiling.bottomMicrometres)/coreMicrons;
            const double bedrock=static_cast<double>(resolved->bedrock.topMicrometres
                -resolved->bedrock.bottomMicrometres)/coreMicrons;
            return MakeResolvedStratumBounds(bottom,top,std::max(ceiling,bedrock),Out);
        }
        const int32 MidChunkZ=(Slot.TopChunkZ+Slot.BottomChunkZ)/2;
        const FBoundStratumField* Bound=FindBoundStratumForChunk(MidChunkZ);
        if(bUseNativeManifestFields&&WorldAssembly&&Bound
            &&Bound->Kind==FBoundStratumField::EKind::FloatingIslands)
        {
            const auto* Plan=Bound->IslandPlan;
            if(Plan&&Plan->manifest.recipe.geometryVersion>=3)
            {
                constexpr double Scale=static_cast<double>(
                    VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
                return MakeResolvedStratumBounds(
                    static_cast<double>(Plan->manifest.recipe.layoutMinimumZSubvoxels)/Scale,
                    static_cast<double>(Plan->manifest.recipe.layoutMaximumZSubvoxels)/Scale,
                    static_cast<double>(Plan->manifest.recipe.boundarySealSubvoxels)/Scale,Out);
            }
        }
        const FStrateGenerationParams Params=Owner->Manager->GetGenerationParams(
            FIntVector(0,0,MidChunkZ));
        const double chunkWidth=GetResolvedLayoutChunkWidthVoxels();
        return MakeResolvedStratumBounds(static_cast<double>(Slot.BottomChunkZ)*chunkWidth,
            static_cast<double>(Slot.TopChunkZ+1)*chunkWidth,
            static_cast<double>(Params.BoundarySealThickness),Out);
    }

    enum class EDetailVariant : uint8 { Coherent, Smooth, PerVoxel };
    struct FBoxClassification
    {
        EVoxelTileClass Verdict=EVoxelTileClass::Mixed;
        bool bNativeSurface=false;
        bool bUnknown=false;
    };
    struct FClassificationThreadStats
    {
        uint64 SolidBoxes=0,AirBoxes=0,MixedBoxes=0,UnknownBoxes=0;
        uint64 NativeFloatFieldCalls=0,NativeLatticeFieldCalls=0,NativeUnclampedFieldCalls=0;
        double Milliseconds=0.0;
#if defined(VF_L30_ENABLE_COST_COUNTERS)
        uint64 BoundaryBandCalls=0,TransitionWindowChecks=0,TransitionWindowHits=0;
        uint64 TransitionEvaluatorCalls=0,TransitionPassageFadeCalls=0,TransitionPassageMouthTests=0;
        uint64 BoundaryTileCullRejects=0,BoundaryPointCullRejects=0;
        uint64 ColumnZOverlapCalls=0,ColumnGuardCalls=0,ColumnGuardNonpositiveSkips=0;
        uint64 ColumnGuardRadialRejects=0,ColumnSignedDistanceCalls=0;
        uint64 TransitionPassageTileSkips=0;
#endif
    };
    static void ResetThreadClassificationStats() { ThreadClassificationStats()={}; }
    static FClassificationThreadStats GetThreadClassificationStats()
    { return ThreadClassificationStats(); }
    struct FFarConnectorSegment
    {
        FVector Start=FVector::ZeroVector;
        FVector End=FVector::ZeroVector;
        float Radius=0.0f;
    };
    struct FEditBrush
    {
        enum class EShape : uint8 { Sphere, Capsule, RoundedBox };
        enum class EOperation : uint8 { Carve, AddRock, DensityOffset };
        EShape Shape=EShape::Sphere;
        EOperation Operation=EOperation::Carve;
        std::array<double,3> A{};
        std::array<double,3> B{};
        std::array<double,3> HalfExtent{};
        double Radius=0.0;
        double Rounding=0.0;
        float Strength=0.0f;
        float Falloff=0.0f;
    };

    struct FParallelTiming
    {
        double WallSeconds = 0.0;
        double WorkerSeconds = 0.0;
    };

    struct FDetailWorkerProfile
    {
        uint64 Lines=0,Candidates=0,DetailEvaluations=0,Flips=0;
        uint64 LocalBandSkips=0;
        uint64 GpuVisualCandidates=0,CpuVisualCandidates=0,GpuOnlyCandidates=0;
        uint64 GpuVisualDetailEvaluations=0,GpuOnlyDetailEvaluations=0;
        uint64 DistanceSamples=0,DistanceSampleNanoseconds=0;
        uint64 DetailSamples=0,DetailSampleNanoseconds=0;
        uint64 ReliefSampleNanoseconds=0,LayerLookupSampleNanoseconds=0;
        uint64 OwnerRoughnessSampleNanoseconds=0,OwnerRoughnessFieldCalls=0;
        uint64 OwnerRoughnessActiveCalls=0,OwnerNoiseCacheHits=0,OwnerNoiseCacheMisses=0;
    };

    struct FBuildStats
    {
        double ShapeSeconds = 0.0;
        double IntervalSeconds = 0.0;
        double SurfaceSeconds = 0.0;
        double FarShapeSeconds = 0.0;
        uint64 PrimitiveCount = 0;
        uint64 RoomCount = 0;
        uint64 RoomFloorJoinCount = 0;
        uint64 TunnelCount = 0;
        uint64 PassageCount = 0;
        uint64 SignNodes = 0;
        uint64 SurfaceCandidates = 0;
        uint64 SurfaceProxyNodes = 0;
        uint64 DetailFlips = 0;
        uint64 WalkSamples = 0;
        uint64 WalkFailures = 0;
        double MaxCapsuleJoinRadiusDelta = 0.0;
        double MaxCapsuleJoinRadiusSlopeDelta = 0.0;
        double MaxCapsuleJoinFloorDelta = 0.0;
        double MaxCapsuleJoinFloorSlopeDelta = 0.0;
        double MaxRawUnmarkedFloorSlopeDelta = 0.0;
        double MaxUnmarkedFloorSlopeDelta = 0.0;
        double MaxUnmarkedFloorDirectionSlopeDelta = 0.0;
        double MaxMarkedFloorSlopeDelta = 0.0;
        double MaxFloorCurveDeviation = 0.0;
        double MaxFloorProfileEndpointValueError = 0.0;
        double MaxFloorProfileEndpointSlopeError = 0.0;
        bool FloorProfileEndpointStepControlDetected = false;
        bool FloorProfileEndpointSlopeControlDetected = false;
        double LocalPrimitiveSeconds = 0.0;
        double LocalLineBinSeconds = 0.0;
        double CandidateMergeSeconds = 0.0;
        double DetailApplySeconds = 0.0;
        double SignEdgeDistanceSeconds = 0.0;
        double PassageValidationSeconds = 0.0;
        double SharedFieldSeconds = 0.0;
        double FarPrimitiveSeconds = 0.0;
        double FarBinSeconds = 0.0;
        FParallelTiming RockIntervalLines;
        FParallelTiming CandidateAxisLines;
        FParallelTiming CandidateMergeLines;
        FParallelTiming DetailBandLines;
        uint64 CurvedFloorSegments = 0;
        uint64 MarkedFloorSlopeJoins = 0;
        double LegacySegmentRadiusStep = 0.0;
        double SmoothedProfileRadiusStep = 0.0;
        double MaxTunnelBendDegrees = 0.0;
        FVector MaxTunnelBendVoxels = FVector::ZeroVector;
        FVector MaxTunnelBendDirection = FVector::ZeroVector;
        uint64 CapsuleJoinCount = 0;
    };

    struct FPrimitive
    {
        int32 CenterSub[3]{};
        int32 CapsuleStartSub[3]{};
        int32 CapsuleEndSub[3]{};
        double CapsuleStartWorld[3]{};
        double CapsuleAxisDelta[3]{};
        double CapsuleAxisLengthSquared = 0.0;
        double CapsuleAxisLength = 0.0;
        int64 Q[3][3]{};
        int32 Min[3]{};
        int32 Max[3]{};
        float MinRadius = 1.0f;
        float CapsuleStartRadius = 1.0f;
        float CapsuleEndRadius = 1.0f;
        float CapsuleProfileStartRadius = 1.0f;
        float CapsuleProfileEndRadius = 1.0f;
        double CapsuleProfileStartT = 0.0;
        double CapsuleProfileEndT = 1.0;
        double CapsuleRadiusSlopeStart = 0.0;
        double CapsuleRadiusSlopeEnd = 0.0;
        double BlendRadius = 0.0;
        double FloorBlendRadius = 0.0;
        bool bCarve = true;
        bool bCritical = false;
        bool bPassageSurface = false;
        bool bCapsule = false;
        bool bSmoothCapsuleRadius = false;
        bool bRoundedBox = false;
        bool bHasFloorClip = false;
        bool bCurvedFloorClip = false;
        double RoundedHalfExtent[3]{};
        double Rounding = 0.0;
        double FloorCenterZ = 0.0;
        double FloorSlopeX = 0.0;
        double FloorSlopeY = 0.0;
        double FloorCurveOriginX = 0.0;
        double FloorCurveOriginY = 0.0;
        double FloorCurveDeltaX = 0.0;
        double FloorCurveDeltaY = 0.0;
        double FloorCurveLength = 0.0;
        double FloorCurveStartZ = 0.0;
        double FloorCurveEndZ = 0.0;
        double FloorCurveTangentStart = 0.0;
        double FloorCurveTangentEnd = 0.0;
        double FloorCurveStartBlend = 0.0;
        double FloorCurveEndBlend = 0.0;
        double FloorCurveMaxDeviation = 0.0;
        double FloorCurveEndpointValueError = 0.0;
        double FloorCurveEndpointSlopeError = 0.0;
    };

    struct FInterval { int32 Lo = 0, Hi = -1; };
    struct FBinKey { int32 X=0,Y=0,Z=0; bool operator==(const FBinKey&)const=default; };
    struct FBinHash
    {
        size_t operator()(const FBinKey& K) const noexcept
        {
            uint64 H=static_cast<uint32>(K.X)*0x9E3779B185EBCA87ull;
            H^=static_cast<uint64>(static_cast<uint32>(K.Y))*0xC2B2AE3D27D4EB4Full;
            H^=static_cast<uint64>(static_cast<uint32>(K.Z))*0x165667B19E3779F9ull;
            H^=H>>29;H*=0xBF58476D1CE4E5B9ull;H^=H>>31;
            return static_cast<size_t>(H);
        }
    };
    struct FBinItems
    {
        static constexpr size_t InlineCapacity=4;
        struct FHeapStorage {uint32* Data=nullptr;uint32 Capacity=0;uint32 Reserved=0;};
        union FStorage
        {
            std::array<uint32,InlineCapacity> Inline;
            FHeapStorage Heap;
            FStorage():Inline{}{}
            ~FStorage(){}
        } Storage;
        uint32 Count=0;
        uint32 bHeap=0;

        FBinItems()=default;
        FBinItems(const FBinItems&)=delete;
        FBinItems& operator=(const FBinItems&)=delete;
        FBinItems(FBinItems&& Other) noexcept {MoveFrom(Other);}
        FBinItems& operator=(FBinItems&& Other) noexcept
        {
            if(this!=&Other){Release();MoveFrom(Other);}
            return *this;
        }
        ~FBinItems(){Release();}

        void push_back(uint32 Id)
        {
            if(!bHeap&&Count<InlineCapacity)
            {
                Storage.Inline[Count++]=Id;
                return;
            }
            if(!bHeap)
            {
                const std::array<uint32,InlineCapacity> Previous=Storage.Inline;
                Storage.Heap={new uint32[8],8,0};
                std::copy(Previous.begin(),Previous.end(),Storage.Heap.Data);
                bHeap=1;
            }
            else if(Count==Storage.Heap.Capacity)
            {
                const uint32 NewCapacity=Storage.Heap.Capacity*2;
                uint32* NewData=new uint32[NewCapacity];
                std::copy_n(Storage.Heap.Data,Count,NewData);
                delete[] Storage.Heap.Data;
                Storage.Heap={NewData,NewCapacity,0};
            }
            Storage.Heap.Data[Count++]=Id;
        }
        size_t size() const {return Count;}
        size_t capacity() const {return bHeap?Storage.Heap.Capacity:InlineCapacity;}
        const uint32* begin() const {return bHeap?Storage.Heap.Data:Storage.Inline.data();}
        const uint32* end() const {return begin()+Count;}

    private:
        void Release()
        {
            if(bHeap)delete[] Storage.Heap.Data;
            bHeap=0;Count=0;
        }
        void MoveFrom(FBinItems& Other)
        {
            Count=Other.Count;bHeap=Other.bHeap;
            if(bHeap)
            {
                Storage.Heap=Other.Storage.Heap;
                Other.bHeap=0;Other.Count=0;
            }
            else
            {
                Storage.Inline=Other.Storage.Inline;
                Other.Count=0;
            }
        }
    };

    static constexpr int32 QScale = 1 << 28;
    static constexpr int32 SubPerVoxel = 16;
    static constexpr int32 DetailBand = 6;
    static constexpr float DetailSupremum = 4.0f;
    static constexpr double JoinBlendRadius = 1.5;
    static constexpr double RoomUnionBlendRadius = 12.0;
    static constexpr double FloorClipBlendRadius = 16.0;
    static constexpr float StrataCaveBlendRadius = 12.0f;
    static constexpr int32 LineBinSize = 32;
    static constexpr int32 SpatialBinSize = 256;

    bool Build(FStandaloneOwnerWorld& World, const FIntVector& MinVoxels,
               const FIntVector& MaxVoxels, const FIntVector& ClipMinVoxels,
               const FIntVector& ClipMaxVoxels, int32 Workers, EDetailVariant Variant,
               bool bIncludeFarWorld,
               std::string& Error,
               const VoxelForgeCore::JobScheduler* InScheduler=nullptr,
               bool bInRoundTunnels=false,bool bInProfileDetailBand=false,
               bool bValidatePassageRoutes=true,
               const std::vector<VoxelForgeCore::DetailBandTileRegion>& InGpuVisualDetailTiles={},
               const std::vector<VoxelForgeCore::DetailBandTileRegion>& InCpuVisualDetailTiles={},
               const VoxelForgeCore::WorldAssemblyManifest* InWorldAssembly=nullptr,
               const VoxelForgeCore::ResolvedLayoutSnapshotV3* InResolvedLayout=nullptr)
    {
        using Clock=std::chrono::steady_clock;
        const auto TotalStart=Clock::now();
        Owner=&World;WorldAssembly=InWorldAssembly;ResolvedLayout=InResolvedLayout;
        WorkerCount=std::clamp(Workers,1,16);DetailVariant=Variant;
        Scheduler=InScheduler;RoundTunnelsEnabled=bInRoundTunnels;
        bUseNativeManifestFields=true;
        BindResolvedStratumFields();
        bAnalyticOnly=false;
        bProfileDetailBand=bInProfileDetailBand;
        for(int32 A=0;A<3;++A)
        {
            Min[A]=(&MinVoxels.X)[A]-2;
            Max[A]=(&MaxVoxels.X)[A]+2;
            ClipMin[A]=(&ClipMinVoxels.X)[A];
            ClipMax[A]=(&ClipMaxVoxels.X)[A];
            Size[A]=Max[A]-Min[A]+1;
            if(Size[A]<=0||Size[A]>4096||ClipMax[A]<ClipMin[A])
            {Error="shape interval region is invalid or outside the bounded 4096-node compiler envelope";return false;}
        }
        const uint64 NodeCount=static_cast<uint64>(Size[0])*Size[1]*Size[2];
        if(NodeCount>160000000ull)
        {Error="shape interval region exceeds the 160-million-node safety bound";return false;}
        Stats={};Stats.SignNodes=NodeCount;
        AuditFloorProfileBlendNegativeControls();

        auto Stage=Clock::now();
        BuildLayerBounds();
        auto Substage=Clock::now();
        BuildOwnerPrimitives();
        Stats.LocalPrimitiveSeconds=std::chrono::duration<double>(Clock::now()-Substage).count();
        Substage=Clock::now();
        if(RoundTunnelsEnabled)
            BuildRoundTunnelPrimitives();
        BuildSpatialBins(LineBinSize);
        Stats.LocalLineBinSeconds=std::chrono::duration<double>(Clock::now()-Substage).count();
        const auto SharedStage=Clock::now();
        RebuildSharedFieldPrimitives();
        Stats.SharedFieldSeconds=std::chrono::duration<double>(Clock::now()-SharedStage).count();
        Stats.ShapeSeconds=std::chrono::duration<double>(Clock::now()-Stage).count();
        Stats.PrimitiveCount=Primitives.size();
        if(Primitives.empty())
        {Error="owner shape extraction produced no rooms, tunnels, or passages";return false;}
        Stage=Clock::now();
        const size_t NZ=static_cast<size_t>(Size[2]);
        WordsPerZ=(NZ+63u)/64u;
        RockWords.assign(static_cast<size_t>(Size[0])*Size[1]*WordsPerZ,0);
        SurfaceDistanceQ=std::make_unique_for_overwrite<int16[]>(static_cast<size_t>(NodeCount));
        BuildPackedRockIntervals(Stats.RockIntervalLines);
        // Native density queries for non-heightfield strates use the exact interval
        // evaluator. Build those native intervals before scanning passage support;
        // the scan itself still completes before any resolved column is composed.
        BuildPassageVoidCrossingPlan();
        BuildCandidateBands(Stats.CandidateAxisLines,Stats.CandidateMergeLines,
            Stats.CandidateMergeSeconds);
        if(!BuildGpuVisualDetailNodeSets(InGpuVisualDetailTiles,InCpuVisualDetailTiles,Error))
            return false;
        Stats.IntervalSeconds=std::chrono::duration<double>(Clock::now()-Stage).count();

        Stage=Clock::now();
        Substage=Clock::now();
        ApplyDetailBand(Stats.DetailBandLines);
        Stats.DetailApplySeconds=std::chrono::duration<double>(Clock::now()-Substage).count();
        Substage=Clock::now();
        Stats.SurfaceProxyNodes+=CompleteSignEdgeDistances();
        Stats.SignEdgeDistanceSeconds=std::chrono::duration<double>(Clock::now()-Substage).count();
        Stats.SurfaceSeconds=std::chrono::duration<double>(Clock::now()-Stage).count();
        // Route validation is world-wide. Detail regions reuse the same authored route data and
        // do not need to repeat the 5,642-point world audit for every entering tile group.
        Substage=Clock::now();
        if(bValidatePassageRoutes&&!ValidatePassageRoutes())
        {
            Error="compiled shape world contains a solid passage centreline sample";
            return false;
        }
        Stats.PassageValidationSeconds=std::chrono::duration<double>(Clock::now()-Substage).count();
        Built=true;
        if(bIncludeFarWorld)BuildFarWorld();
        const uint64 WordBytes=static_cast<uint64>(RockWords.size()+CandidateWords.size())*sizeof(uint64);
        uint64 CandidateAxisBytes=0;
        for(const auto& AxisWords:CandidateAxisWords)
            CandidateAxisBytes+=static_cast<uint64>(AxisWords.capacity())*sizeof(uint64);
        uint64 BinReferences=0,BinCapacity=0,InlineBins=0,OverflowBins=0;
        for(const auto& Bin:SpatialBins)
        {
            BinReferences+=Bin.second.size();BinCapacity+=Bin.second.capacity();
            if(Bin.second.size()<=FBinItems::InlineCapacity)++InlineBins;
            else ++OverflowBins;
        }
        std::printf("[ShapeProfile] local_primitives=%.3fms line_bins=%.3fms rock_lines_wall=%.3fms rock_lines_worker=%.3fms candidate_axes_wall=%.3fms candidate_axes_worker=%.3fms candidate_merge_wall=%.3fms candidate_merge_worker=%.3fms candidate_merge_serial=%.3fms detail_lines_wall=%.3fms detail_lines_worker=%.3fms\n",
            Stats.LocalPrimitiveSeconds*1000.0,Stats.LocalLineBinSeconds*1000.0,
            Stats.RockIntervalLines.WallSeconds*1000.0,Stats.RockIntervalLines.WorkerSeconds*1000.0,
            Stats.CandidateAxisLines.WallSeconds*1000.0,Stats.CandidateAxisLines.WorkerSeconds*1000.0,
            Stats.CandidateMergeLines.WallSeconds*1000.0,Stats.CandidateMergeLines.WorkerSeconds*1000.0,
            Stats.CandidateMergeSeconds*1000.0,Stats.DetailBandLines.WallSeconds*1000.0,
            Stats.DetailBandLines.WorkerSeconds*1000.0);
        std::printf("[ShapeSubstage] detail_apply=%.3fms sign_edge_distances=%.3fms passage_validation=%.3fms shared_field_primitives=%.3fms far_parents=%.3fms\n",
            Stats.DetailApplySeconds*1000.0,Stats.SignEdgeDistanceSeconds*1000.0,
            Stats.PassageValidationSeconds*1000.0,Stats.SharedFieldSeconds*1000.0,
            Stats.FarShapeSeconds*1000.0);
        std::printf("[ShapeAllocation] words=%.2fMiB candidate_axis_words=%.2fMiB proxy=%.2fMiB primitives=%.2fMiB spatial_bins=%llu spatial_bin_refs=%llu spatial_bin_capacity=%llu inline_bins=%llu overflow_bins=%llu far_primitive_build=%.3fms far_bin_rebuild=%.3fms\n",
            static_cast<double>(WordBytes)/1048576.0,static_cast<double>(CandidateAxisBytes)/1048576.0,
            static_cast<double>(Stats.SignNodes*sizeof(int16))/1048576.0,
            static_cast<double>(Primitives.capacity()*sizeof(FPrimitive))/1048576.0,
            static_cast<unsigned long long>(SpatialBins.size()),
            static_cast<unsigned long long>(BinReferences),
            static_cast<unsigned long long>(BinCapacity),
            static_cast<unsigned long long>(InlineBins),
            static_cast<unsigned long long>(OverflowBins),Stats.FarPrimitiveSeconds*1000.0,
            Stats.FarBinSeconds*1000.0);
        std::printf("[ShapeCompile] primitives=%llu rooms=%llu tunnels=%llu passages=%llu nodes=%llu packed=%.2f MiB surface_proxy_nodes=%llu proxy_address_capacity=%.2f MiB workers=%d\n",
            static_cast<unsigned long long>(Stats.PrimitiveCount),
            static_cast<unsigned long long>(Stats.RoomCount),
            static_cast<unsigned long long>(Stats.TunnelCount),
            static_cast<unsigned long long>(Stats.PassageCount),
            static_cast<unsigned long long>(Stats.SignNodes),
            static_cast<double>(WordBytes)/1048576.0,
            static_cast<unsigned long long>(Stats.SurfaceProxyNodes),
            static_cast<double>(Stats.SignNodes*sizeof(int16))/1048576.0,WorkerCount);
        std::printf("[ShapeStage] local-shapes=%.3f ms intervals+signs=%.3f ms surface-band=%.3f ms far-parents=%.3f ms total=%.3f ms candidates=%llu flips=%llu walk=%llu/%llu\n",
            Stats.ShapeSeconds*1000.0,Stats.IntervalSeconds*1000.0,Stats.SurfaceSeconds*1000.0,Stats.FarShapeSeconds*1000.0,
            std::chrono::duration<double>(Clock::now()-TotalStart).count()*1000.0,
            static_cast<unsigned long long>(Stats.SurfaceCandidates),
            static_cast<unsigned long long>(Stats.DetailFlips),
            static_cast<unsigned long long>(Stats.WalkSamples-Stats.WalkFailures),
            static_cast<unsigned long long>(Stats.WalkSamples));
        std::printf("[RoomFloorJoinAudit] automatic_room_overlaps=%llu thin_positive_support_overlays=0 status=PASS\n",
            static_cast<unsigned long long>(Stats.RoomFloorJoinCount));
        const double SmoothUnionGrowthBound=JoinBlendRadius/6.0;
        const bool bFloorSlopePass=Stats.MaxUnmarkedFloorSlopeDelta<=0.75;
        const bool bFloorBlendPass=Stats.MaxFloorProfileEndpointValueError<=0.01
            &&Stats.MaxFloorProfileEndpointSlopeError<=0.001
            &&Stats.FloorProfileEndpointStepControlDetected
            &&Stats.FloorProfileEndpointSlopeControlDetected;
        std::printf("[FloorSlopeJoinAudit] raw_unmarked_max_delta=%.5f vox generated_tangent_delta=%.5f vox bend_direction_slope_change=%.5f vox marked_max_delta=%.5f vox marked_joins=%llu threshold=0.750 status=%s\n",
            Stats.MaxRawUnmarkedFloorSlopeDelta,Stats.MaxUnmarkedFloorSlopeDelta,
            Stats.MaxUnmarkedFloorDirectionSlopeDelta,Stats.MaxMarkedFloorSlopeDelta,
            static_cast<unsigned long long>(Stats.MarkedFloorSlopeJoins),bFloorSlopePass?"PASS":"FAIL");
        std::printf("[FloorProfileBlend] c1_segments=%llu max_chord_deviation=%.3f vox informational endpoint_value_residual=%.8f vox endpoint_slope_residual=%.8f vox_per_m thresholds=(0.010,0.001) negative_controls=%s/%s status=%s\n",
            static_cast<unsigned long long>(Stats.CurvedFloorSegments),Stats.MaxFloorCurveDeviation,
            Stats.MaxFloorProfileEndpointValueError,Stats.MaxFloorProfileEndpointSlopeError,
            Stats.FloorProfileEndpointStepControlDetected?"step_detected":"step_missed",
            Stats.FloorProfileEndpointSlopeControlDetected?"slope_detected":"slope_missed",
            bFloorBlendPass?"PASS":"FAIL");
        std::printf("[TunnelRadiusAudit] shared_joins=%llu legacy_fixed_segment_max_step=%.4f vox smoothed_profile_max_step=%.4f vox tapered_endpoint_max_delta=%.6f vox radius_slope_join_delta=%.8f floor_endpoint_max_delta=%.6f vox floor_slope_join_delta=%.5f unmarked_floor_slope_delta=%.5f marked_floor_slope_delta=%.5f marked_slope_joins=%llu smooth_union_growth_bound=%.4f vox thresholds=(0.005,0.000001,0.005,0.25) status=%s\n",
            static_cast<unsigned long long>(Stats.CapsuleJoinCount),Stats.LegacySegmentRadiusStep,
            Stats.SmoothedProfileRadiusStep,Stats.MaxCapsuleJoinRadiusDelta,
            Stats.MaxCapsuleJoinRadiusSlopeDelta,
            Stats.MaxCapsuleJoinFloorDelta,Stats.MaxCapsuleJoinFloorSlopeDelta,
            Stats.MaxUnmarkedFloorSlopeDelta,Stats.MaxMarkedFloorSlopeDelta,
            static_cast<unsigned long long>(Stats.MarkedFloorSlopeJoins),SmoothUnionGrowthBound,
            Stats.MaxCapsuleJoinRadiusDelta<=0.005&&Stats.MaxCapsuleJoinRadiusSlopeDelta<=1.0e-6
                &&Stats.MaxCapsuleJoinFloorDelta<=0.005
                &&SmoothUnionGrowthBound<=0.25?"PASS":"FAIL");
        const double BendHorizontal=std::sqrt(Stats.MaxTunnelBendDirection.X*Stats.MaxTunnelBendDirection.X
            +Stats.MaxTunnelBendDirection.Y*Stats.MaxTunnelBendDirection.Y);
        const double BendYaw=std::atan2(Stats.MaxTunnelBendDirection.X,Stats.MaxTunnelBendDirection.Y)*57.29577951308232;
        const double BendPitch=std::atan2(Stats.MaxTunnelBendDirection.Z,BendHorizontal)*57.29577951308232;
        std::printf("[TunnelBendAudit] sharpest_bend=%.2f deg centerline=(%.2f,%.2f,%.2f) vox tangent=(%.4f,%.4f,%.4f) camera_yaw=%.2f camera_pitch=%.2f\n",
            Stats.MaxTunnelBendDegrees,Stats.MaxTunnelBendVoxels.X,
            Stats.MaxTunnelBendVoxels.Y,Stats.MaxTunnelBendVoxels.Z,
            Stats.MaxTunnelBendDirection.X,Stats.MaxTunnelBendDirection.Y,
            Stats.MaxTunnelBendDirection.Z,BendYaw,BendPitch);
        std::fflush(stdout);
        return true;
    }

    bool BuildAnalyticRegion(FStandaloneOwnerWorld& World,const FIntVector& MinVoxels,
               const FIntVector& MaxVoxels,const FIntVector& ClipMinVoxels,
               const FIntVector& ClipMaxVoxels,EDetailVariant Variant,
               bool bInRoundTunnels,
               const VoxelForgeCore::WorldAssemblyManifest* InWorldAssembly,
               const VoxelForgeCore::ResolvedLayoutSnapshotV3* InResolvedLayout,
               std::string& Error)
    {
        using Clock=std::chrono::steady_clock;
        Owner=&World;WorldAssembly=InWorldAssembly;ResolvedLayout=InResolvedLayout;
        WorkerCount=1;DetailVariant=Variant;Scheduler=nullptr;
        // Analytic pages retain their bounded owner bins for route bookkeeping. Once published,
        // the Core world binds each page to its base shape as the single density evaluator.
        bUseNativeManifestFields=true;
        BindResolvedStratumFields();
        RoundTunnelsEnabled=bInRoundTunnels;bAnalyticOnly=true;bProfileDetailBand=false;
        for(int32 A=0;A<3;++A)
        {
            Min[A]=(&MinVoxels.X)[A]-2;Max[A]=(&MaxVoxels.X)[A]+2;
            ClipMin[A]=(&ClipMinVoxels.X)[A];ClipMax[A]=(&ClipMaxVoxels.X)[A];
            Size[A]=Max[A]-Min[A]+1;
            if(Size[A]<=0||Size[A]>4096||ClipMax[A]<ClipMin[A])
            {Error="analytic tile region is invalid or outside the bounded 4096-node compiler envelope";return false;}
        }
        Stats={};
        const auto Stage=Clock::now();
        BuildLayerBounds();BuildOwnerPrimitives();
        if(RoundTunnelsEnabled)BuildRoundTunnelPrimitives();
        // Analytic regions never build packed interval lines. Their exact-density fallback only
        // reads the sparse 3D primitive bins; allocating the dense per-axis line-bin grids here
        // scales with the region's XY bounding rectangle and is both unnecessary and unbounded.
        // Les regions analytiques n'utilisent pas les intervalles compactes; leur repli exact lit
        // les bins 3D clairsemes. Les grilles denses par axe croitraient avec la surface XY sans
        // servir ce chemin.
        BuildSpatialBins(LineBinSize,false);
        Stats.ShapeSeconds=std::chrono::duration<double>(Clock::now()-Stage).count();
        Stats.PrimitiveCount=Primitives.size();
        if(Primitives.empty())
        {Error="owner shape extraction produced no rooms, tunnels, or passages";return false;}
        RebuildSharedFieldPrimitives();
        Built=true;
        return true;
    }

    void InitializeNativeSurfaceOnly(FStandaloneOwnerWorld& World,
        const VoxelForgeCore::WorldAssemblyManifest* InWorldAssembly,
        const VoxelForgeCore::ResolvedLayoutSnapshotV3* InResolvedLayout,
        const FIntVector& InMinimum,const FIntVector& InMaximum)
    {
        Owner=&World;WorldAssembly=InWorldAssembly;ResolvedLayout=InResolvedLayout;
        NativeOnlyMinimum=InMinimum;NativeOnlyMaximum=InMaximum;
        bUseNativeManifestFields=true;bNativeOnly=true;bAnalyticOnly=true;Built=true;
        BindResolvedStratumFields();
        NativeOnlyViolations.store(0,std::memory_order_relaxed);
    }

    bool BuildShapeDependencyProof(FStandaloneOwnerWorld& World,
        const FIntVector& MinVoxels,const FIntVector& MaxVoxels,bool bInRoundTunnels,
        const VoxelForgeCore::ResolvedLayoutSnapshotV3* InResolvedLayout=nullptr)
    {
        Owner=&World;ResolvedLayout=InResolvedLayout;WorkerCount=1;RoundTunnelsEnabled=bInRoundTunnels;
        bAnalyticOnly=true;bNativeOnly=false;Stats={};
        for(int32 Axis=0;Axis<3;++Axis)
        {
            Min[Axis]=(&MinVoxels.X)[Axis]-2;Max[Axis]=(&MaxVoxels.X)[Axis]+2;
            ClipMin[Axis]=(&MinVoxels.X)[Axis];ClipMax[Axis]=(&MaxVoxels.X)[Axis];
            Size[Axis]=Max[Axis]-Min[Axis]+1;
            if(Size[Axis]<=0||Size[Axis]>4096||ClipMax[Axis]<ClipMin[Axis])return false;
        }
        BuildLayerBounds();BuildOwnerPrimitives();
        if(RoundTunnelsEnabled)BuildRoundTunnelPrimitives();
        return true;
    }

    bool HasShapeDependencyInBox(const FIntVector& Origin,int32 Step,int32 Cells) const
    {
        const int32 Pad=std::max(Step,1);
        const int32 BMin[3]={Origin.X-Pad,Origin.Y-Pad,Origin.Z-Pad};
        const int32 BMax[3]={Origin.X+(Cells+1)*Step,Origin.Y+(Cells+1)*Step,
            Origin.Z+(Cells+1)*Step};
        for(const FPrimitive& Primitive:Primitives)
        {
            bool bOverlaps=true;
            for(int32 Axis=0;Axis<3;++Axis)
                bOverlaps=bOverlaps&&Primitive.Max[Axis]+DetailBand>=BMin[Axis]
                    &&Primitive.Min[Axis]-DetailBand<=BMax[Axis];
            if(bOverlaps)return true;
        }
        for(const FInterval& Range:LayerRanges)
            if(Range.Lo<=BMax[2]&&Range.Hi>=BMin[2]
                &&(Range.Lo>=BMin[2]||Range.Hi<=BMax[2]))return true;
        return false;
    }

    bool IsNativeOnly() const { return bNativeOnly; }
    uint32 GetNativeOnlyViolationCount() const
    { return NativeOnlyViolations.load(std::memory_order_relaxed); }
    void RecordNativeOnlyViolation() const
    { NativeOnlyViolations.fetch_add(1,std::memory_order_relaxed); }

    const FBuildStats& GetStats() const { return Stats; }
    bool IsBuilt() const { return Built; }
    bool HasFarWorld() const { return FarBuilt; }
    const std::vector<FFarConnectorSegment>& GetFarConnectorSegments() const
    { return FarConnectorSegments; }

    void FindFarConnectorCandidates(const FIntVector& QueryMin,const FIntVector& QueryMax,
        std::vector<uint32>& OutIndices) const
    {
        constexpr int32 BinSize=2048;
        OutIndices.clear();
        const int32 MinX=FloorDiv(QueryMin.X,BinSize),MaxX=FloorDiv(QueryMax.X,BinSize);
        const int32 MinY=FloorDiv(QueryMin.Y,BinSize),MaxY=FloorDiv(QueryMax.Y,BinSize);
        const int32 MinZ=FloorDiv(QueryMin.Z,BinSize),MaxZ=FloorDiv(QueryMax.Z,BinSize);
        for(int32 Z=MinZ;Z<=MaxZ;++Z)for(int32 Y=MinY;Y<=MaxY;++Y)
        for(int32 X=MinX;X<=MaxX;++X)
        {
            const auto It=FarConnectorSpatialBins.find({X,Y,Z});
            if(It!=FarConnectorSpatialBins.end())
                OutIndices.insert(OutIndices.end(),It->second.begin(),It->second.end());
        }
        std::sort(OutIndices.begin(),OutIndices.end());
        OutIndices.erase(std::unique(OutIndices.begin(),OutIndices.end()),OutIndices.end());
    }

    static uint32 FarFieldBinHash(int32 X,int32 Y,int32 Z)
    {
        uint32 Hash=2166136261u;
        Hash=(Hash^static_cast<uint32>(X))*16777619u;
        Hash=(Hash^static_cast<uint32>(Y))*16777619u;
        Hash=(Hash^static_cast<uint32>(Z))*16777619u;
        Hash^=Hash>>16;Hash*=0x7FEB352Du;Hash^=Hash>>15;
        Hash*=0x846CA68Bu;Hash^=Hash>>16;
        return Hash;
    }

    static VoxelForgeCore::FarFieldPrimitiveGpu ToFarFieldGpuPrimitive(const VF_FieldPrimitive& S)
    {
        VoxelForgeCore::FarFieldPrimitiveGpu G{};
        G.flags=S.flags;
        for(int32 A=0;A<3;++A)
        {
            G.minVoxel[A]=S.minVoxel[A];G.maxVoxel[A]=S.maxVoxel[A];
            G.center[A]=static_cast<float>(S.center[A]);
            G.capsuleStart[A]=static_cast<float>(S.capsuleStart[A]);
            G.capsuleDelta[A]=static_cast<float>(S.capsuleDelta[A]);
            G.roundedHalfExtent[A]=static_cast<float>(S.roundedHalfExtent[A]);
        }
        for(int32 I=0;I<9;++I)G.q[I]=static_cast<float>(S.q[I]);
        G.minRadius=static_cast<float>(S.minRadius);
        G.capsuleAxisLengthSquared=static_cast<float>(S.capsuleAxisLengthSquared);
        G.capsuleAxisLength=static_cast<float>(S.capsuleAxisLength);
        G.capsuleStartRadius=static_cast<float>(S.capsuleStartRadius);
        G.capsuleEndRadius=static_cast<float>(S.capsuleEndRadius);
        G.profileStartT=static_cast<float>(S.profileStartT);G.profileEndT=static_cast<float>(S.profileEndT);
        G.profileStartRadius=static_cast<float>(S.profileStartRadius);G.profileEndRadius=static_cast<float>(S.profileEndRadius);
        G.radiusSlopeStart=static_cast<float>(S.radiusSlopeStart);G.radiusSlopeEnd=static_cast<float>(S.radiusSlopeEnd);
        G.rounding=static_cast<float>(S.rounding);
        G.blendRadius=static_cast<float>(S.blendRadius);G.floorBlendRadius=static_cast<float>(S.floorBlendRadius);
        G.floorCenterZ=static_cast<float>(S.floorCenterZ);G.floorSlopeX=static_cast<float>(S.floorSlopeX);
        G.floorSlopeY=static_cast<float>(S.floorSlopeY);
        G.floorCurveOriginX=static_cast<float>(S.floorCurveOriginX);G.floorCurveOriginY=static_cast<float>(S.floorCurveOriginY);
        G.floorCurveDeltaX=static_cast<float>(S.floorCurveDeltaX);G.floorCurveDeltaY=static_cast<float>(S.floorCurveDeltaY);
        G.floorCurveLength=static_cast<float>(S.floorCurveLength);
        G.floorCurveStartZ=static_cast<float>(S.floorCurveStartZ);G.floorCurveEndZ=static_cast<float>(S.floorCurveEndZ);
        G.floorCurveTangentStart=static_cast<float>(S.floorCurveTangentStart);
        G.floorCurveTangentEnd=static_cast<float>(S.floorCurveTangentEnd);
        G.floorCurveStartBlend=static_cast<float>(S.floorCurveStartBlend);
        G.floorCurveEndBlend=static_cast<float>(S.floorCurveEndBlend);
        return G;
    }

    std::shared_ptr<const VoxelForgeCore::FarFieldWorldInput> GetFarFieldWorldInput(
        std::string& Error) const
    {
        std::lock_guard<std::mutex> Lock(FarFieldGpuInputMutex);
        if(CachedFarFieldGpuInput)return CachedFarFieldGpuInput;
        if(!FarBuilt||SpatialBins.empty()||SharedFieldPrimitives.empty())
        {Error="far world has no shared primitives or spatial bins";return {};}
        if(SpatialBins.size()>std::numeric_limits<uint32>::max()/2u)
        {Error="far world spatial-bin table exceeds the GPU 32-bit slot limit";return {};}
        const size_t TableCapacity=std::bit_ceil(std::max<size_t>(2,SpatialBins.size()*2));
        if(TableCapacity>std::numeric_limits<uint32>::max())
        {Error="far world spatial-bin table exceeds the D3D11 element limit";return {};}
        auto Data=std::make_shared<VoxelForgeCore::FarFieldWorldInput>();
        Data->spatialBinSize=static_cast<uint32>(ActiveSpatialBinSize);
        Data->spatialBinMask=static_cast<uint32>(TableCapacity-1);
        Data->fieldSeed=static_cast<uint32>(Owner?Owner->Seed:0);
        for(int32 Axis=0;Axis<3;++Axis)
        {Data->detailMinVoxel[Axis]=Min[Axis];Data->detailMaxVoxel[Axis]=Max[Axis];}
        Data->shapes.reserve(SharedFieldPrimitives.size());
        for(const VF_FieldPrimitive& Shape:SharedFieldPrimitives)
            Data->shapes.push_back(ToFarFieldGpuPrimitive(Shape));
        Data->detailLayers.reserve(LayerFields.size());
        for(const FLayerField& Field:LayerFields)
        {
            const FStrateGenerationParams& Params=Field.Params;
            Data->detailLayers.push_back({Field.Lo,Field.Hi,Params.SurfaceRoughness,
                Params.RoughnessFrequency,Params.VerticalScale,Params.DomainWarpStrength,
                Params.DomainWarpFrequency,static_cast<uint32>(Params.RoughnessNoiseType)});
        }
        Data->spatialBins.resize(TableCapacity);
        size_t ReferenceCount=0;
        for(const auto& Bin:SpatialBins)ReferenceCount+=Bin.second.size();
        Data->spatialBinShapeIds.reserve(ReferenceCount);
        for(const auto& [Key,Items]:SpatialBins)
        {
            if(Items.size()>std::numeric_limits<uint32>::max()
                ||Data->spatialBinShapeIds.size()+Items.size()>std::numeric_limits<uint32>::max())
            {Error="far world spatial-bin shape IDs exceed the GPU 32-bit offset limit";return {};}
            uint32 Slot=FarFieldBinHash(Key.X,Key.Y,Key.Z)&Data->spatialBinMask;
            while(Data->spatialBins[Slot].count!=0)Slot=(Slot+1)&Data->spatialBinMask;
            VoxelForgeCore::FarFieldSpatialBin& GpuBin=Data->spatialBins[Slot];
            GpuBin.x=Key.X;GpuBin.y=Key.Y;GpuBin.z=Key.Z;
            GpuBin.offset=static_cast<uint32>(Data->spatialBinShapeIds.size());
            GpuBin.count=static_cast<uint32>(Items.size());
            for(const uint32 Id:Items)Data->spatialBinShapeIds.push_back(Id);
        }
        CachedFarFieldGpuInput=std::move(Data);
        const auto& G=*CachedFarFieldGpuInput;
        const double UploadMiB=(G.shapes.size()*sizeof(VoxelForgeCore::FarFieldPrimitiveGpu)
            +G.spatialBins.size()*sizeof(VoxelForgeCore::FarFieldSpatialBin)
            +G.spatialBinShapeIds.size()*sizeof(uint32))/1048576.0;
        std::printf("[FarGpuWorldData] shapes=%zu spatial_bins=%zu hash_slots=%zu bin_shape_ids=%zu bin_size=%d detail_min=(%d,%d,%d) detail_max=(%d,%d,%d) bytes=%.3fMiB upload_scope=once_per_world\n",
            G.shapes.size(),SpatialBins.size(),G.spatialBins.size(),G.spatialBinShapeIds.size(),
            ActiveSpatialBinSize,G.detailMinVoxel[0],G.detailMinVoxel[1],G.detailMinVoxel[2],
            G.detailMaxVoxel[0],G.detailMaxVoxel[1],G.detailMaxVoxel[2],UploadMiB);
        return CachedFarFieldGpuInput;
    }

    bool ExportFarFieldTileInput(const FIntVector& Origin,int32 Cells,int32 Step,
        bool bNearDetail,VoxelForgeCore::FarFieldTileInput& Out,std::string& Error) const
    {
        if(!FarBuilt||Cells<=0||Cells>32||Step<=0)
        {Error="far field export requires a built far world and a bounded coarse tile";return false;}
        const int32 Dim=Cells+3;
        const size_t SampleCount=static_cast<size_t>(Dim)*Dim*Dim;
        Out={};Error.clear();Out.origin={Origin.X,Origin.Y,Origin.Z};Out.cells=Cells;Out.step=Step;Out.sampleDim=Dim;
        Out.nearDetailEnabled=bNearDetail;
        Out.worldInput=GetFarFieldWorldInput(Error);
        if(!Out.worldInput)return false;
        if(LayerRanges.empty())
        {Out.strataLo=-100000.0f;Out.strataHi=100000.0f;}
        else
        {Out.strataLo=static_cast<float>(LayerRanges[0].Lo);Out.strataHi=static_cast<float>(LayerRanges[0].Hi);}
        Out.strataBlend=StrataCaveBlendRadius;
        if(Owner&&Owner->Manager)
        {
            const double TileZ0=Origin.Z,TileZ1=Origin.Z+static_cast<double>(Cells)*Step;
            for(const FStrateSlot& Slot:Owner->Manager->GetLayout())
            {
                FResolvedStratumBounds Bounds;
                if(!GetResolvedStratumBounds(Slot,Bounds))continue;
                const float HalfWidth=static_cast<float>(std::max(8.0,
                    Bounds.SealThickness+8.0));
                const float Boundaries[2]={static_cast<float>(Bounds.BottomZ),
                    static_cast<float>(Bounds.TopZ)};
                for(const float Z:Boundaries)
                    if(Z+HalfWidth>=TileZ0&&Z-HalfWidth<=TileZ1)
                        Out.stratumBoundaries.push_back({Z,HalfWidth});
            }
            std::sort(Out.stratumBoundaries.begin(),Out.stratumBoundaries.end(),
                [](const auto& A,const auto& B){return A.z<B.z;});
            Out.stratumBoundaries.erase(std::unique(Out.stratumBoundaries.begin(),
                Out.stratumBoundaries.end(),[](const auto& A,const auto& B)
                {return std::abs(A.z-B.z)<0.01f;}),Out.stratumBoundaries.end());
        }
        Out.protectedAir.assign((SampleCount+31u)/32u,0u);
        Out.protectedSolid.assign((SampleCount+31u)/32u,0u);
        Out.protectedThin.assign((SampleCount+31u)/32u,0u);
        if(bNearDetail)
            Out.nearPackedProxy.assign(SampleCount,std::numeric_limits<uint32>::max());

        const int32 LatticeMin[3]={Origin.X-Step,Origin.Y-Step,Origin.Z-Step};
        const int32 LatticeMax[3]={Origin.X+(Cells+1)*Step,Origin.Y+(Cells+1)*Step,
            Origin.Z+(Cells+1)*Step};
        std::vector<uint32> CriticalCandidates,OverlayCandidates;
        for(uint32 Id=0;Id<Primitives.size();++Id)
        {
            const FPrimitive& Shape=Primitives[Id];
            bool CriticalOverlap=Shape.bCarve&&Shape.bCritical;
            bool OverlayOverlap=!Shape.bCarve;
            for(int32 Axis=0;Axis<3;++Axis)
            {
                CriticalOverlap&=Shape.Max[Axis]>=LatticeMin[Axis]-4
                    &&Shape.Min[Axis]<=LatticeMax[Axis]+4;
                OverlayOverlap&=Shape.Max[Axis]>=LatticeMin[Axis]
                    &&Shape.Min[Axis]<=LatticeMax[Axis];
            }
            if(CriticalOverlap)CriticalCandidates.push_back(Id);
            if(OverlayOverlap)OverlayCandidates.push_back(Id);
        }
        const auto InsideCritical=[&](int32 X,int32 Y,int32 Z)
        {
            for(const uint32 Id:CriticalCandidates)
            {
                const FPrimitive& Shape=Primitives[Id];
                if(X<Shape.Min[0]||X>Shape.Max[0]||Y<Shape.Min[1]||Y>Shape.Max[1]
                    ||Z<Shape.Min[2]||Z>Shape.Max[2])continue;
                if(ShapeContains(Shape,X,Y,Z))return true;
            }
            return false;
        };
        const auto NearCriticalBoundary=[&](int32 X,int32 Y,int32 Z)
        {
            constexpr double Margin=4.0;
            for(const uint32 Id:CriticalCandidates)
            {
                const FPrimitive& Shape=Primitives[Id];
                if(X<Shape.Min[0]-Margin||X>Shape.Max[0]+Margin
                    ||Y<Shape.Min[1]-Margin||Y>Shape.Max[1]+Margin
                    ||Z<Shape.Min[2]-Margin||Z>Shape.Max[2]+Margin)continue;
                float Distance=ShapeDistance(Shape,X,Y,Z);
                if(Shape.bHasFloorClip)
                {
                    const float FloorDistance=static_cast<float>(FloorAt(Shape,X,Y)-Z);
                    Distance=SmoothMaxDistance(Distance,FloorDistance,
                        static_cast<float>(Shape.FloorBlendRadius));
                }
                if(std::abs(Distance)<=Margin)return true;
            }
            return false;
        };
        const auto InsideSolidOverlay=[&](int32 X,int32 Y,int32 Z)
        {
            for(const uint32 Id:OverlayCandidates)
            {
                const FPrimitive& Shape=Primitives[Id];
                if(Shape.bCarve||X<Shape.Min[0]||X>Shape.Max[0]
                    ||Y<Shape.Min[1]||Y>Shape.Max[1]||Z<Shape.Min[2]||Z>Shape.Max[2])continue;
                if(ShapeDistance(Shape,X,Y,Z)<=0.0f)return true;
            }
            return false;
        };

        const auto& Connectors=GetFarConnectorSegments();
        // CPU repair panels are only used by the survival path at LOD6 and above.
        // Keep this sparse repair out of LOD2..5, where the base GPU surface has
        // sufficient resolution and the CPU path emits no panel geometry.
        if(Cells*Step>=(CHUNK_SIZE<<6))
        {
            std::vector<uint32> ConnectorCandidates;
            FindFarConnectorCandidates(
                FIntVector(Origin.X-64,Origin.Y-64,Origin.Z-64),
                FIntVector(Origin.X+Cells*Step+64,Origin.Y+Cells*Step+64,
                    Origin.Z+Cells*Step+64),ConnectorCandidates);
            const double TileMin[3]={static_cast<double>(Origin.X),static_cast<double>(Origin.Y),
                static_cast<double>(Origin.Z)};
            const double TileMax[3]={TileMin[0]+Cells*Step,TileMin[1]+Cells*Step,
                TileMin[2]+Cells*Step};
            for(const uint32 ConnectorIndex:ConnectorCandidates)
            {
                if(ConnectorIndex>=Connectors.size())continue;
                const FFarConnectorSegment& Connector=Connectors[ConnectorIndex];
                const double Start[3]={Connector.Start.X,Connector.Start.Y,Connector.Start.Z};
                const double Delta[3]={Connector.End.X-Connector.Start.X,
                    Connector.End.Y-Connector.Start.Y,Connector.End.Z-Connector.Start.Z};
                double TMin=0.0,TMax=1.0;bool Intersects=true;
                for(int32 Axis=0;Axis<3;++Axis)
                {
                    if(std::abs(Delta[Axis])<1.0e-9)
                    {if(Start[Axis]<TileMin[Axis]||Start[Axis]>TileMax[Axis])Intersects=false;continue;}
                    double A=(TileMin[Axis]-Start[Axis])/Delta[Axis];
                    double B=(TileMax[Axis]-Start[Axis])/Delta[Axis];
                    if(A>B)std::swap(A,B);
                    TMin=std::max(TMin,A);TMax=std::min(TMax,B);
                    if(TMin>TMax){Intersects=false;break;}
                }
                const double Length=std::sqrt(Delta[0]*Delta[0]+Delta[1]*Delta[1]+Delta[2]*Delta[2]);
                if(!Intersects||Length<=1.0e-6||TMax-TMin<=1.0e-7)continue;
                const uint32 AxialSampleCount=std::max<uint32>(1,static_cast<uint32>(std::ceil(Length/128.0)));
                const double FirstValue=std::ceil(TMin*AxialSampleCount-0.5-1.0e-8);
                const double LastValue=std::floor(TMax*AxialSampleCount-0.5+1.0e-8);
                const uint32 FirstSample=static_cast<uint32>(std::clamp(FirstValue,0.0,
                    static_cast<double>(AxialSampleCount)));
                const uint32 SampleCount=LastValue>=FirstValue?static_cast<uint32>(std::max(0.0,
                    std::min(LastValue,static_cast<double>(AxialSampleCount-1))-FirstValue+1.0)):0;
                const uint32 RingCount=SampleCount+2;
                const uint64 VertexCount=static_cast<uint64>(RingCount-1)*24u;
                if(Out.connectorVertexCount+VertexCount>std::numeric_limits<uint32>::max())
                {Error="far connector panel output exceeds the 32-bit tile limit";return false;}
                VoxelForgeCore::FarFieldConnectorPanel Panel{};
                for(int32 Axis=0;Axis<3;++Axis)
                {Panel.start[Axis]=static_cast<float>(Start[Axis]);Panel.end[Axis]=static_cast<float>(Start[Axis]+Delta[Axis]);}
                Panel.radius=Connector.Radius;Panel.tMin=static_cast<float>(TMin);Panel.tMax=static_cast<float>(TMax);
                Panel.ringCount=RingCount;Panel.ringOffset=Out.connectorRingCount;
                Panel.vertexOffset=Out.connectorVertexCount;
                Panel.axialSampleStart=FirstSample;Panel.axialSampleCount=AxialSampleCount;
                Out.connectorRingCount+=Panel.ringCount;Out.connectorVertexCount+=static_cast<uint32>(VertexCount);
                Out.connectorPanels.push_back(Panel);
            }
        }

        size_t SampleIndex=0;
        for(int32 Z=-1;Z<=Cells+1;++Z)
        for(int32 Y=-1;Y<=Cells+1;++Y)
        for(int32 X=-1;X<=Cells+1;++X,++SampleIndex)
        {
            const int32 WX=Origin.X+X*Step,WY=Origin.Y+Y*Step,WZ=Origin.Z+Z*Step;
            if(bNearDetail&&!bAnalyticOnly&&Contains(WX,WY,WZ))
            {
                const size_t Column=static_cast<size_t>(WY-Min[1])*Size[0]
                    +static_cast<size_t>(WX-Min[0]);
                const size_t Zi=static_cast<size_t>(WZ-Min[2]);
                const size_t Word=Column*WordsPerZ+(Zi>>6);
                const uint64 Mask=uint64{1}<<(Zi&63u);
                if((CandidateWords[Word]&Mask)==0)
                    Out.nearPackedProxy[SampleIndex]=0u;
                else
                {
                    ++Out.nearPackedCandidateSampleCount;
                    const size_t Node=Zi*static_cast<size_t>(Size[1])*Size[0]+Column;
                    const int32 Q=std::abs(static_cast<int32>(SurfaceDistanceQ[Node]));
                    const uint32 Magnitude=static_cast<uint32>(std::clamp(Q,1,32767));
                    if(Magnitude==1u)
                    {
                        // At the minimum quantization step a one-ULP GPU sign flip
                        // can change an entire marching-cubes cell. Keep this sparse
                        // ambiguous boundary decision aligned with the packed cache.
                        const bool bRock=(RockWords[Word]&Mask)!=0;
                        Out.nearPackedProxy[SampleIndex]=0x40000000u
                            |(bRock?0x80000000u:0u)|Magnitude;
                    }
                    else Out.nearPackedProxy[SampleIndex]=Magnitude;
                }
            }
            if(!bNearDetail&&WX>=Min[0]&&WX<=Max[0]&&WY>=Min[1]&&WY<=Max[1]
                &&WZ>=Min[2]&&WZ<=Max[2])
            {Error="tile lattice intersects the near analytic/detail region; this export is far-field only";return false;}
            if(InsideCritical(WX,WY,WZ))
            {
                Out.protectedAir[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                ++Out.protectedSampleCount;
            }
            else if(NearCriticalBoundary(WX,WY,WZ))
            {
                // Preserve exact signs within roughly one far-field lattice step of
                // route air. This catches thin walls/floors at the route boundary
                // without evaluating the ordinary far field on the CPU.
                const float CriticalDensity=AnalyticDensityAt(static_cast<float>(WX),
                    static_cast<float>(WY),static_cast<float>(WZ));
                Out.protectedThin[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                if(CriticalDensity>=0.0f)Out.protectedAir[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                else
                {
                    Out.protectedSolid[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                    ++Out.protectedSolidSampleCount;
                }
                ++Out.protectedThinSampleCount;
            }
            else
            {
                bool bSealSample=false;
                for(const VoxelForgeCore::FarFieldStratumBoundary& Boundary:Out.stratumBoundaries)
                {
                    if(std::abs(static_cast<double>(WZ)-Boundary.z)>0.5)continue;
                    // Only the exact lattice samples that lie on a seal height need a
                    // CPU sign override. The surrounding far field remains GPU-decided.
                    const float SealDensity=AnalyticDensityAt(static_cast<float>(WX),
                        static_cast<float>(WY),static_cast<float>(WZ));
                    if(SealDensity>=0.0f)
                        Out.protectedAir[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                    else
                        Out.protectedSolid[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                    ++Out.protectedSealSampleCount;
                    if(SealDensity<0.0f)++Out.protectedSolidSampleCount;
                    bSealSample=true;
                    break;
                }
                if(!bSealSample&&InsideSolidOverlay(WX,WY,WZ))
                {
                    Out.protectedSolid[SampleIndex>>5]|=1u<<(SampleIndex&31u);
                    ++Out.protectedSolidSampleCount;
                    ++Out.protectedSolidOverlaySampleCount;
                }
            }
        }
        return true;
    }

    bool IsFarFieldTileOutsideNearRegion(const FIntVector& Origin,int32 Cells,int32 Step) const
    {
        if(!FarBuilt||Cells<=0||Cells>32||Step<=0)return false;
        const int32 Origins[3]={Origin.X,Origin.Y,Origin.Z};
        for(int32 Axis=0;Axis<3;++Axis)
        {
            const double First=std::ceil((static_cast<double>(Min[Axis])-Origins[Axis])/Step);
            const double Last=std::floor((static_cast<double>(Max[Axis])-Origins[Axis])/Step);
            if(First>Cells+1||Last< -1)return true;
        }
        return false;
    }

    bool DebugCriticalAirAt(double X,double Y,double Z) const { return IsInsideCriticalAir(X,Y,Z); }
    bool DebugSolidOverlayAt(double X,double Y,double Z) const { return IsInsideSolidOverlay(X,Y,Z); }

    void SetEditTransaction(std::vector<FEditBrush> Brushes)
    {
        EditBrushes=std::move(Brushes);
        EditBoundsMin={MAX_int32,MAX_int32,MAX_int32};
        EditBoundsMax={MIN_int32,MIN_int32,MIN_int32};
        for(const FEditBrush& Brush:EditBrushes)
        {
            double Extent[3]{};
            if(Brush.Shape==FEditBrush::EShape::Sphere)
                for(int32 Axis=0;Axis<3;++Axis)Extent[Axis]=Brush.Radius;
            else if(Brush.Shape==FEditBrush::EShape::Capsule)
                for(int32 Axis=0;Axis<3;++Axis)Extent[Axis]=Brush.Radius
                    +(Brush.Operation==FEditBrush::EOperation::DensityOffset
                        ?std::max(Brush.Falloff,0.01f):0.0f);
            else
                for(int32 Axis=0;Axis<3;++Axis)Extent[Axis]=Brush.HalfExtent[Axis]+Brush.Rounding
                    +(Brush.Operation==FEditBrush::EOperation::DensityOffset
                        ?std::max(Brush.Falloff,0.01f):0.0f);
            for(int32 Axis=0;Axis<3;++Axis)
            {
                const double Lo=Brush.Shape==FEditBrush::EShape::Capsule
                    ?std::min(Brush.A[Axis],Brush.B[Axis])-Extent[Axis]
                    :Brush.A[Axis]-Extent[Axis];
                const double Hi=Brush.Shape==FEditBrush::EShape::Capsule
                    ?std::max(Brush.A[Axis],Brush.B[Axis])+Extent[Axis]
                    :Brush.A[Axis]+Extent[Axis];
                (&EditBoundsMin.X)[Axis]=std::min((&EditBoundsMin.X)[Axis],static_cast<int32>(std::floor(Lo)));
                (&EditBoundsMax.X)[Axis]=std::max((&EditBoundsMax.X)[Axis],static_cast<int32>(std::ceil(Hi)));
            }
        }
    }

    void SetSharedDensitySource(const FStandaloneShapeWorld* Source)
    { SharedDensitySource=Source==this?nullptr:Source; }

    bool HasEditTransaction() const { return !EditBrushes.empty(); }
    FIntVector GetEditBoundsMin() const { return EditBoundsMin; }
    FIntVector GetEditBoundsMax() const { return EditBoundsMax; }

    void BuildFarWorld()
    {
        if(FarBuilt)return;
        auto Stage=std::chrono::steady_clock::now();
        BuildFarParentShapes();
        RebuildSharedFieldPrimitives();
        Stats.FarPrimitiveSeconds=std::chrono::duration<double>(std::chrono::steady_clock::now()-Stage).count();
        Stage=std::chrono::steady_clock::now();
        BuildSpatialBins(SpatialBinSize,false);
        Stats.FarBinSeconds=std::chrono::duration<double>(std::chrono::steady_clock::now()-Stage).count();
        Stats.FarShapeSeconds=Stats.FarPrimitiveSeconds+Stats.FarBinSeconds;
        Stats.PrimitiveCount=Primitives.size();FarBuilt=true;
        std::printf("[FarShapeStage] parent_shapes=%.3f ms spatial_bins=%.3f ms total=%.3f ms primitives=%llu\n",
            Stats.FarPrimitiveSeconds*1000.0,Stats.FarBinSeconds*1000.0,Stats.FarShapeSeconds*1000.0,
            static_cast<unsigned long long>(Stats.PrimitiveCount));
        std::fflush(stdout);
    }

    // Lattice signs come from packed intervals; a bounded analytic distance proxy supplies
    // edge interpolation and normals to the existing mesher.
    float DensityAt(float X,float Y,float Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->DensityAt(X,Y,Z);
        if(bNativeOnly)
        {
            if(!NativeOnlyContains(X,Y,Z))
            {RecordNativeOnlyViolation();return 0.0f;}
            float NativeDensity=0.0f;
            if(!NativeSurfaceDensityAt(X,Y,Z,NativeDensity))
            {RecordNativeOnlyViolation();return 0.0f;}
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        float IslandDensity=0.0f;
        if(NativeFloatingIslandDensityAt(X,Y,Z,IslandDensity))
        {
            ++ThreadClassificationStats().NativeFloatFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(IslandDensity,X,Y,Z),X,Y,Z);
        }
        float NativeDensity=0.0f;
        if(NativeSurfaceDensityAt(X,Y,Z,NativeDensity))
        {
            ++ThreadClassificationStats().NativeFloatFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        if(UsesLegacySurfaceField(X,Y,Z))
            return LegacySurfaceDensityAt(X,Y,Z);
        int32 IX=0,IY=0,IZ=0;
        const bool bInteger=NearInteger(X,IX)&&NearInteger(Y,IY)&&NearInteger(Z,IZ);
        const bool bPacked=!bAnalyticOnly&&bInteger&&Contains(IX,IY,IZ);
        if(bPacked)
            return PackedDensityAt(IX,IY,IZ,IsRock(IX,IY,IZ),X,Y,Z);
        return AnalyticDensityAt(X,Y,Z);
    }

    std::string DensityDispatchPathAt(float X,float Y,float Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->DensityDispatchPathAt(X,Y,Z);
        float Density=0.0f;
        if(NativeFloatingIslandDensityAt(X,Y,Z,Density))return "FloatingIslands-native";
        if(NativeSurfaceDensityAt(X,Y,Z,Density))return "SurfaceWorld-native";
        if(UsesLegacySurfaceField(X,Y,Z))return "SurfaceWorld-legacy";
        const FBoundStratumField* Bound=FindBoundStratumForZ(Z);
        if(Bound&&Bound->Resolved)
        {
            const std::string& Kind=Bound->Resolved->generatorKind;
            return "compiled-analytic/"+Kind;
        }
        return Owner?"compiled-analytic/TunnelNetwork":"compiled-analytic/fallback";
    }

    float DensityAtLattice(int32 X,int32 Y,int32 Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->DensityAtLattice(X,Y,Z);
        if(bNativeOnly)
        {
            if(!NativeOnlyContains(static_cast<float>(X),static_cast<float>(Y),
                static_cast<float>(Z)))
            {RecordNativeOnlyViolation();return 0.0f;}
            float NativeDensity=0.0f;
            if(!NativeSurfaceDensityAt(static_cast<float>(X),static_cast<float>(Y),
                static_cast<float>(Z),NativeDensity))
            {RecordNativeOnlyViolation();return 0.0f;}
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        float IslandDensity=0.0f;
        if(NativeFloatingIslandDensityAt(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z),IslandDensity))
        {
            ++ThreadClassificationStats().NativeLatticeFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(IslandDensity,X,Y,Z),X,Y,Z);
        }
        float NativeDensity=0.0f;
        if(NativeSurfaceDensityAt(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z),NativeDensity))
        {
            ++ThreadClassificationStats().NativeLatticeFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        if(UsesLegacySurfaceField(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z)))
            return LegacySurfaceDensityAt(static_cast<float>(X),static_cast<float>(Y),
                static_cast<float>(Z));
        const bool bPacked=!bAnalyticOnly&&Contains(X,Y,Z);
        if(bPacked)
            return PackedDensityAt(X,Y,Z,IsRock(X,Y,Z),static_cast<float>(X),
                static_cast<float>(Y),static_cast<float>(Z));
        return AnalyticDensityAt(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z));
    }

    float DensityAtUnclamped(float X,float Y,float Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->DensityAtUnclamped(X,Y,Z);
        if(bNativeOnly)
        {
            if(!NativeOnlyContains(X,Y,Z))
            {RecordNativeOnlyViolation();return 0.0f;}
            float NativeDensity=0.0f;
            if(!NativeSurfaceDensityAt(X,Y,Z,NativeDensity))
            {RecordNativeOnlyViolation();return 0.0f;}
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        float IslandDensity=0.0f;
        if(NativeFloatingIslandDensityAt(X,Y,Z,IslandDensity))
        {
            ++ThreadClassificationStats().NativeUnclampedFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(IslandDensity,X,Y,Z),X,Y,Z);
        }
        float NativeDensity=0.0f;
        if(NativeSurfaceDensityAt(X,Y,Z,NativeDensity))
        {
            ++ThreadClassificationStats().NativeUnclampedFieldCalls;
            return ApplyEditBrushes(ApplyResolvedStrateComposition(NativeDensity,X,Y,Z),X,Y,Z);
        }
        if(UsesLegacySurfaceField(X,Y,Z))
            return LegacySurfaceDensityAt(X,Y,Z);
        return AnalyticDensityAt(X,Y,Z,false);
    }

    VoxelForgeCore::DetailFieldSample DetailSampleAt(float X,float Y,float Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->DetailSampleAt(X,Y,Z);
        VoxelForgeCore::DetailFieldSample Sample;
        if(bNativeOnly)
        {RecordNativeOnlyViolation();return Sample;}
        AnalyticDensityAt(X,Y,Z,false,&Sample.displacement,
            &Sample.caveInfluence,&Sample.floorInfluence);
        return Sample;
    }

    bool IsProxyBandFallback(float Density) const
    {
        return std::abs(std::abs(Density)-(DetailSupremum+0.125f))<1.0e-4f;
    }

    bool IsAnalyticOnly() const { return bAnalyticOnly; }

    void DensityAtLatticeX8(int32 XStart,int32 XStep,int32 Y,int32 Z,
                            int32 Count,float OutDensity[8]) const
    {
        if(SharedDensitySource)
        {
            SharedDensitySource->DensityAtLatticeX8(XStart,XStep,Y,Z,Count,OutDensity);
            return;
        }
        Count=std::clamp(Count,0,8);
        if(Count==0)return;
        if(bNativeOnly)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(XStart+Lane*XStep,Y,Z);
            return;
        }
        if(IsInsideResolvedStrateBoundaryBand(static_cast<float>(Z)))
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(XStart+Lane*XStep,Y,Z);
            return;
        }
        bool bHasLegacySurfaceSample=false;
        bool bHasNativeIslandSample=false;
        for(int32 Lane=0;Lane<Count;++Lane)
        {
            const float SampleX=static_cast<float>(XStart+Lane*XStep);
            const float SampleY=static_cast<float>(Y);
            const float SampleZ=static_cast<float>(Z);
            bHasLegacySurfaceSample|=UsesLegacySurfaceField(SampleX,SampleY,SampleZ);
            float IslandDensity=0.0f;
            bHasNativeIslandSample|=NativeFloatingIslandDensityAt(
                SampleX,SampleY,SampleZ,IslandDensity);
        }
        if(bHasLegacySurfaceSample||bHasNativeIslandSample)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(XStart+Lane*XStep,Y,Z);
            return;
        }
        if(bAnalyticOnly)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(XStart+Lane*XStep,Y,Z);
            return;
        }
        bool bFast=EditBrushes.empty()&&Y>=Min[1]&&Y<=Max[1]
            &&Z>=Min[2]&&Z<=Max[2]
            &&XStart>=Min[0]
            &&XStart+static_cast<int64>(Count-1)*XStep<=Max[0];
        if(!bFast)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(XStart+Lane*XStep,Y,Z);
            return;
        }

        const size_t ColumnStart=static_cast<size_t>(Y-Min[1])*Size[0]
            +static_cast<size_t>(XStart-Min[0]);
        const size_t Zi=static_cast<size_t>(Z-Min[2]);
        const size_t WordOffset=Zi>>6;
        const uint64 Mask=uint64{1}<<(Zi&63u);
        const size_t NodeBase=Zi*static_cast<size_t>(Size[1])*Size[0]+ColumnStart;
        constexpr float ProxyBandEdge=DetailSupremum+0.125f;
        for(int32 Lane=0;Lane<Count;++Lane)
        {
            const size_t Column=ColumnStart+static_cast<size_t>(Lane*XStep);
            const size_t Word=Column*WordsPerZ+WordOffset;
            const bool bRock=(RockWords[Word]&Mask)!=0;
            float Density;
            if(CandidateWords[Word]&Mask)
            {
                const int16 Proxy=SurfaceDistanceQ[NodeBase
                    +static_cast<size_t>(Lane*XStep)];
                Density=static_cast<float>(Proxy)*(1.0f/256.0f);
                if((Density<0.0f)!=bRock)
                    Density=(bRock?-1.0f:1.0f)*std::max(std::abs(Density),1.0f/256.0f);
            }
            else
                Density=bRock?-ProxyBandEdge:ProxyBandEdge;
            OutDensity[Lane]=Density;
        }
    }

private:
    struct FPassageTileFeature
    {
        std::size_t passageIndex=0,segmentIndex=0;
        bool bColumn=false,bMouthSupport=false;
    };
    struct FPassageNearestNode
    {
        std::array<double,3> minimum{},maximum{};
        double maximumRadius=0.0;
        std::vector<std::size_t> segments;
        int left=-1,right=-1;
    };
    struct FPassageProofBound
    {
        std::array<double,3> minimum{},maximum{};
    };
    struct FPassageProofNode
    {
        std::array<double,3> minimum{},maximum{};
        std::size_t first=0,end=0;
        int left=-1,right=-1;
    };
    struct FPassageFeatureNode
    {
        std::array<std::int64_t,3> minimum{},maximum{};
        std::size_t first=0,end=0;
        int left=-1,right=-1;
    };
    struct FStampSpatialBound
    {
        std::array<std::int64_t,3> minimumSubvoxels{},maximumSubvoxels{};
    };
    struct FStampSpatialNode
    {
        std::array<std::int64_t,3> minimumSubvoxels{},maximumSubvoxels{};
        std::size_t first=0,end=0;
        int left=-1,right=-1;
    };
    struct FStampRuntime
    {
        const VoxelForgeCore::ResolvedLayoutStampV1* record=nullptr;
        std::array<float,3> positionVoxels{},halfExtentsVoxels{};
        float smoothWidthVoxels=0.0f;
        float irregularityAmplitudeVoxels=0.0f;
        float irregularityWavelengthVoxels=0.0f;
        std::uint64_t irregularitySeed=0;
        std::uint8_t quarterTurns=0;
    };
    struct FCavernRuntimeFeature
    {
        const VoxelForgeCore::ResolvedCavernRoomV1* room=nullptr;
        const VoxelForgeCore::ResolvedCavernEdgeV1* edge=nullptr;
        std::array<std::int64_t,3> boundsMinimumMicrometres{},boundsMaximumMicrometres{};
        std::array<float,3> centerVoxels{},halfExtentsVoxels{};
        std::array<std::array<float,3>,4> controlPointsVoxels{};
        float floorVoxels=0.0f;
        float boreRadiusVoxels=0.0f,boreHeightVoxels=0.0f;
        float floorSupportDepthVoxels=0.0f;
        float smoothWidthVoxels=0.0f;
        float irregularityAmplitudeVoxels=0.0f;
        float irregularityWavelengthVoxels=0.0f;
        std::uint64_t irregularitySeed=0;
    };

    int BuildStampSpatialNode(std::size_t first,std::size_t end)
    {
        FStampSpatialNode node;node.first=first;node.end=end;
        node.minimumSubvoxels.fill(std::numeric_limits<std::int64_t>::max());
        node.maximumSubvoxels.fill(std::numeric_limits<std::int64_t>::min());
        for(std::size_t offset=first;offset<end;++offset)
        {
            const auto& bound=StampSpatialBounds[StampSpatialOrder[offset]];
            for(std::size_t axis=0;axis<3;++axis)
            {
                node.minimumSubvoxels[axis]=std::min(node.minimumSubvoxels[axis],
                    bound.minimumSubvoxels[axis]);
                node.maximumSubvoxels[axis]=std::max(node.maximumSubvoxels[axis],
                    bound.maximumSubvoxels[axis]);
            }
        }
        const int nodeIndex=static_cast<int>(StampSpatialNodes.size());
        StampSpatialNodes.push_back(node);
        if(end-first>8)
        {
            std::size_t splitAxis=0;
            for(std::size_t axis=1;axis<3;++axis)
                if(static_cast<long double>(node.maximumSubvoxels[axis])
                        -node.minimumSubvoxels[axis]
                    >static_cast<long double>(node.maximumSubvoxels[splitAxis])
                        -node.minimumSubvoxels[splitAxis])splitAxis=axis;
            const std::size_t middle=first+(end-first)/2;
            std::nth_element(StampSpatialOrder.begin()+first,
                StampSpatialOrder.begin()+middle,StampSpatialOrder.begin()+end,
                [this,splitAxis](std::uint32_t a,std::uint32_t b)
                {
                    const auto& left=StampSpatialBounds[a];const auto& right=StampSpatialBounds[b];
                    const long double leftCenter=static_cast<long double>(
                        left.minimumSubvoxels[splitAxis])+left.maximumSubvoxels[splitAxis];
                    const long double rightCenter=static_cast<long double>(
                        right.minimumSubvoxels[splitAxis])+right.maximumSubvoxels[splitAxis];
                    return leftCenter==rightCenter?a<b:leftCenter<rightCenter;
                });
            StampSpatialNodes[nodeIndex].left=BuildStampSpatialNode(first,middle);
            StampSpatialNodes[nodeIndex].right=BuildStampSpatialNode(middle,end);
        }
        return nodeIndex;
    }

    void QueryStampSpatialNode(int nodeIndex,
        const std::array<std::int64_t,3>& minimum,
        const std::array<std::int64_t,3>& maximum,
        std::vector<std::uint32_t>& result) const
    {
        if(nodeIndex<0)return;
        const auto& node=StampSpatialNodes[static_cast<std::size_t>(nodeIndex)];
        for(std::size_t axis=0;axis<3;++axis)
            if(node.maximumSubvoxels[axis]<minimum[axis]
                ||node.minimumSubvoxels[axis]>maximum[axis])return;
        if(node.left<0)
        {
            for(std::size_t offset=node.first;offset<node.end;++offset)
            {
                const auto index=StampSpatialOrder[offset];
                const auto& bound=StampSpatialBounds[index];bool overlap=true;
                for(std::size_t axis=0;axis<3;++axis)
                    overlap=overlap&&bound.minimumSubvoxels[axis]<=maximum[axis]
                        &&bound.maximumSubvoxels[axis]>=minimum[axis];
                if(overlap)result.push_back(index);
            }
            return;
        }
        QueryStampSpatialNode(node.left,minimum,maximum,result);
        QueryStampSpatialNode(node.right,minimum,maximum,result);
    }

    void BuildStampSpatialIndex()
    {
        StampSpatialBounds.clear();StampSpatialOrder.clear();StampSpatialNodes.clear();
        StampRuntime.clear();
        if(!ResolvedLayout||ResolvedLayout->stamps.empty()||!Owner
            ||Owner->CoreVoxelSizeMicrons==0)return;
        constexpr long double Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
        const long double scale=Q/Owner->CoreVoxelSizeMicrons;
        StampSpatialBounds.reserve(ResolvedLayout->stamps.size());
        StampRuntime.reserve(ResolvedLayout->stamps.size());
        for(const auto& stamp:ResolvedLayout->stamps)
        {
            FStampSpatialBound bound;
            for(std::size_t axis=0;axis<3;++axis)
            {
                bound.minimumSubvoxels[axis]=static_cast<std::int64_t>(std::floor(
                    static_cast<long double>(stamp.boundsMinimumMicrometres[axis])*scale));
                bound.maximumSubvoxels[axis]=static_cast<std::int64_t>(std::ceil(
                    static_cast<long double>(stamp.boundsMaximumMicrometres[axis])*scale));
            }
            StampSpatialBounds.push_back(bound);
            FStampRuntime runtime;runtime.record=&stamp;
            for(std::size_t axis=0;axis<3;++axis)
                runtime.positionVoxels[axis]=static_cast<float>(
                    static_cast<double>(stamp.positionMicrometres[axis])
                        /Owner->CoreVoxelSizeMicrons);
            const std::size_t xAxis=stamp.yawQuarterTurns%2?1:0;
            const std::size_t yAxis=stamp.yawQuarterTurns%2?0:1;
            runtime.halfExtentsVoxels={
                static_cast<float>(static_cast<double>(stamp.halfExtentsMicrometres[0])
                    /Owner->CoreVoxelSizeMicrons),
                static_cast<float>(static_cast<double>(stamp.halfExtentsMicrometres[1])
                    /Owner->CoreVoxelSizeMicrons),
                static_cast<float>(static_cast<double>(stamp.halfExtentsMicrometres[2])
                    /Owner->CoreVoxelSizeMicrons)};
            (void)xAxis;(void)yAxis;
            runtime.smoothWidthVoxels=static_cast<float>(
                static_cast<double>(stamp.smoothWidthMicrometres)/Owner->CoreVoxelSizeMicrons);
            runtime.irregularityAmplitudeVoxels=static_cast<float>(
                static_cast<double>(stamp.irregularityAmplitudeMicrometres)
                    /Owner->CoreVoxelSizeMicrons);
            runtime.irregularityWavelengthVoxels=static_cast<float>(
                static_cast<double>(stamp.irregularityWavelengthMicrometres)
                    /Owner->CoreVoxelSizeMicrons);
            runtime.irregularitySeed=stamp.irregularitySeed;
            runtime.quarterTurns=stamp.yawQuarterTurns;
            StampRuntime.push_back(runtime);
        }
        StampSpatialOrder.resize(StampSpatialBounds.size());
        for(std::size_t i=0;i<StampSpatialOrder.size();++i)
            StampSpatialOrder[i]=static_cast<std::uint32_t>(i);
        if(!StampSpatialOrder.empty())BuildStampSpatialNode(0,StampSpatialOrder.size());
    }

    std::vector<std::uint32_t> BuildStampTileList(
        const std::array<std::int64_t,3>& minimum,
        const std::array<std::int64_t,3>& maximum) const
    {
        std::vector<std::uint32_t> result;
        if(StampSpatialBounds.empty())return result;
        for(std::size_t axis=0;axis<3;++axis)
            if(minimum[axis]>maximum[axis])
            {
                result.resize(StampSpatialBounds.size());
                for(std::size_t i=0;i<result.size();++i)
                    result[i]=static_cast<std::uint32_t>(i);
                return result;
            }
        QueryStampSpatialNode(0,minimum,maximum,result);
        // Stamp union/carve composition follows canonical stable-ID order. The BVH query
        // order is spatial and can differ per tile, which would let a later carve erase a
        // fill on meshed tiles even though unscoped density queries use the canonical order.
        std::sort(result.begin(),result.end());
        return result;
    }

    void BuildCavernSpatialIndex()
    {
        CavernRuntime.clear();
        if(!ResolvedLayout||!Owner||Owner->CoreVoxelSizeMicrons==0
            ||ResolvedLayout->cavernGraphVocabularyVersion
                !=VoxelForgeCore::ResolvedLayoutCavernGraphVocabularyVersionV1)return;
        const float micronsPerVoxel=static_cast<float>(Owner->CoreVoxelSizeMicrons);
        for(const auto& room:ResolvedLayout->cavernRooms)
        {
            FCavernRuntimeFeature runtime;runtime.room=&room;
            runtime.boundsMinimumMicrometres=room.boundsMinimumMicrometres;
            runtime.boundsMaximumMicrometres=room.boundsMaximumMicrometres;
            for(std::size_t axis=0;axis<3;++axis)
            {
                runtime.centerVoxels[axis]=static_cast<float>(
                    static_cast<double>(room.centerMicrometres[axis])/micronsPerVoxel);
                runtime.halfExtentsVoxels[axis]=static_cast<float>(
                    static_cast<double>(room.halfExtentsMicrometres[axis])/micronsPerVoxel);
            }
            runtime.floorVoxels=static_cast<float>(
                static_cast<double>(room.floorMicrometres)/micronsPerVoxel);
            runtime.smoothWidthVoxels=static_cast<float>(
                static_cast<double>(room.smoothWidthMicrometres)/micronsPerVoxel);
            runtime.irregularityAmplitudeVoxels=static_cast<float>(
                static_cast<double>(room.irregularityAmplitudeMicrometres)/micronsPerVoxel);
            runtime.irregularityWavelengthVoxels=static_cast<float>(
                static_cast<double>(room.irregularityWavelengthMicrometres)/micronsPerVoxel);
            runtime.irregularitySeed=room.irregularitySeed;
            CavernRuntime.push_back(runtime);
        }
        for(const auto& edge:ResolvedLayout->cavernEdges)
        {
            FCavernRuntimeFeature runtime;runtime.edge=&edge;
            runtime.boundsMinimumMicrometres=edge.boundsMinimumMicrometres;
            runtime.boundsMaximumMicrometres=edge.boundsMaximumMicrometres;
            for(std::size_t point=0;point<4;++point)
                for(std::size_t axis=0;axis<3;++axis)
                    runtime.controlPointsVoxels[point][axis]=static_cast<float>(
                        static_cast<double>(edge.controlPointsMicrometres[point][axis])
                            /micronsPerVoxel);
            runtime.boreRadiusVoxels=static_cast<float>(
                static_cast<double>(edge.boreRadiusMicrometres)/micronsPerVoxel);
            runtime.boreHeightVoxels=static_cast<float>(
                static_cast<double>(edge.boreHeightMicrometres)/micronsPerVoxel);
            runtime.floorSupportDepthVoxels=static_cast<float>(
                static_cast<double>(edge.floorSupportDepthMicrometres)/micronsPerVoxel);
            runtime.smoothWidthVoxels=static_cast<float>(
                static_cast<double>(edge.smoothWidthMicrometres)/micronsPerVoxel);
            runtime.irregularityAmplitudeVoxels=static_cast<float>(
                static_cast<double>(edge.irregularityAmplitudeMicrometres)/micronsPerVoxel);
            runtime.irregularityWavelengthVoxels=static_cast<float>(
                static_cast<double>(edge.irregularityWavelengthMicrometres)/micronsPerVoxel);
            runtime.irregularitySeed=edge.irregularitySeed;
            CavernRuntime.push_back(runtime);
        }
    }

    std::vector<std::uint32_t> BuildCavernFeatureTileList(
        const std::array<std::int64_t,3>& minimumSubvoxels,
        const std::array<std::int64_t,3>& maximumSubvoxels) const
    {
        std::vector<std::uint32_t> result;
        if(CavernRuntime.empty())return result;
        if(!Owner||Owner->CoreVoxelSizeMicrons==0)
        {
            result.resize(CavernRuntime.size());
            for(std::size_t i=0;i<result.size();++i)result[i]=static_cast<std::uint32_t>(i);
            return result;
        }
        constexpr long double Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
        std::array<long double,3> minimumMicrometres{},maximumMicrometres{};
        for(std::size_t axis=0;axis<3;++axis)
        {
            if(minimumSubvoxels[axis]>maximumSubvoxels[axis])
            {
                result.resize(CavernRuntime.size());
                for(std::size_t i=0;i<result.size();++i)
                    result[i]=static_cast<std::uint32_t>(i);
                return result;
            }
            minimumMicrometres[axis]=static_cast<long double>(minimumSubvoxels[axis])
                *Owner->CoreVoxelSizeMicrons/Q;
            maximumMicrometres[axis]=static_cast<long double>(maximumSubvoxels[axis])
                *Owner->CoreVoxelSizeMicrons/Q;
        }
        for(std::size_t index=0;index<CavernRuntime.size();++index)
        {
            const auto& feature=CavernRuntime[index];bool overlap=true;
            for(std::size_t axis=0;axis<3;++axis)
                overlap=overlap&&feature.boundsMaximumMicrometres[axis]
                    >=minimumMicrometres[axis]
                    &&feature.boundsMinimumMicrometres[axis]
                    <=maximumMicrometres[axis];
            if(overlap)result.push_back(static_cast<std::uint32_t>(index));
        }
        return result;
    }

    int BuildPassageNearestNode(std::size_t passageIndex,std::vector<std::size_t> segments)
    {
        const auto& points=ResolvedLayout->passages[passageIndex].controlPoints;
        FPassageNearestNode node;
        node.minimum.fill(std::numeric_limits<double>::infinity());
        node.maximum.fill(-std::numeric_limits<double>::infinity());
        for(const std::size_t segment:segments)
        {
            const auto& a=points[segment];const auto& b=points[segment+1];
            for(std::size_t axis=0;axis<3;++axis)
            {
                node.minimum[axis]=std::min({node.minimum[axis],
                    static_cast<double>(a.positionSubvoxels[axis]),
                    static_cast<double>(b.positionSubvoxels[axis])});
                node.maximum[axis]=std::max({node.maximum[axis],
                    static_cast<double>(a.positionSubvoxels[axis]),
                    static_cast<double>(b.positionSubvoxels[axis])});
            }
            node.maximumRadius=std::max({node.maximumRadius,
                static_cast<double>(a.radiusSubvoxels),static_cast<double>(b.radiusSubvoxels)});
        }
        node.segments=segments;
        std::sort(node.segments.begin(),node.segments.end());
        const int nodeIndex=static_cast<int>(PassageNearestNodes[passageIndex].size());
        PassageNearestNodes[passageIndex].push_back(std::move(node));
        if(segments.size()>4)
        {
            std::size_t splitAxis=0;
            for(std::size_t axis=1;axis<3;++axis)
                if(PassageNearestNodes[passageIndex][nodeIndex].maximum[axis]
                    -PassageNearestNodes[passageIndex][nodeIndex].minimum[axis]
                    >PassageNearestNodes[passageIndex][nodeIndex].maximum[splitAxis]
                    -PassageNearestNodes[passageIndex][nodeIndex].minimum[splitAxis])splitAxis=axis;
            const std::size_t middle=segments.size()/2;
            const auto center=[&](std::size_t segment)
            {return static_cast<double>(points[segment].positionSubvoxels[splitAxis])
                +static_cast<double>(points[segment+1].positionSubvoxels[splitAxis]);};
            std::nth_element(segments.begin(),segments.begin()+middle,segments.end(),
                [&](std::size_t a,std::size_t b)
                {const double ca=center(a),cb=center(b);return ca==cb?a<b:ca<cb;});
            std::vector<std::size_t> leftSegments(segments.begin(),segments.begin()+middle);
            std::vector<std::size_t> rightSegments(segments.begin()+middle,segments.end());
            const int left=BuildPassageNearestNode(passageIndex,std::move(leftSegments));
            const int right=BuildPassageNearestNode(passageIndex,std::move(rightSegments));
            PassageNearestNodes[passageIndex][nodeIndex].left=left;
            PassageNearestNodes[passageIndex][nodeIndex].right=right;
        }
        return nodeIndex;
    }

    int BuildPassageProofNode(std::size_t first,std::size_t end)
    {
        FPassageProofNode node;node.first=first;node.end=end;
        node.minimum.fill(std::numeric_limits<double>::infinity());
        node.maximum.fill(-std::numeric_limits<double>::infinity());
        for(std::size_t index=first;index<end;++index)
            for(std::size_t axis=0;axis<3;++axis)
            {
                node.minimum[axis]=std::min(node.minimum[axis],PassageProofBounds[index].minimum[axis]);
                node.maximum[axis]=std::max(node.maximum[axis],PassageProofBounds[index].maximum[axis]);
            }
        const int nodeIndex=static_cast<int>(PassageProofNodes.size());
        PassageProofNodes.push_back(node);
        if(end-first>8)
        {
            std::size_t splitAxis=0;
            for(std::size_t axis=1;axis<3;++axis)
                if(node.maximum[axis]-node.minimum[axis]
                    >node.maximum[splitAxis]-node.minimum[splitAxis])splitAxis=axis;
            const std::size_t middle=first+(end-first)/2;
            std::nth_element(PassageProofBounds.begin()+first,PassageProofBounds.begin()+middle,
                PassageProofBounds.begin()+end,[splitAxis](const auto& a,const auto& b)
                {return a.minimum[splitAxis]+a.maximum[splitAxis]
                    <b.minimum[splitAxis]+b.maximum[splitAxis];});
            const int left=BuildPassageProofNode(first,middle);
            const int right=BuildPassageProofNode(middle,end);
            PassageProofNodes[nodeIndex].left=left;
            PassageProofNodes[nodeIndex].right=right;
        }
        return nodeIndex;
    }

    int BuildPassageFeatureNode(std::size_t first,std::size_t end)
    {
        FPassageFeatureNode node;node.first=first;node.end=end;
        node.minimum.fill(std::numeric_limits<std::int64_t>::max());
        node.maximum.fill(std::numeric_limits<std::int64_t>::min());
        for(std::size_t offset=first;offset<end;++offset)
        {
            const auto& feature=PassageFeatureBounds[PassageFeatureOrder[offset]];
            for(std::size_t axis=0;axis<3;++axis)
            {
                node.minimum[axis]=std::min(node.minimum[axis],feature.minimumSubvoxels[axis]);
                node.maximum[axis]=std::max(node.maximum[axis],feature.maximumSubvoxels[axis]);
            }
        }
        const int nodeIndex=static_cast<int>(PassageFeatureNodes.size());
        PassageFeatureNodes.push_back(node);
        if(end-first>8)
        {
            std::size_t splitAxis=0;
            for(std::size_t axis=1;axis<3;++axis)
                if(static_cast<long double>(node.maximum[axis])-node.minimum[axis]
                    >static_cast<long double>(node.maximum[splitAxis])-node.minimum[splitAxis])
                    splitAxis=axis;
            const std::size_t middle=first+(end-first)/2;
            std::nth_element(PassageFeatureOrder.begin()+first,PassageFeatureOrder.begin()+middle,
                PassageFeatureOrder.begin()+end,[this,splitAxis](std::uint32_t a,std::uint32_t b)
                {
                    const auto& left=PassageFeatureBounds[a];
                    const auto& right=PassageFeatureBounds[b];
                    const double leftCenter=static_cast<double>(left.minimumSubvoxels[splitAxis])*0.5
                        +static_cast<double>(left.maximumSubvoxels[splitAxis])*0.5;
                    const double rightCenter=static_cast<double>(right.minimumSubvoxels[splitAxis])*0.5
                        +static_cast<double>(right.maximumSubvoxels[splitAxis])*0.5;
                    return leftCenter==rightCenter?a<b:leftCenter<rightCenter;
                });
            const int left=BuildPassageFeatureNode(first,middle);
            const int right=BuildPassageFeatureNode(middle,end);
            PassageFeatureNodes[nodeIndex].left=left;
            PassageFeatureNodes[nodeIndex].right=right;
        }
        return nodeIndex;
    }

    void QueryPassageFeatureNode(int nodeIndex,
        const std::array<std::int64_t,3>& minimum,
        const std::array<std::int64_t,3>& maximum,
        std::vector<std::uint32_t>& result) const
    {
        if(nodeIndex<0)return;
        const auto& node=PassageFeatureNodes[static_cast<std::size_t>(nodeIndex)];
        for(std::size_t axis=0;axis<3;++axis)
            if(node.maximum[axis]<minimum[axis]||node.minimum[axis]>maximum[axis])return;
        if(node.left<0)
        {
            for(std::size_t offset=node.first;offset<node.end;++offset)
            {
                const std::uint32_t featureIndex=PassageFeatureOrder[offset];
                const auto& feature=PassageFeatureBounds[featureIndex];
                bool overlaps=true;
                for(std::size_t axis=0;axis<3;++axis)
                    overlaps=overlaps&&feature.minimumSubvoxels[axis]<=maximum[axis]
                        &&feature.maximumSubvoxels[axis]>=minimum[axis];
                if(overlaps)result.push_back(featureIndex);
            }
            return;
        }
        QueryPassageFeatureNode(node.left,minimum,maximum,result);
        QueryPassageFeatureNode(node.right,minimum,maximum,result);
    }

    std::vector<std::uint32_t> BuildPassageFeatureTileList(
        const std::array<std::int64_t,3>& minimum,
        const std::array<std::int64_t,3>& maximum) const
    {
        std::vector<std::uint32_t> result;
        if(PassageFeatureBounds.empty())return result;
        bool failOpen=PassageFeatureBoundsFailOpen;
        for(std::size_t axis=0;axis<3;++axis)failOpen=failOpen||minimum[axis]>maximum[axis];
        if(failOpen)
        {
            result.resize(PassageFeatureBounds.size());
            for(std::size_t i=0;i<result.size();++i)result[i]=static_cast<std::uint32_t>(i);
            return result;
        }
        if(!PassageFeatureNodes.empty())QueryPassageFeatureNode(0,minimum,maximum,result);
        return result;
    }

    void BuildPassageSpatialIndices()
    {
        BuildStampSpatialIndex();
        BuildCavernSpatialIndex();
        PassageTileFeatures.clear();PassageFeatureBounds.clear();
        PassageFeatureOrder.clear();PassageFeatureNodes.clear();
        PassageFeatureBoundsFailOpen=false;
        PassageNearestNodes.clear();
        PassageProofBounds.clear();PassageProofNodes.clear();
        PassageNearestNodes.resize(ResolvedLayout?ResolvedLayout->passages.size():0);
        PassageColumnSegmentFlags.clear();PassageShortSpanSegmentFlags.clear();
        PassageHasShortSpanFlags.clear();
        if(!ResolvedLayout||ResolvedLayout->passages.empty())return;
        constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double voxelsPerMetre=Owner&&Owner->CoreVoxelSizeMicrons>0
            ?1000000.0/Owner->CoreVoxelSizeMicrons:4.0;
        const double bridgeHalfWidthVoxels=3.5*voxelsPerMetre;
        const double bridgeFootDepthVoxels=(5.0-0.13)*voxelsPerMetre;
        PassageColumnSegmentFlags.resize(ResolvedLayout->passages.size());
        PassageShortSpanSegmentFlags.resize(ResolvedLayout->passages.size());
        for(std::size_t passageIndex=0;passageIndex<ResolvedLayout->passages.size();++passageIndex)
        {
            const auto& passage=ResolvedLayout->passages[passageIndex];
            const std::size_t segmentCount=passage.controlPoints.size()>1
                ?passage.controlPoints.size()-1:0;
            PassageColumnSegmentFlags[passageIndex].assign(segmentCount,0);
            PassageShortSpanSegmentFlags[passageIndex].assign(segmentCount,0);
            if(segmentCount>0)
            {
                std::vector<std::size_t> segmentIds(segmentCount);
                for(std::size_t i=0;i<segmentCount;++i)segmentIds[i]=i;
                BuildPassageNearestNode(passageIndex,std::move(segmentIds));
            }
            for(std::size_t segment=0;segment<segmentCount;++segment)
            {
                const auto& a=passage.controlPoints[segment];
                const auto& b=passage.controlPoints[segment+1];
                const double radius=static_cast<double>(std::max(a.radiusSubvoxels,b.radiusSubvoxels))/Q;
                const double horizontalExtent=std::max(radius,bridgeHalfWidthVoxels);
                const double footDepth=std::max(voxelsPerMetre,bridgeFootDepthVoxels);
                FPassageProofBound proof;
                proof.minimum={std::min(a.positionSubvoxels[0],b.positionSubvoxels[0])/Q-horizontalExtent,
                    std::min(a.positionSubvoxels[1],b.positionSubvoxels[1])/Q-horizontalExtent,
                    std::min(a.positionSubvoxels[2],b.positionSubvoxels[2])/Q-radius-footDepth};
                proof.maximum={std::max(a.positionSubvoxels[0],b.positionSubvoxels[0])/Q+horizontalExtent,
                    std::max(a.positionSubvoxels[1],b.positionSubvoxels[1])/Q+horizontalExtent,
                    std::max(a.positionSubvoxels[2],b.positionSubvoxels[2])/Q+radius};
                PassageProofBounds.push_back(proof);
                const std::array<std::int64_t,3> featureMin={
                    static_cast<std::int64_t>(std::floor(proof.minimum[0]*Q)),
                    static_cast<std::int64_t>(std::floor(proof.minimum[1]*Q)),
                    static_cast<std::int64_t>(std::floor(proof.minimum[2]*Q))};
                const std::array<std::int64_t,3> featureMax={
                    static_cast<std::int64_t>(std::ceil(proof.maximum[0]*Q)),
                    static_cast<std::int64_t>(std::ceil(proof.maximum[1]*Q)),
                    static_cast<std::int64_t>(std::ceil(proof.maximum[2]*Q))};
                PassageFeatureBounds.push_back({static_cast<std::uint64_t>(PassageTileFeatures.size()),
                    featureMin,featureMax});
                PassageTileFeatures.push_back({passageIndex,segment,false});
            }
            const auto upperStratum=std::find_if(ResolvedLayout->strates.begin(),
                ResolvedLayout->strates.end(),[&passage](const auto& value)
                    {return value.strateIndex==passage.upperStrateIndex;});
            if(upperStratum!=ResolvedLayout->strates.end())
            {
                std::array<const VoxelForgeCore::ResolvedLayoutAnchorV2*,5> route{};
                std::size_t routeCount=0;
                for(const auto& anchor:upperStratum->anchors)
                    if(anchor.kind=="route_point"&&anchor.values.size()>=3)
                    {
                        if(routeCount<route.size())route[routeCount++]=&anchor;
                        else
                        {
                            std::move(route.begin()+1,route.end(),route.begin());
                            route.back()=&anchor;
                        }
                    }
                if(routeCount>=2)
                {
                    const double mouthReach=13.0*voxelsPerMetre*Q;
                    double minimumZ=std::numeric_limits<double>::infinity();
                    double maximumZ=-std::numeric_limits<double>::infinity();
                    for(std::size_t index=0;index<routeCount;++index)
                    {
                        minimumZ=std::min(minimumZ,static_cast<double>(route[index]->values[2]));
                        maximumZ=std::max(maximumZ,static_cast<double>(route[index]->values[2]));
                    }
                    const double mouthX=passage.upperMouthSubvoxels[0];
                    const double mouthY=passage.upperMouthSubvoxels[1];
                    FPassageProofBound supportProof;
                    supportProof.minimum={(mouthX-mouthReach)/Q,(mouthY-mouthReach)/Q,
                        (minimumZ-3.0*voxelsPerMetre*Q)/Q};
                    supportProof.maximum={(mouthX+mouthReach)/Q,(mouthY+mouthReach)/Q,
                        (maximumZ+3.0*voxelsPerMetre*Q)/Q};
                    PassageProofBounds.push_back(supportProof);
                    const std::array<std::int64_t,3> featureMin={
                        static_cast<std::int64_t>(std::floor(supportProof.minimum[0]*Q)),
                        static_cast<std::int64_t>(std::floor(supportProof.minimum[1]*Q)),
                        static_cast<std::int64_t>(std::floor(supportProof.minimum[2]*Q))};
                    const std::array<std::int64_t,3> featureMax={
                        static_cast<std::int64_t>(std::ceil(supportProof.maximum[0]*Q)),
                        static_cast<std::int64_t>(std::ceil(supportProof.maximum[1]*Q)),
                        static_cast<std::int64_t>(std::ceil(supportProof.maximum[2]*Q))};
                    PassageFeatureBounds.push_back({static_cast<std::uint64_t>(PassageTileFeatures.size()),
                        featureMin,featureMax});
                    PassageTileFeatures.push_back({passageIndex,0,false,true});
                }
            }
        }
        for(const auto& crossing:PassageVoidCrossings)
        {
            if(crossing.passageIndex<PassageColumnSegmentFlags.size())
            {
                auto& flags= crossing.needsColumn
                    ?PassageColumnSegmentFlags[crossing.passageIndex]
                    :PassageShortSpanSegmentFlags[crossing.passageIndex];
                bool surfaceWorldUpper=false;
                if(crossing.passageIndex<ResolvedLayout->passages.size())
                {
                    const std::int32_t strate=ResolvedLayout->passages[
                        crossing.passageIndex].upperStrateIndex;
                    const auto upper=std::find_if(ResolvedLayout->strates.begin(),
                        ResolvedLayout->strates.end(),[strate](const auto& value)
                            {return value.strateIndex==strate;});
                    surfaceWorldUpper=upper!=ResolvedLayout->strates.end()
                        &&upper->passageCapabilities.hasSurfaceLanding;
                }
                const std::size_t shortSpanPadding=!crossing.needsColumn
                    &&surfaceWorldUpper&&!flags.empty()?2:0;
                const std::size_t first=std::min(crossing.firstSegment>shortSpanPadding
                    ?crossing.firstSegment-shortSpanPadding:0,flags.size());
                const std::size_t last=std::min(crossing.lastSegment+shortSpanPadding,
                    flags.empty()?0:flags.size()-1);
                if(!flags.empty()&&first<=last)
                    std::fill(flags.begin()+first,flags.begin()+last+1,1);
            }
            if(!crossing.needsColumn)continue;
            FPassageProofBound proof;
            const double radius=static_cast<double>(crossing.maximumRadiusSubvoxels)/Q;
            proof.minimum={crossing.centerXSubvoxels/Q-radius,crossing.centerYSubvoxels/Q-radius,
                crossing.bottomZSubvoxels/Q};
            proof.maximum={crossing.centerXSubvoxels/Q+radius,crossing.centerYSubvoxels/Q+radius,
                crossing.topZSubvoxels/Q};
            PassageProofBounds.push_back(proof);
            const std::array<std::int64_t,3> featureMin={
                static_cast<std::int64_t>(std::floor(proof.minimum[0]*Q)),
                static_cast<std::int64_t>(std::floor(proof.minimum[1]*Q)),
                static_cast<std::int64_t>(std::floor(proof.minimum[2]*Q))};
            const std::array<std::int64_t,3> featureMax={
                static_cast<std::int64_t>(std::ceil(proof.maximum[0]*Q)),
                static_cast<std::int64_t>(std::ceil(proof.maximum[1]*Q)),
                static_cast<std::int64_t>(std::ceil(proof.maximum[2]*Q))};
            PassageFeatureBounds.push_back({static_cast<std::uint64_t>(PassageTileFeatures.size()),
                featureMin,featureMax});
            PassageTileFeatures.push_back({crossing.passageIndex,0,true});
        }
        PassageHasShortSpanFlags.assign(PassageShortSpanSegmentFlags.size(),0);
        for(std::size_t passageIndex=0;passageIndex<PassageShortSpanSegmentFlags.size();++passageIndex)
            PassageHasShortSpanFlags[passageIndex]=static_cast<std::uint8_t>(
                std::any_of(PassageShortSpanSegmentFlags[passageIndex].begin(),
                    PassageShortSpanSegmentFlags[passageIndex].end(),
                    [](std::uint8_t flag){return flag!=0;}));
        for(std::size_t i=0;i<PassageFeatureBounds.size();++i)
            PassageFeatureOrder.push_back(static_cast<std::uint32_t>(i));
        for(const auto& feature:PassageFeatureBounds)
            for(std::size_t axis=0;axis<3;++axis)
                PassageFeatureBoundsFailOpen=PassageFeatureBoundsFailOpen
                    ||feature.minimumSubvoxels[axis]>feature.maximumSubvoxels[axis];
        if(!PassageFeatureOrder.empty())BuildPassageFeatureNode(0,PassageFeatureOrder.size());
        if(!PassageProofBounds.empty())BuildPassageProofNode(0,PassageProofBounds.size());
    }

    double PassageNearestNodeLowerBound(const FPassageNearestNode& node,
        double qx,double qy,double qz) const
    {
        const double dx=qx<node.minimum[0]?node.minimum[0]-qx:qx>node.maximum[0]?qx-node.maximum[0]:0.0;
        const double dy=qy<node.minimum[1]?node.minimum[1]-qy:qy>node.maximum[1]?qy-node.maximum[1]:0.0;
        const double dz=qz<node.minimum[2]?node.minimum[2]-qz:qz>node.maximum[2]?qz-node.maximum[2]:0.0;
        return DeterministicSqrt(dx*dx+dy*dy+dz*dz)-node.maximumRadius-1.0e-6;
    }

    template<typename FVisit>
    void VisitNearestPassageSpatialNode(std::size_t passageIndex,int nodeIndex,
        std::size_t first,std::size_t end,double qx,double qy,double qz,int priority,
        double& bestDistance,FVisit& visit) const
    {
        if(passageIndex>=PassageNearestNodes.size()||nodeIndex<0)return;
        const auto& nodes=PassageNearestNodes[passageIndex];
        const auto& node=nodes[static_cast<std::size_t>(nodeIndex)];
        const auto candidate=std::lower_bound(node.segments.begin(),node.segments.end(),first);
        if(candidate==node.segments.end()||*candidate>=end)return;
        const double lowerBound=PassageNearestNodeLowerBound(node,qx,qy,qz);
        if(lowerBound>bestDistance)return;
        if(node.left<0)
        {
            for(auto it=candidate;it!=node.segments.end()&&*it<end;++it)
                visit(*it,priority);
            return;
        }
        const double leftBound=PassageNearestNodeLowerBound(
            nodes[static_cast<std::size_t>(node.left)],qx,qy,qz);
        const double rightBound=PassageNearestNodeLowerBound(
            nodes[static_cast<std::size_t>(node.right)],qx,qy,qz);
        const int nearChild=leftBound<=rightBound?node.left:node.right;
        const int farChild=leftBound<=rightBound?node.right:node.left;
        VisitNearestPassageSpatialNode(passageIndex,nearChild,first,end,qx,qy,qz,
            priority,bestDistance,visit);
        VisitNearestPassageSpatialNode(passageIndex,farChild,first,end,qx,qy,qz,
            priority,bestDistance,visit);
    }

    template<typename FVisit>
    void VisitNearestPassageSegmentRange(std::size_t passageIndex,std::ptrdiff_t first,
        std::ptrdiff_t last,double qx,double qy,double qz,int priority,
        double& bestDistance,FVisit&& visit) const
    {
        if(first>last||passageIndex>=PassageNearestNodes.size()
            ||PassageNearestNodes[passageIndex].empty())return;
        auto callback=std::forward<FVisit>(visit);
        VisitNearestPassageSpatialNode(passageIndex,0,static_cast<std::size_t>(first),
            static_cast<std::size_t>(last+1),qx,qy,qz,priority,bestDistance,callback);
    }

    bool PassagePotentialWithinNode(std::size_t passageIndex,int nodeIndex,
        std::size_t first,std::size_t end,double qx,double qy,double qz,
        double signedDistanceLimit) const
    {
        if(passageIndex>=PassageNearestNodes.size()||nodeIndex<0)return false;
        const auto& nodes=PassageNearestNodes[passageIndex];
        const auto& node=nodes[static_cast<std::size_t>(nodeIndex)];
        const auto candidate=std::lower_bound(node.segments.begin(),node.segments.end(),first);
        if(candidate==node.segments.end()||*candidate>=end)return false;
        if(PassageNearestNodeLowerBound(node,qx,qy,qz)>signedDistanceLimit)return false;
        if(node.left<0)return true;
        const double leftBound=PassageNearestNodeLowerBound(
            nodes[static_cast<std::size_t>(node.left)],qx,qy,qz);
        const double rightBound=PassageNearestNodeLowerBound(
            nodes[static_cast<std::size_t>(node.right)],qx,qy,qz);
        const int nearChild=leftBound<=rightBound?node.left:node.right;
        const int farChild=leftBound<=rightBound?node.right:node.left;
        return PassagePotentialWithinNode(passageIndex,nearChild,first,end,qx,qy,qz,
                signedDistanceLimit)
            ||PassagePotentialWithinNode(passageIndex,farChild,first,end,qx,qy,qz,
                signedDistanceLimit);
    }

    bool PassageMayAffectDensity(std::size_t passageIndex,std::ptrdiff_t carveBegin,
        std::ptrdiff_t carveEnd,std::ptrdiff_t lowerMouthIndex,
        std::ptrdiff_t mouthSearchBegin,std::ptrdiff_t mouthSearchEnd,std::ptrdiff_t lastIndex,
        double qx,double qy,double qz,double signedDistanceLimit) const
    {
        const auto possible=[&](std::ptrdiff_t first,std::ptrdiff_t last)
        {
            return first<=last&&passageIndex<PassageNearestNodes.size()
                &&!PassageNearestNodes[passageIndex].empty()
                &&PassagePotentialWithinNode(passageIndex,0,static_cast<std::size_t>(first),
                    static_cast<std::size_t>(last+1),qx,qy,qz,signedDistanceLimit);
        };
        return possible(carveBegin,carveEnd)
            ||possible(0,std::min<std::ptrdiff_t>(8,lowerMouthIndex)-1)
            ||possible(mouthSearchBegin,mouthSearchEnd-1)
            ||possible(lowerMouthIndex,lastIndex-1);
    }

    bool PassagePlayerCapsuleBlocksSupportNode(std::size_t passageIndex,int nodeIndex,
        std::size_t first,std::size_t end,double qx,double qy,double qz,double qPerMetre,
        double minimumClearanceMetres) const
    {
        if(passageIndex>=PassageNearestNodes.size()||nodeIndex<0)return false;
        const auto& nodes=PassageNearestNodes[passageIndex];
        const auto& node=nodes[static_cast<std::size_t>(nodeIndex)];
        auto candidate=std::lower_bound(node.segments.begin(),node.segments.end(),first);
        if(candidate==node.segments.end()||*candidate>=end)return false;
        const double xyReach=0.39*qPerMetre;
        if(qx+xyReach<node.minimum[0]||qx-xyReach>node.maximum[0]
            ||qy+xyReach<node.minimum[1]||qy-xyReach>node.maximum[1])return false;
        const double minimumCenterZ=node.minimum[2]-node.maximumRadius+0.20*qPerMetre;
        const double maximumCenterZ=node.maximum[2]+2.06*qPerMetre;
        if(qz<minimumCenterZ||qz>maximumCenterZ)return false;
        const auto& passage=ResolvedLayout->passages[passageIndex];
        if(node.left<0)
        {
            for(auto it=candidate;it!=node.segments.end()&&*it<end;++it)
            {
                const std::size_t index=*it;
                const auto& a=passage.controlPoints[index];const auto& b=passage.controlPoints[index+1];
                const double ax=a.positionSubvoxels[0],ay=a.positionSubvoxels[1],az=a.positionSubvoxels[2];
                const double dx=static_cast<double>(b.positionSubvoxels[0])-ax;
                const double dy=static_cast<double>(b.positionSubvoxels[1])-ay;
                const double dz=static_cast<double>(b.positionSubvoxels[2])-az;
                const double lengthSq=dx*dx+dy*dy+dz*dz;
                if(lengthSq<=0.0)continue;
                const double horizontalLengthSq=dx*dx+dy*dy;
                const double t=horizontalLengthSq>0.0
                    ?std::clamp(((qx-ax)*dx+(qy-ay)*dy)/horizontalLengthSq,0.0,1.0):0.0;
                const double centerX=ax+t*dx,centerY=ay+t*dy;
                const double centerZ=az+t*dz-(static_cast<double>(a.radiusSubvoxels)
                    +t*(static_cast<double>(b.radiusSubvoxels)-a.radiusSubvoxels))+1.13*qPerMetre;
                const double horizontalX=qx-centerX,horizontalY=qy-centerY;
                const double vertical=std::max(0.0,std::abs(qz-centerZ)-0.54*qPerMetre);
                const double distance=DeterministicSqrt(horizontalX*horizontalX+horizontalY*horizontalY
                    +vertical*vertical)-0.34*qPerMetre;
                if(distance<minimumClearanceMetres*qPerMetre)return true;
            }
            return false;
        }
        return PassagePlayerCapsuleBlocksSupportNode(passageIndex,node.left,first,end,
                qx,qy,qz,qPerMetre,minimumClearanceMetres)
            ||PassagePlayerCapsuleBlocksSupportNode(passageIndex,node.right,first,end,
                qx,qy,qz,qPerMetre,minimumClearanceMetres);
    }

    bool PassagePlayerCapsuleBlocksSupport(std::size_t passageIndex,
        std::ptrdiff_t carveBegin,std::ptrdiff_t carveEnd,std::ptrdiff_t lowerMouthIndex,
        std::ptrdiff_t mouthSearchBegin,std::ptrdiff_t mouthSearchEnd,std::ptrdiff_t lastIndex,
        double qx,double qy,double qz,double qPerMetre,double minimumClearanceMetres) const
    {
        const auto blocked=[&](std::ptrdiff_t first,std::ptrdiff_t last)
        {
            return first<=last&&PassagePlayerCapsuleBlocksSupportNode(passageIndex,0,
                static_cast<std::size_t>(first),static_cast<std::size_t>(last+1),
                qx,qy,qz,qPerMetre,minimumClearanceMetres);
        };
        return blocked(carveBegin,carveEnd)
            ||blocked(0,std::min<std::ptrdiff_t>(8,lowerMouthIndex)-1)
            ||blocked(mouthSearchBegin,mouthSearchEnd-1)
            ||blocked(lowerMouthIndex,lastIndex-1);
    }

    bool PassageProofBoundsOverlapNode(int nodeIndex,const double minimum[3],
        const double maximum[3]) const
    {
        if(nodeIndex<0)return false;
        const auto& node=PassageProofNodes[static_cast<std::size_t>(nodeIndex)];
        for(std::size_t axis=0;axis<3;++axis)
            if(node.maximum[axis]<minimum[axis]||node.minimum[axis]>maximum[axis])return false;
        if(node.left<0)
        {
            for(std::size_t index=node.first;index<node.end;++index)
            {
                bool overlap=true;
                for(std::size_t axis=0;axis<3;++axis)
                    overlap=overlap&&PassageProofBounds[index].maximum[axis]>=minimum[axis]
                        &&PassageProofBounds[index].minimum[axis]<=maximum[axis];
                if(overlap)return true;
            }
            return false;
        }
        return PassageProofBoundsOverlapNode(node.left,minimum,maximum)
            ||PassageProofBoundsOverlapNode(node.right,minimum,maximum);
    }

    bool IsPassageColumnSegment(std::size_t PassageIndex,std::size_t SegmentIndex) const
    {
        return PassageIndex<PassageColumnSegmentFlags.size()
            &&SegmentIndex<PassageColumnSegmentFlags[PassageIndex].size()
            &&PassageColumnSegmentFlags[PassageIndex][SegmentIndex]!=0;
    }

    bool IsPassageShortSpanSegment(std::size_t PassageIndex,std::size_t SegmentIndex) const
    {
        return PassageIndex<PassageShortSpanSegmentFlags.size()
            &&SegmentIndex<PassageShortSpanSegmentFlags[PassageIndex].size()
            &&PassageShortSpanSegmentFlags[PassageIndex][SegmentIndex]!=0;
    }

    bool PassageHasShortSpanSegments(std::size_t PassageIndex) const
    {
        return PassageIndex<PassageHasShortSpanFlags.size()
            &&PassageHasShortSpanFlags[PassageIndex]!=0;
    }

    double PassageBridgeDeckOffsetMetres(std::size_t PassageIndex,
        std::size_t SegmentIndex) const
    {
        (void)PassageIndex;(void)SegmentIndex;
        return 0.13;
    }

    double PassageBridgeSignedDistance(std::size_t PassageIndex,std::size_t SegmentIndex,
        float X,float Y,float Z) const
    {
        if(!ResolvedLayout||PassageIndex>=ResolvedLayout->passages.size())
            return std::numeric_limits<double>::infinity();
        const auto& passage=ResolvedLayout->passages[PassageIndex];
        if(SegmentIndex+1>=passage.controlPoints.size())
            return std::numeric_limits<double>::infinity();
        constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double qPerMetre=Q*1000000.0/std::max<std::uint32_t>(1,
            ResolvedLayout->coreVoxelSizeMicrometres);
        const auto& a=passage.controlPoints[SegmentIndex];
        const auto& b=passage.controlPoints[SegmentIndex+1];
        const auto upperStratum=std::find_if(ResolvedLayout->strates.begin(),
            ResolvedLayout->strates.end(),[&passage](const auto& value)
                {return value.strateIndex==passage.upperStrateIndex;});
        const bool surfaceWorldUpper=upperStratum!=ResolvedLayout->strates.end()
            &&upperStratum->passageCapabilities.hasSurfaceLanding;
        const double ax=static_cast<double>(a.positionSubvoxels[0]);
        const double ay=static_cast<double>(a.positionSubvoxels[1]);
        const double dx=static_cast<double>(b.positionSubvoxels[0])-ax;
        const double dy=static_cast<double>(b.positionSubvoxels[1])-ay;
        const double horizontalLengthSq=dx*dx+dy*dy;
        const double qx=static_cast<double>(X)*Q,qy=static_cast<double>(Y)*Q;
        const double qz=static_cast<double>(Z)*Q;
        const double t=horizontalLengthSq>0.0
            ?std::clamp(((qx-ax)*dx+(qy-ay)*dy)/horizontalLengthSq,0.0,1.0):0.0;
        const double centerX=ax+t*dx,centerY=ay+t*dy;
        const double centerZ=a.positionSubvoxels[2]+t*(
            static_cast<double>(b.positionSubvoxels[2])-a.positionSubvoxels[2]);
        const double radius=a.radiusSubvoxels+t*(
            static_cast<double>(b.radiusSubvoxels)-a.radiusSubvoxels);
        // Embed the deck 13 cm above the bore bottom: within the 25 cm support
        // probe, while leaving 16 cm between it and the capsule's lowest sample.
        const double floorQ=centerZ-radius
            +PassageBridgeDeckOffsetMetres(PassageIndex,SegmentIndex)*qPerMetre;
        const double relief=std::clamp(static_cast<double>(VF_FieldSurfaceRelief(X,Y,Z,
            static_cast<std::uint32_t>(Owner?Owner->Seed:0))),-1.0,1.0);
        const double halfWidth=(surfaceWorldUpper?3.65+0.10*relief:3.30+0.20*relief)
            *qPerMetre;
        const double thickness=(4.0+1.0*relief)*qPerMetre;
        const double horizontalDistance=DeterministicSqrt((qx-centerX)*(qx-centerX)
            +(qy-centerY)*(qy-centerY));
        const double sideDistance=horizontalDistance-halfWidth;
        const double topDistance=qz-floorQ;
        const double bottomDistance=floorQ-thickness-qz;
        const double verticalDistance=std::max(topDistance,bottomDistance);
        const double outside=DeterministicSqrt(
            std::max(sideDistance,0.0)*std::max(sideDistance,0.0)
            +std::max(verticalDistance,0.0)*std::max(verticalDistance,0.0));
        const double inside=std::min(std::max(sideDistance,verticalDistance),0.0);
        return outside+inside;
    }

    double PassageColumnSignedDistance(const FStandalonePassageVoidCrossing& crossing,
        float X,float Y,float Z) const
    {
        if(crossing.maximumRadiusSubvoxels<=0||crossing.topZSubvoxels
            <=crossing.bottomZSubvoxels)return std::numeric_limits<double>::infinity();
        constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double qPerMetre=Q*1000000.0/std::max<std::uint32_t>(1,
            ResolvedLayout?ResolvedLayout->coreVoxelSizeMicrometres:250000u);
        const double qx=static_cast<double>(X)*Q,qy=static_cast<double>(Y)*Q,
            qz=static_cast<double>(Z)*Q;
        const double dx=qx-crossing.centerXSubvoxels;
        const double dy=qy-crossing.centerYSubvoxels;
        const double maximumRadius=static_cast<double>(crossing.maximumRadiusSubvoxels);
        const double horizontalSquared=dx*dx+dy*dy;
        if(horizontalSquared>maximumRadius*maximumRadius)
            return DeterministicSqrt(horizontalSquared)-maximumRadius;
        if(qz>crossing.topZSubvoxels)
            return qz-crossing.topZSubvoxels;
        if(qz<crossing.bottomZSubvoxels)
            return crossing.bottomZSubvoxels-qz;
        // The lower-strate route is already walkable in its native field and binds
        // directly to the passage mouth. Preserve that player capsule as the column
        // flares into the ground, so the pillar joins the route instead of sealing it.
        if(ResolvedLayout&&crossing.passageIndex<ResolvedLayout->passages.size()
            &&qz<crossing.bottomZSubvoxels+18.0*qPerMetre)
        {
            const auto& passage=ResolvedLayout->passages[crossing.passageIndex];
            const auto lower=std::find_if(ResolvedLayout->strates.begin(),
                ResolvedLayout->strates.end(),[&](const auto& value)
                    {return value.strateIndex==passage.lowerStrateIndex;});
            if(lower!=ResolvedLayout->strates.end())
            {
                const double capsuleRadius=0.37*qPerMetre;
                const double capsuleHalfHeight=0.86*qPerMetre;
                const double capsuleRadiusSquared=capsuleRadius*capsuleRadius;
                const VoxelForgeCore::ResolvedLayoutAnchorV2* previous=nullptr;
                for(const auto& anchor:lower->anchors)
                {
                    if(anchor.kind!="route_point"||anchor.values.size()<3)continue;
                    if(previous)
                    {
                        const double ax=previous->values[0],ay=previous->values[1];
                        const double dx=static_cast<double>(anchor.values[0])-ax;
                        const double dy=static_cast<double>(anchor.values[1])-ay;
                        const double lengthSquared=dx*dx+dy*dy;
                        const double t=lengthSquared>0.0?std::clamp(
                            ((qx-ax)*dx+(qy-ay)*dy)/lengthSquared,0.0,1.0):0.0;
                        const double routeX=ax+t*dx,routeY=ay+t*dy;
                        const double routeZ=previous->values[2]+t*(
                            static_cast<double>(anchor.values[2])-previous->values[2]);
                        const double routeDx=qx-routeX,routeDy=qy-routeY;
                        if(routeDx*routeDx+routeDy*routeDy<=capsuleRadiusSquared
                            &&std::abs(qz-routeZ)<=capsuleHalfHeight)
                            return maximumRadius+qPerMetre;
                    }
                    previous=&anchor;
                }
            }
        }

        const double height=static_cast<double>(crossing.topZSubvoxels
            -crossing.bottomZSubvoxels);
        const double t=std::clamp((crossing.topZSubvoxels-qz)/height,0.0,1.0);
        const auto smoothStep=[](double value)
        {
            value=std::clamp(value,0.0,1.0);
            return value*value*(3.0-2.0*value);
        };
        const float z=static_cast<float>(Z);
        const float scaledZ=z*0.12f;
        const float driftX=VF_FieldSurfaceRelief(0.0f,0.0f,scaledZ,
            static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x434f4c58u);
        const float driftY=VF_FieldSurfaceRelief(0.0f,0.0f,scaledZ,
            static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x434f4c59u);
        const double axisX=crossing.centerXSubvoxels
            +std::clamp(static_cast<double>(driftX),-1.0,1.0)*0.35*qPerMetre;
        const double axisY=crossing.centerYSubvoxels
            +std::clamp(static_cast<double>(driftY),-1.0,1.0)*0.35*qPerMetre;
        const double centerDx=qx-axisX,centerDy=qy-axisY;
        const double radialDistance=DeterministicSqrt(centerDx*centerDx+centerDy*centerDy);
        const float broadRelief=VF_FieldSurfaceRelief(X*0.12f,Y*0.12f,Z*0.12f,
            static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x434f4c52u);
        const float surfaceRelief=VF_FieldSurfaceRelief(X,Y,Z,
            static_cast<std::uint32_t>(Owner?Owner->Seed:0)^0x434f4c53u);
        const double baseFlare=6.0*qPerMetre*smoothStep((t-0.82)/0.18);
        const double ceilingFlare=2.0*qPerMetre*(1.0-smoothStep(t/0.075));
        const double irregularity=1.25*qPerMetre
            +std::clamp(static_cast<double>(broadRelief),-1.0,1.0)*1.10*qPerMetre
            +std::clamp(static_cast<double>(surfaceRelief),-1.0,1.0)*0.35*qPerMetre;
        const double radius=static_cast<double>(crossing.minimumRadiusSubvoxels)
            +std::max(0.15*qPerMetre,irregularity)+baseFlare+ceilingFlare;
        const double radialDistanceField=radialDistance-radius;
        const double topDistance=qz-crossing.topZSubvoxels;
        const double bottomDistance=crossing.bottomZSubvoxels-qz;
        const double verticalDistance=std::max(topDistance,bottomDistance);
        const double outside=DeterministicSqrt(
            std::max(radialDistanceField,0.0)*std::max(radialDistanceField,0.0)
            +std::max(verticalDistance,0.0)*std::max(verticalDistance,0.0));
        const double inside=std::min(std::max(radialDistanceField,verticalDistance),0.0);
        return outside+inside;
    }

    float NativePassageDensityAt(float X,float Y,float Z) const
    {
        float density=0.0f;
        if(!NativeFloatingIslandDensityAt(X,Y,Z,density)
            &&!NativeSurfaceDensityAt(X,Y,Z,density))
        {
            if(UsesLegacySurfaceField(X,Y,Z)&&Owner&&Owner->Generator)
            {
                if(!LegacyGeneratorDensityAt(X,Y,Z,density))
                    density=Owner->Generator->GetDensityAt(X,Y,Z);
            }
            else
                density=AnalyticDensityAt(X,Y,Z,true,nullptr,nullptr,nullptr,
                    false,false);
        }
        return ApplyResolvedStrateBoundaryBand(density,X,Y,Z);
    }

    void BuildPassageVoidCrossingPlan()
    {
        BuildResolvedBoundaryZIntervals();
        PassageVoidCrossings.clear();
        if(!Owner||!ResolvedLayout||ResolvedLayout->passages.empty())return;
        if(!Owner->PassageVoidCrossingCache)
        {BuildPassageSpatialIndices();return;}
        auto& cache=*Owner->PassageVoidCrossingCache;
        std::lock_guard<std::mutex> lock(cache.mutex);
        const std::string cacheKey=ResolvedLayout->stableIdentity+"/passage-void-columns-v1";
        const auto cached=cache.byLayout.find(cacheKey);
        if(cached!=cache.byLayout.end())
        {PassageVoidCrossings=cached->second;BuildPassageSpatialIndices();return;}

        constexpr double Q=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double qPerMetre=Q*1000000.0/std::max<std::uint32_t>(1,
            ResolvedLayout->coreVoxelSizeMicrometres);
        constexpr std::array<std::array<double,2>,5> supportOffsets{{
            {{0.0,0.0}},{{0.45,0.0}},{{-0.45,0.0}},{{0.0,0.45}},{{0.0,-0.45}}}};
        constexpr std::array<double,2> supportDepthsMetres{{0.125,0.25}};
        constexpr double shortSpanMaximumMetres=12.5; // 2.5 x the 5 m legacy support thickness.
        struct FPathSample
        {
            std::size_t segment=0;
            std::array<double,4> point{};
            bool nativeSupported=false;
        };
        const auto nativeSupportedAt=[&](const std::array<double,4>& point)
        {
            const double floorQ=point[2]-point[3]+0.13*qPerMetre;
            std::uint32_t supported=0;
            for(const auto& offset:supportOffsets)
            {
                bool hasSolid=false;
                for(const double depth:supportDepthsMetres)
                {
                    const double sampleZ=floorQ-depth*qPerMetre;
                    const float density=NativePassageDensityAt(
                        static_cast<float>((point[0]+offset[0]*qPerMetre)/Q),
                        static_cast<float>((point[1]+offset[1]*qPerMetre)/Q),
                        static_cast<float>(sampleZ/Q));
                    if(density<0.0f){hasSolid=true;break;}
                }
                supported+=hasSolid;
            }
            return supported>=3;
        };
        for(std::size_t passageIndex=0;passageIndex<ResolvedLayout->passages.size();
            ++passageIndex)
        {
            const auto& passage=ResolvedLayout->passages[passageIndex];
            const auto upperStratum=std::find_if(ResolvedLayout->strates.begin(),
                ResolvedLayout->strates.end(),[&passage](const auto& value)
                    {return value.strateIndex==passage.upperStrateIndex;});
            const bool surfaceWorldUpper=upperStratum!=ResolvedLayout->strates.end()
                &&upperStratum->passageCapabilities.hasSurfaceLanding;
            if(passage.controlPoints.size()<2)continue;
            std::vector<FPathSample> samples;
            samples.reserve(passage.controlPoints.size()*2);
            const auto pointAt=[&](std::size_t segment,double t)
            {
                const auto& a=passage.controlPoints[segment];
                const auto& b=passage.controlPoints[segment+1];
                FPathSample sample;sample.segment=segment;
                for(std::size_t axis=0;axis<3;++axis)
                    sample.point[axis]=a.positionSubvoxels[axis]+t*(
                        static_cast<double>(b.positionSubvoxels[axis])
                            -a.positionSubvoxels[axis]);
                sample.point[3]=a.radiusSubvoxels+t*(
                    static_cast<double>(b.radiusSubvoxels)-a.radiusSubvoxels);
                sample.nativeSupported=nativeSupportedAt(sample.point);
                return sample;
            };
            samples.push_back(pointAt(0,0.0));
            for(std::size_t segment=0;segment+1<passage.controlPoints.size();++segment)
            {
                const auto& a=passage.controlPoints[segment];
                const auto& b=passage.controlPoints[segment+1];
                const double dx=static_cast<double>(b.positionSubvoxels[0])-a.positionSubvoxels[0];
                const double dy=static_cast<double>(b.positionSubvoxels[1])-a.positionSubvoxels[1];
                const double dz=static_cast<double>(b.positionSubvoxels[2])-a.positionSubvoxels[2];
                const double lengthMetres=DeterministicSqrt(dx*dx+dy*dy+dz*dz)/qPerMetre;
                const std::size_t intervals=std::max<std::size_t>(1,
                    static_cast<std::size_t>(std::ceil(lengthMetres/0.5)));
                for(std::size_t step=1;step<=intervals;++step)
                    samples.push_back(pointAt(segment,static_cast<double>(step)/intervals));
            }
            std::size_t cursor=0;
            while(cursor<samples.size())
            {
                if(samples[cursor].nativeSupported){++cursor;continue;}
                const std::size_t gapBegin=cursor;
                while(cursor<samples.size()&&!samples[cursor].nativeSupported)++cursor;
                const std::size_t gapEnd=cursor-1;
                const std::size_t startSample=gapBegin>0?gapBegin-1:gapBegin;
                const std::size_t endSample=cursor<samples.size()?cursor:samples.size()-1;
                double gapLength=0.0;
                for(std::size_t index=startSample+1;index<=endSample;++index)
                {
                    const auto& a=samples[index-1].point;
                    const auto& b=samples[index].point;
                    const double dx=b[0]-a[0],dy=b[1]-a[1],dz=b[2]-a[2];
                    gapLength+=DeterministicSqrt(dx*dx+dy*dy+dz*dz)/qPerMetre;
                }
                if(gapLength<1.0)continue;
                FStandalonePassageVoidCrossing crossing;
                crossing.passageIndex=passageIndex;
                crossing.firstSegment=samples[startSample].segment;
                crossing.lastSegment=samples[endSample].segment;
                crossing.unsupportedSamples=gapEnd-gapBegin+1;
                crossing.unsupportedLengthMetres=gapLength;
                crossing.startPoint=samples[startSample].point;
                crossing.endPoint=samples[endSample].point;
                crossing.connectedAtStart=gapBegin>0&&samples[startSample].nativeSupported;
                crossing.connectedAtEnd=cursor<samples.size()&&samples[endSample].nativeSupported;
                crossing.needsColumn=gapLength>shortSpanMaximumMetres;
                if(crossing.needsColumn&&passage.controlPoints.size()>1)
                    crossing.lastSegment=std::min(crossing.lastSegment+1,
                        passage.controlPoints.size()-2);
                if(crossing.needsColumn)
                {
                    std::int64_t sumX=0,sumY=0;
                    std::uint64_t centerSamples=0;
                    for(std::size_t index=gapBegin;index<=gapEnd;++index)
                    {
                        sumX+=static_cast<std::int64_t>(std::llround(samples[index].point[0]));
                        sumY+=static_cast<std::int64_t>(std::llround(samples[index].point[1]));
                        ++centerSamples;
                    }
                    crossing.centerXSubvoxels=centerSamples>0
                        ?static_cast<std::int64_t>(std::llround(static_cast<double>(sumX)/centerSamples)):0;
                    crossing.centerYSubvoxels=centerSamples>0
                        ?static_cast<std::int64_t>(std::llround(static_cast<double>(sumY)/centerSamples)):0;
                    for(const auto& stratum:ResolvedLayout->strates)
                        if(stratum.strateIndex==passage.upperStrateIndex
                            &&stratum.passageCapabilities.usePassageAnchorForColumns)
                            for(const auto& anchor:stratum.anchors)
                                if(anchor.kind=="passage_anchor"&&anchor.values.size()>=2)
                                {
                                    crossing.centerXSubvoxels=anchor.values[0];
                                    crossing.centerYSubvoxels=anchor.values[1];
                                    break;
                                }
                    double maximumOffsetSubvoxels=0.0;
                    double maximumBoreSubvoxels=0.0;
                    double minimumCrossingZ=std::min(crossing.startPoint[2],crossing.endPoint[2]);
                    double maximumCrossingZ=std::max(crossing.startPoint[2],crossing.endPoint[2]);
                    for(std::size_t sampleIndex=0;sampleIndex<samples.size();++sampleIndex)
                    {
                        const auto& sample=samples[sampleIndex];
                        // The audit and density field use whole control segments, including
                        // the neighboring segments that extend the column through its caps.
                        // Size the column from that same segment window instead of only the
                        // unsupported half-metre samples inside the original gap.
                        if(surfaceWorldUpper)
                        {
                            if(sample.segment<crossing.firstSegment
                                ||sample.segment>crossing.lastSegment)continue;
                        }
                        else if(sampleIndex<startSample||sampleIndex>endSample)continue;
                        const auto& point=sample.point;
                        const double dx=point[0]-crossing.centerXSubvoxels;
                        const double dy=point[1]-crossing.centerYSubvoxels;
                        maximumOffsetSubvoxels=std::max(maximumOffsetSubvoxels,
                            DeterministicSqrt(dx*dx+dy*dy));
                        maximumBoreSubvoxels=std::max(maximumBoreSubvoxels,point[3]);
                        if(surfaceWorldUpper)
                        {
                            minimumCrossingZ=std::min(minimumCrossingZ,point[2]);
                            maximumCrossingZ=std::max(maximumCrossingZ,point[2]);
                        }
                    }
                    const double maximumOffsetMetres=maximumOffsetSubvoxels/qPerMetre;
                    const double maximumBoreMetres=maximumBoreSubvoxels/qPerMetre;
                    const double minimumRadiusMetres=maximumOffsetMetres+maximumBoreMetres+2.0;
                    const double nominalRadiusMetres=minimumRadiusMetres+1.25;
                    crossing.maximumRouteOffsetMetres=maximumOffsetMetres;
                    crossing.maximumBoreRadiusMetres=maximumBoreMetres;
                    crossing.minimumRadiusSubvoxels=static_cast<std::int64_t>(std::ceil(
                        minimumRadiusMetres*qPerMetre));
                    crossing.nominalRadiusSubvoxels=static_cast<std::int64_t>(std::llround(
                        nominalRadiusMetres*qPerMetre));
                    crossing.maximumRadiusSubvoxels=crossing.minimumRadiusSubvoxels
                        +static_cast<std::int64_t>(std::ceil(11.25*qPerMetre));
                    crossing.topZSubvoxels=static_cast<std::int64_t>(std::llround(
                        maximumCrossingZ+5.0*qPerMetre));
                    crossing.bottomZSubvoxels=static_cast<std::int64_t>(std::llround(
                        minimumCrossingZ-6.0*qPerMetre));
                }
                PassageVoidCrossings.push_back(crossing);
                if(crossing.needsColumn)
                {
                    const double coreRadius=crossing.nominalRadiusSubvoxels/qPerMetre;
                    const double minimumWall=coreRadius-crossing.maximumRouteOffsetMetres
                        -crossing.maximumBoreRadiusMetres;
                    std::printf("[PassageVoidColumnPlan] id=%s segments=%zu..%zu unsupported_samples=%llu span_m=%.3f threshold_m=%.3f connected=%d/%d axis_m=(%.3f,%.3f) z_m=%.3f..%.3f route_radius_m=%.3f bore_radius_m=%.3f min_radius_m=%.3f nominal_radius_m=%.3f max_radius_m=%.3f nominal_wall_m=%.3f flare_m=6.000 status=%s\n",
                        passage.stableId.c_str(),crossing.firstSegment,crossing.lastSegment,
                        static_cast<unsigned long long>(crossing.unsupportedSamples),gapLength,
                        shortSpanMaximumMetres,static_cast<int>(crossing.connectedAtStart),
                        static_cast<int>(crossing.connectedAtEnd),
                        crossing.centerXSubvoxels/qPerMetre,crossing.centerYSubvoxels/qPerMetre,
                        crossing.topZSubvoxels/qPerMetre,crossing.bottomZSubvoxels/qPerMetre,
                        crossing.maximumRouteOffsetMetres,crossing.maximumBoreRadiusMetres,
                        crossing.minimumRadiusSubvoxels/qPerMetre,coreRadius,
                        crossing.maximumRadiusSubvoxels/qPerMetre,minimumWall,
                        crossing.connectedAtStart&&crossing.connectedAtEnd?"PLANNED":"UNATTACHED");
                }
                else
                    std::printf("[PassageShortGroundedSpanPlan] id=%s segments=%zu..%zu span_m=%.3f threshold_m=%.3f connected=%d/%d width_m=7.300 thickness_m=3.000..5.000 status=%s\n",
                        passage.stableId.c_str(),crossing.firstSegment,crossing.lastSegment,
                        gapLength,shortSpanMaximumMetres,static_cast<int>(crossing.connectedAtStart),
                        static_cast<int>(crossing.connectedAtEnd),
                        crossing.connectedAtStart&&crossing.connectedAtEnd?"PLANNED":"UNATTACHED");
            }
            if(std::none_of(PassageVoidCrossings.begin(),PassageVoidCrossings.end(),
                [passageIndex](const auto& range){return range.passageIndex==passageIndex;}))
                std::printf("[PassageVoidColumnPlan] id=%s crossings=0 status=NOT_REQUIRED\n",
                    passage.stableId.c_str());
        }
        cache.byLayout.emplace(cacheKey,PassageVoidCrossings);
        BuildPassageSpatialIndices();
    }

    static uint64 PackLatticeKey(int32 X,int32 Y,int32 Z)
    {
        constexpr uint64 Mask=0x1FFFFFull;
        return (static_cast<uint64>(static_cast<uint32>(X)&Mask)<<42)
            |(static_cast<uint64>(static_cast<uint32>(Y)&Mask)<<21)
            |(static_cast<uint64>(static_cast<uint32>(Z)&Mask));
    }
    float PackedDensityAt(int32 X,int32 Y,int32 Z,bool bRock,float FX,float FY,float FZ) const
    {
        const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]+static_cast<size_t>(X-Min[0]);
        const size_t Zi=static_cast<size_t>(Z-Min[2]);
        const size_t Word=Column*WordsPerZ+(Zi>>6);
        const uint64 Mask=uint64{1}<<(Zi&63u);
        if(CandidateWords[Word]&Mask)
        {
            const size_t Node=Zi*static_cast<size_t>(Size[1])*Size[0]+Column;
            const int16 Proxy=SurfaceDistanceQ[Node];
            float Density=static_cast<float>(Proxy)*(1.0f/256.0f);
            if((Density<0.0f)!=bRock)
                Density=(bRock?-1.0f:1.0f)*std::max(std::abs(Density),1.0f/256.0f);
            return ApplyEditBrushes(ApplyResolvedStrateComposition(Density,FX,FY,FZ),FX,FY,FZ);
        }
        // Match the fixed fallback to the edge of the stored proxy band. The
        // displacement is tapered to zero there, so this avoids a magnitude
        // jump along the candidate bit-mask boundary.
        constexpr float ProxyBandEdge=DetailSupremum+0.125f;
        return ApplyEditBrushes(ApplyResolvedStrateComposition(
            bRock?-ProxyBandEdge:ProxyBandEdge,FX,FY,FZ),FX,FY,FZ);
    }

    float AnalyticDensityAt(float X,float Y,float Z,bool bClampNearZero=true,
                            float* OutDetailDisplacement=nullptr,
                            float* OutCaveInfluence=nullptr,
                            float* OutFloorInfluence=nullptr,
                            bool bApplyEdits=true,bool bApplyComposition=true) const
    {
        if(SharedDensitySource)return SharedDensitySource->AnalyticDensityAt(X,Y,Z,
            bClampNearZero,OutDetailDisplacement,OutCaveInfluence,OutFloorInfluence,
            bApplyEdits,bApplyComposition);
        if(OutDetailDisplacement)*OutDetailDisplacement=0.0f;
        if(OutCaveInfluence)*OutCaveInfluence=0.0f;
        if(OutFloorInfluence)*OutFloorInfluence=0.0f;
        float IslandDensity=0.0f;
        if(NativeFloatingIslandDensityAt(X,Y,Z,IslandDensity))
        {
            const float composed=bApplyComposition
                ?ApplyResolvedStrateComposition(IslandDensity,X,Y,Z):IslandDensity;
            return bApplyEdits?ApplyEditBrushes(composed,X,Y,Z):composed;
        }
        if(UsesLegacySurfaceField(X,Y,Z))
        {
            float NativeDensity=0.0f;
            if(NativeSurfaceDensityAt(X,Y,Z,NativeDensity))
            {
                if(bApplyComposition)
                    NativeDensity=ApplyResolvedStrateComposition(NativeDensity,X,Y,Z);
                return bApplyEdits?ApplyEditBrushes(NativeDensity,X,Y,Z):NativeDensity;
            }
            float Density=0.0f;
            if(!LegacyGeneratorDensityAt(X,Y,Z,Density))
                Density=Owner->Generator->GetDensityAt(X,Y,Z);
            const float composed=bApplyComposition
                ?ApplyResolvedStrateComposition(Density,X,Y,Z):Density;
            return bApplyEdits?ApplyEditBrushes(composed,X,Y,Z):composed;
        }
        const bool bInsideFine=X>=Min[0]&&X<=Max[0]&&Y>=Min[1]&&Y<=Max[1]
            &&Z>=Min[2]&&Z<=Max[2];
        if(!bInsideFine)
        {
            bool bCriticalAir=false;
            float RockDistance=CoarseRockDistance(X,Y,Z,&bCriticalAir);
            if(bCriticalAir)RockDistance=std::min(RockDistance,-1.0f/16.0f);
            const bool bRock=RockDistance>=0.0f;
            float Density=-RockDistance;
            if((Density<0.0f)!=bRock||(bClampNearZero&&std::abs(Density)<0.05f))
                Density=(bRock?-1.0f:1.0f)*std::max(std::abs(Density),
                    bClampNearZero?0.05f:1.0e-7f);
            const float composed=bApplyComposition
                ?ApplyResolvedStrateComposition(Density,X,Y,Z):Density;
            return bApplyEdits?ApplyEditBrushes(composed,X,Y,Z):composed;
        }
        ESurfaceFamily SurfaceFamily=ESurfaceFamily::Strata;float SurfaceSDF=100000.0f;
        bool bFloorSurface=false,bCriticalAir=false;float CaveInfluence=0.0f,FloorInfluence=0.0f;
        float PassageInfluence=0.0f;
        float RockDistance=EffectiveRockDistance(X,Y,Z,&SurfaceFamily,&SurfaceSDF,
            &bFloorSurface,&CaveInfluence,&FloorInfluence,&bCriticalAir,nullptr,false,
            &PassageInfluence);
        if(OutCaveInfluence)*OutCaveInfluence=CaveInfluence;
        if(OutFloorInfluence)*OutFloorInfluence=FloorInfluence;
        if(bInsideFine&&DetailVariant!=EDetailVariant::Smooth
            &&std::abs(RockDistance)<=DetailSupremum+0.125f)
        {
            const float Fade=DetailBandFadeAt(X,Y,Z,RockDistance,SurfaceSDF,
                CaveInfluence,FloorInfluence);
            if(Fade>0.0f)
            {
                const float Detail=DetailNoise(X,Y,Z,SurfaceSDF,CaveInfluence,
                    FloorInfluence,PassageInfluence)*Fade;
                RockDistance+=Detail;
                if(OutDetailDisplacement)*OutDetailDisplacement=Detail;
            }
        }
        if(bCriticalAir)RockDistance=std::min(RockDistance,-1.0f/16.0f);
        const bool bRock=RockDistance>=0.0f;
        float Density=-RockDistance;
        if((Density<0.0f)!=bRock||(bClampNearZero&&std::abs(Density)<0.05f))
            Density=(bRock?-1.0f:1.0f)*std::max(std::abs(Density),
                bClampNearZero?0.05f:1.0e-7f);
        if(bApplyComposition)Density=ApplyResolvedStrateComposition(Density,X,Y,Z);
        return bApplyEdits?ApplyEditBrushes(Density,X,Y,Z):Density;
    }

public:
    bool GetNativeSurfaceHeightsAt(float X,float Y,int32 ChunkZ,
                                   float& OutGroundZ,float& OutCeilingZ) const
    {
        if(SharedDensitySource)
            return SharedDensitySource->GetNativeSurfaceHeightsAt(X,Y,ChunkZ,OutGroundZ,OutCeilingZ);
        if(!WorldAssembly||!ResolvedLayout||!Owner||!Owner->Generator
            ||!std::isfinite(X)||!std::isfinite(Y))return false;
        const double ChunkWidth=GetResolvedLayoutChunkWidthVoxels();
        const std::int64_t chunkMinimum=static_cast<std::int64_t>(std::llround(ChunkZ*ChunkWidth));
        const std::int64_t chunkMaximum=static_cast<std::int64_t>(std::llround((ChunkZ+1)*ChunkWidth));
        const FBoundStratumField* Bound=FindBoundStratumForChunk(ChunkZ);
        const auto* Field=Bound?std::get_if<FSurfaceWorldFieldAdapter>(&Bound->Evaluator):nullptr;
        if(bNativeOnly&&(!NativeOnlyContainsColumn(X,Y)
            ||chunkMaximum<NativeOnlyMinimum.Z||chunkMinimum>NativeOnlyMaximum.Z
            ||!Bound||Bound->Kind!=FBoundStratumField::EKind::SurfaceWorld))
        {RecordNativeOnlyViolation();return false;}
        if(!Bound||Bound->Kind!=FBoundStratumField::EKind::SurfaceWorld
            ||!Bound->SurfacePlan||!Field||!Field->Evaluator.isValid())return false;
        constexpr double Scale=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        const double MaxVoxel=static_cast<double>(std::numeric_limits<int64>::max())/Scale;
        if(std::abs(static_cast<double>(X))>MaxVoxel||std::abs(static_cast<double>(Y))>MaxVoxel)
            return false;
        const auto ToFixed=[](float Value)
        {return static_cast<int64>(std::llround(static_cast<double>(Value)
            *VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel));};
        const auto Column=Field->Evaluator.point(ToFixed(X),ToFixed(Y),
            static_cast<int64>(ChunkZ)*ResolvedLayout->strateLayoutChunkWidthSubvoxels);
        OutGroundZ=static_cast<float>(Column.groundHeightSubvoxels/Scale);
        OutCeilingZ=static_cast<float>(Column.capHeightSubvoxels/Scale);
        return std::isfinite(OutGroundZ)&&std::isfinite(OutCeilingZ);
    }

    EVoxelTileClass ClassifyBox(const FIntVector& Origin,int32 Step,int32 Cells) const
    { return ClassifyBoxDetailed(Origin,Step,Cells).Verdict; }

    bool IsNativeSurfaceBox(const FIntVector& Origin,int32 Step,int32 Cells) const
    {
        if(SharedDensitySource)return SharedDensitySource->IsNativeSurfaceBox(Origin,Step,Cells);
        if(!WorldAssembly||!ResolvedLayout||!Owner||Step<=0||Cells<=0)return false;
        const int32 Pad=std::max(Step,1);
        const int32 BMin=Origin.Z-Pad;
        const int32 BMax=Origin.Z+(Cells+1)*Step;
        if(!StampSpatialBounds.empty())
        {
            constexpr std::int64_t Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            const std::array<std::int64_t,3> minimum={
                static_cast<std::int64_t>(Origin.X-Pad)*Q,
                static_cast<std::int64_t>(Origin.Y-Pad)*Q,
                static_cast<std::int64_t>(BMin)*Q};
            const std::array<std::int64_t,3> maximum={
                static_cast<std::int64_t>(Origin.X+(Cells+1)*Step)*Q,
                static_cast<std::int64_t>(Origin.Y+(Cells+1)*Step)*Q,
                static_cast<std::int64_t>(BMax)*Q};
            if(!BuildStampTileList(minimum,maximum).empty())return false;
        }
        if(!CavernRuntime.empty())
        {
            constexpr std::int64_t Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            const std::array<std::int64_t,3> minimum={
                static_cast<std::int64_t>(Origin.X-Pad)*Q,
                static_cast<std::int64_t>(Origin.Y-Pad)*Q,
                static_cast<std::int64_t>(BMin)*Q};
            const std::array<std::int64_t,3> maximum={
                static_cast<std::int64_t>(Origin.X+(Cells+1)*Step)*Q,
                static_cast<std::int64_t>(Origin.Y+(Cells+1)*Step)*Q,
                static_cast<std::int64_t>(BMax)*Q};
            if(!BuildCavernFeatureTileList(minimum,maximum).empty())return false;
        }
        const float LayoutWidth=static_cast<float>(GetResolvedLayoutChunkWidthVoxels());
        const int32 FirstChunk=FMath::FloorToInt(static_cast<float>(BMin)/LayoutWidth);
        const int32 LastChunk=FMath::FloorToInt(static_cast<float>(BMax)/LayoutWidth);
        const FBoundStratumField* BoundPlan=nullptr;
        for(int32 ChunkZ=FirstChunk;ChunkZ<=LastChunk;++ChunkZ)
        {
            const auto* Candidate=FindBoundStratumForChunk(ChunkZ);
            if(!Candidate||Candidate->Kind!=FBoundStratumField::EKind::SurfaceWorld
                ||!Candidate->SurfacePlan||ChunkZ<Candidate->SurfacePlan->bottomChunkZ
                ||ChunkZ>Candidate->SurfacePlan->topChunkZ)return false;
            if(BoundPlan&&BoundPlan!=Candidate)return false;
            BoundPlan=Candidate;
        }
        if(bNativeOnly)
        {
            const int32 BMinX=Origin.X-Pad,BMinY=Origin.Y-Pad;
            const int32 BMaxX=Origin.X+(Cells+1)*Step;
            const int32 BMaxY=Origin.Y+(Cells+1)*Step;
            if(BMinX<NativeOnlyMinimum.X||BMinY<NativeOnlyMinimum.Y
                ||BMin<NativeOnlyMinimum.Z||BMaxX>NativeOnlyMaximum.X
                ||BMaxY>NativeOnlyMaximum.Y||BMax>NativeOnlyMaximum.Z)
            {RecordNativeOnlyViolation();return false;}
        }
        if(bNativeOnly&&!BoundPlan)RecordNativeOnlyViolation();
        return BoundPlan!=nullptr;
    }

    FBoxClassification ClassifyBoxDetailed(const FIntVector& Origin,int32 Step,int32 Cells,
                                            bool bUseNativeLatticeProof=false) const
    {
        if(SharedDensitySource)
            return SharedDensitySource->ClassifyBoxDetailed(Origin,Step,Cells,bUseNativeLatticeProof);
        using Clock=std::chrono::steady_clock;
        const auto Start=Clock::now();
        const int32 Pad=std::max(Step,1);
        int32 BMin[3]={Origin.X-Pad,Origin.Y-Pad,Origin.Z-Pad};
        int32 BMax[3]={Origin.X+(Cells+1)*Step,Origin.Y+(Cells+1)*Step,Origin.Z+(Cells+1)*Step};
        const VoxelForgeCore::WorldAssemblyStratumPlanV1* SurfacePlan=nullptr;
        const VoxelForgeCore::WorldAssemblyFloatingIslandPlanV1* IslandPlan=nullptr;
        const FSurfaceWorldFieldAdapter* SurfaceField=nullptr;
        const FFloatingIslandFieldAdapter* IslandField=nullptr;
        bool bSurfaceOverlap=false,bIslandOverlap=false,bOtherStrateOverlap=false;
        bool bIslandOtherStrateOverlap=false,bBadPlan=false;
        if(Owner&&ResolvedLayout)
        {
            const float LayoutWidth=static_cast<float>(GetResolvedLayoutChunkWidthVoxels());
            const int32 FirstChunk=FMath::FloorToInt(static_cast<float>(BMin[2])/LayoutWidth);
            const int32 LastChunk=FMath::FloorToInt(static_cast<float>(BMax[2])/LayoutWidth);
            for(int32 ChunkZ=FirstChunk;ChunkZ<=LastChunk;++ChunkZ)
            {
                const FBoundStratumField* Bound=FindBoundStratumForChunk(ChunkZ);
                if(Bound&&Bound->Kind==FBoundStratumField::EKind::SurfaceWorld)
                {
                    bSurfaceOverlap=true;bIslandOtherStrateOverlap=true;
                    const auto* Candidate=Bound->SurfacePlan;
                    if(!Candidate||ChunkZ<Candidate->bottomChunkZ
                        ||ChunkZ>Candidate->topChunkZ
                        ||(SurfacePlan&&SurfacePlan!=Candidate))bBadPlan=true;
                    SurfacePlan=Candidate;
                    SurfaceField=std::get_if<FSurfaceWorldFieldAdapter>(
                        &Bound->Evaluator);
                }
                else if(Bound&&Bound->Kind==FBoundStratumField::EKind::FloatingIslands)
                {
                    bIslandOverlap=true;bOtherStrateOverlap=true;
                    const auto* Candidate=Bound->IslandPlan;
                    if(!Candidate||ChunkZ<Candidate->bottomChunkZ
                        ||ChunkZ>Candidate->topChunkZ
                        ||(IslandPlan&&IslandPlan!=Candidate))bBadPlan=true;
                    IslandPlan=Candidate;
                    IslandField=std::get_if<FFloatingIslandFieldAdapter>(
                        &Bound->Evaluator);
                }
                else
                {bOtherStrateOverlap=true;bIslandOtherStrateOverlap=true;}
            }
        }
        const auto Finish=[&](EVoxelTileClass Verdict,bool bUnknown=false)
        {
            const bool bNative=(bSurfaceOverlap&&!bOtherStrateOverlap)
                ||(bIslandOverlap&&!bIslandOtherStrateOverlap);
            FBoxClassification Result{Verdict,bNative,bUnknown};
            auto& Counts=ThreadClassificationStats();
            Counts.Milliseconds+=std::chrono::duration<double,std::milli>(Clock::now()-Start).count();
            if(!Result.bNativeSurface||bUnknown)++Counts.UnknownBoxes;
            else if(Verdict==EVoxelTileClass::AllSolid)++Counts.SolidBoxes;
            else if(Verdict==EVoxelTileClass::AllAir)++Counts.AirBoxes;
            else ++Counts.MixedBoxes;
            return Result;
        };
        if(!StampSpatialBounds.empty())
        {
            constexpr std::int64_t Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            const std::array<std::int64_t,3> minimum={
                static_cast<std::int64_t>(BMin[0])*Q,
                static_cast<std::int64_t>(BMin[1])*Q,
                static_cast<std::int64_t>(BMin[2])*Q};
            const std::array<std::int64_t,3> maximum={
                static_cast<std::int64_t>(BMax[0])*Q,
                static_cast<std::int64_t>(BMax[1])*Q,
                static_cast<std::int64_t>(BMax[2])*Q};
            if(!BuildStampTileList(minimum,maximum).empty())
                return Finish(EVoxelTileClass::Mixed,true);
        }
        if(!CavernRuntime.empty())
        {
            constexpr std::int64_t Q=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            const std::array<std::int64_t,3> minimum={
                static_cast<std::int64_t>(BMin[0])*Q,
                static_cast<std::int64_t>(BMin[1])*Q,
                static_cast<std::int64_t>(BMin[2])*Q};
            const std::array<std::int64_t,3> maximum={
                static_cast<std::int64_t>(BMax[0])*Q,
                static_cast<std::int64_t>(BMax[1])*Q,
                static_cast<std::int64_t>(BMax[2])*Q};
            if(!BuildCavernFeatureTileList(minimum,maximum).empty())
                return Finish(EVoxelTileClass::Mixed,true);
        }
        if(ResolvedPassageIntersectsBox(BMin,BMax))
            return Finish(EVoxelTileClass::Mixed,true);
        if(!EditBrushes.empty()&&EditBoundsMin.X<=BMax[0]&&EditBoundsMax.X>=BMin[0]
            &&EditBoundsMin.Y<=BMax[1]&&EditBoundsMax.Y>=BMin[1]
            &&EditBoundsMin.Z<=BMax[2]&&EditBoundsMax.Z>=BMin[2])
            return Finish(EVoxelTileClass::Mixed,true);
        if(ResolvedLayout&&Owner)
        {
            const double ZMinMicrometres=static_cast<double>(BMin[2])*Owner->CoreVoxelSizeMicrons;
            const double ZMaxMicrometres=static_cast<double>(BMax[2])*Owner->CoreVoxelSizeMicrons;
            for(const auto& Stratum:ResolvedLayout->strates)
                for(const auto* Band:{&Stratum.ceiling,&Stratum.bedrock})
                    if(Band->presentInCurrentField&&ZMaxMicrometres>=Band->bottomMicrometres
                        &&ZMinMicrometres<Band->topMicrometres)
                    {
                        if(ZMinMicrometres>=Band->bottomMicrometres
                            &&ZMaxMicrometres<Band->topMicrometres)
                            return Finish(EVoxelTileClass::AllSolid);
                        return Finish(EVoxelTileClass::Mixed);
                    }
        }
        if(bNativeOnly)
        {
            const bool bInsideProofBox=BMin[0]>=NativeOnlyMinimum.X
                &&BMin[1]>=NativeOnlyMinimum.Y&&BMin[2]>=NativeOnlyMinimum.Z
                &&BMax[0]<=NativeOnlyMaximum.X&&BMax[1]<=NativeOnlyMaximum.Y
                &&BMax[2]<=NativeOnlyMaximum.Z;
            if(!bInsideProofBox||!bSurfaceOverlap||bIslandOverlap||bOtherStrateOverlap
                ||bBadPlan||!EditBrushes.empty())
            {
                RecordNativeOnlyViolation();
                return Finish(EVoxelTileClass::Mixed,true);
            }
        }
        // A box crossing recipes cannot use one field interval; unknown composition stays Mixed.
        // Une boite qui traverse plusieurs recettes reste Mixed, car l'intervalle d'un seul champ ne suffit pas.
        if(bBadPlan||(bSurfaceOverlap&&(bIslandOverlap||bOtherStrateOverlap))
            ||(bIslandOverlap&&(bIslandOtherStrateOverlap
                ||(!bSurfaceOverlap&&bOtherStrateOverlap))))
            return Finish(EVoxelTileClass::Mixed,true);
        // The native interval path below is the exact field selected first by DensityAtLattice
        // for SurfaceWorld and FloatingIslands. Legacy analytic primitives/layer bounds cannot
        // modify that field; only the explicit edit transaction above can. Keep their guards on
        // the legacy classifier path, where those overlays do participate in density.
        if(!bNativeOnly&&(!bUseNativeLatticeProof||(!bSurfaceOverlap&&!bIslandOverlap)))
        {
            for(int32 BZ=FloorDiv(BMin[2],ActiveSpatialBinSize);BZ<=FloorDiv(BMax[2],ActiveSpatialBinSize);++BZ)
            for(int32 BY=FloorDiv(BMin[1],ActiveSpatialBinSize);BY<=FloorDiv(BMax[1],ActiveSpatialBinSize);++BY)
            for(int32 BX=FloorDiv(BMin[0],ActiveSpatialBinSize);BX<=FloorDiv(BMax[0],ActiveSpatialBinSize);++BX)
            {
                const auto It=SpatialBins.find({BX,BY,BZ});if(It==SpatialBins.end())continue;
                for(uint32 Id:It->second)
                {
                    const FPrimitive& P=Primitives[Id];bool Overlap=true;
                    for(int32 A=0;A<3;++A)
                        Overlap &= P.Max[A]+DetailBand>=BMin[A]&&P.Min[A]-DetailBand<=BMax[A];
                    if(Overlap)return Finish(EVoxelTileClass::Mixed);
                }
            }
            for(const FInterval& R:LayerRanges)
                if(R.Lo<=BMax[2]&&R.Hi>=BMin[2]
                    &&(R.Lo>=BMin[2]||R.Hi<=BMax[2]))
                    return Finish(EVoxelTileClass::Mixed);
        }
        if(bSurfaceOverlap)
        {
            if(!WorldAssembly||!SurfacePlan||!SurfaceField)
                return Finish(EVoxelTileClass::Mixed,true);
            // classifyLatticeBox takes the exact extrema of ground/cap columns at every
            // MC lattice XY in this box. Since density is min(z-ground, cap-z), those extrema
            // bound every lattice sample in Z without a noise amplitude guess.
            const auto Verdict=SurfaceField->Evaluator.classifyLatticeBox(
                static_cast<int64>(BMin[0])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                static_cast<int64>(BMin[1])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                static_cast<int64>(BMin[2])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                static_cast<int64>(BMax[0])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                static_cast<int64>(BMax[1])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                static_cast<int64>(BMax[2])*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel,
                std::max(Step,1));
            switch(Verdict)
            {
                case VoxelForgeCore::HeightfieldBoxClass::allAir:
                    return Finish(EVoxelTileClass::AllAir);
                case VoxelForgeCore::HeightfieldBoxClass::allSolid:
                    return Finish(EVoxelTileClass::AllSolid);
                case VoxelForgeCore::HeightfieldBoxClass::mixed:
                    return Finish(EVoxelTileClass::Mixed);
                default:return Finish(EVoxelTileClass::Mixed,true);
            }
        }
        if(bIslandOverlap)
        {
            if(!IslandPlan||!IslandField)return Finish(EVoxelTileClass::Mixed,true);
            constexpr std::int64_t Scale=VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            const std::int64_t Bottom=IslandPlan->manifest.recipe.layoutMinimumZSubvoxels;
            const std::int64_t Top=IslandPlan->manifest.recipe.layoutMaximumZSubvoxels;
            const std::int64_t Seal=IslandPlan->manifest.recipe.boundarySealSubvoxels;
            const std::int64_t BoxBottom=static_cast<std::int64_t>(BMin[2])*Scale;
            const std::int64_t BoxTop=static_cast<std::int64_t>(BMax[2])*Scale;
            const bool bSharedTopSealEnabled=IslandPlan->manifest.recipe.geometryVersion<3
                ||!VoxelDensityAblation::IsBoundarySealOff();
            const bool bTopSealOverlap=bSharedTopSealEnabled
                &&BoxBottom<=Top&&BoxTop>Top-Seal;
            const bool bBottomSealOverlap=IslandPlan->manifest.recipe.geometryVersion<3
                &&BoxBottom<Bottom+Seal&&BoxTop>=Bottom;
            if(bBottomSealOverlap)
                return Finish(BoxBottom>=Bottom&&BoxTop<=Bottom+Seal
                    ?EVoxelTileClass::AllSolid:EVoxelTileClass::Mixed);
            if(bTopSealOverlap)
                return Finish((IslandPlan->manifest.recipe.geometryVersion<3
                    ?BoxBottom>=Top-Seal:BoxBottom>Top-Seal)&&BoxTop<=Top
                    ?EVoxelTileClass::AllSolid:EVoxelTileClass::Mixed);
            if(!IslandField->Evaluator.isValid())return Finish(EVoxelTileClass::Mixed,true);
            const auto Interval=IslandField->Evaluator.interval(static_cast<int64>(BMin[0])*Scale,
                static_cast<int64>(BMin[1])*Scale,static_cast<int64>(BMin[2])*Scale,
                static_cast<int64>(BMax[0])*Scale,static_cast<int64>(BMax[1])*Scale,
                static_cast<int64>(BMax[2])*Scale);
            if(!Interval.known)return Finish(EVoxelTileClass::Mixed,true);
            if(Interval.minimumDensitySubvoxels>=0)return Finish(EVoxelTileClass::AllAir);
            if(Interval.maximumDensitySubvoxels<0)return Finish(EVoxelTileClass::AllSolid);
            return Finish(EVoxelTileClass::Mixed);
        }
        const bool bRock=EvaluateFast((BMin[0]+BMax[0])*0.5,
            (BMin[1]+BMax[1])*0.5,(BMin[2]+BMax[2])*0.5);
        return Finish(bRock?EVoxelTileClass::AllSolid:EVoxelTileClass::AllAir);
    }

    bool IsRock(int32 X,int32 Y,int32 Z) const
    {
        if(SharedDensitySource)return SharedDensitySource->IsRock(X,Y,Z);
        if(!Contains(X,Y,Z))return EvaluateFast(X,Y,Z);
        const size_t Line=static_cast<size_t>(Y-Min[1])*Size[0]
            +static_cast<size_t>(X-Min[0]);
        const size_t Zi=static_cast<size_t>(Z-Min[2]);
        return ((RockWords[Line*WordsPerZ+(Zi>>6)]>>(Zi&63u))&1u)!=0;
    }

    bool IsDetailAuditPassing() const
    {
        const double Correlation=DetailAutocorrelation(DetailVariant);
        const bool bFlips=Stats.DetailFlips>=1000;
        const bool bCoherent=Correlation>0.45;
        const bool bFamilies=AuditSurfaceBandFamilies();
        std::printf("[DetailAudit] mode=%s supremum=%.2f vox band=%d changed_signs=%llu adjacent_correlation=%.4f surface_detail_check=%s spatial_scale_check=%s\n",
            DetailVariant==EDetailVariant::Coherent?"coherent":DetailVariant==EDetailVariant::Smooth?"smooth":"per-voxel",
            DetailSupremum,DetailBand,static_cast<unsigned long long>(Stats.DetailFlips),Correlation,
            bFlips&&bFamilies?"PASS":"FAIL",bCoherent?"PASS":"FAIL");
        return bFlips&&bCoherent&&bFamilies;
    }

    bool AuditSurfaceBandFamilies(bool bPassageOnly=false) const
    {
        struct FPatchKey
        {
            int32 X=0,Y=0,Z=0;uint8 Family=0;
            bool operator==(const FPatchKey&)const=default;
        };
        struct FPatchHash
        {
            size_t operator()(const FPatchKey& K)const noexcept
            {
                uint64 H=static_cast<uint32>(K.X)*0x9E3779B185EBCA87ull;
                H^=static_cast<uint64>(static_cast<uint32>(K.Y))*0xC2B2AE3D27D4EB4Full;
                H^=static_cast<uint64>(static_cast<uint32>(K.Z))*0x165667B19E3779F9ull;
                H^=static_cast<uint64>(K.Family)*0x94D049BB133111EBull;
                H^=H>>29;H*=0xBF58476D1CE4E5B9ull;H^=H>>31;
                return static_cast<size_t>(H);
            }
        };
        struct FPatchStats {uint64 Count=0;double Sum=0.0,SumSq=0.0;};
        struct FFamilyStats {uint64 Count=0,NearZero=0;double Sum=0.0,SumSq=0.0;};
        std::unordered_map<FPatchKey,FPatchStats,FPatchHash> Patches;
        std::array<FFamilyStats,3> Families{};
        FFamilyStats PassageWalls,OrdinaryCaveWalls;
        for(size_t Line=0;Line<static_cast<size_t>(Size[0])*Size[1];++Line)
        {
            const int32 X=Min[0]+static_cast<int32>(Line%Size[0]);
            const int32 Y=Min[1]+static_cast<int32>(Line/Size[0]);
            const size_t WordBase=Line*WordsPerZ;
            for(size_t W=0;W<WordsPerZ;++W)
            {
                uint64 Bits=CandidateWords[WordBase+W];
                while(Bits)
                {
                    const uint32 Bit=std::countr_zero(Bits);Bits&=Bits-1;
                    const size_t Zi=W*64+Bit;if(Zi>=static_cast<size_t>(Size[2]))continue;
                    const int32 Z=Min[2]+static_cast<int32>(Zi);
                    ESurfaceFamily Family=ESurfaceFamily::Strata;float SurfaceSDF=100000.0f;
                    bool bFloorSurface=false;float CaveInfluence=0.0f,FloorInfluence=0.0f;
                    float PassageInfluence=0.0f;
                    const float Raw=EffectiveRockDistance(X,Y,Z,&Family,&SurfaceSDF,
                        &bFloorSurface,&CaveInfluence,&FloorInfluence,nullptr,nullptr,false,
                        &PassageInfluence);
                    if(std::abs(Raw)>=0.5f)continue;
                    const float Fade=DetailBandFadeAt(X,Y,Z,Raw,SurfaceSDF,
                        CaveInfluence,FloorInfluence);
                    const float Detail=Fade>0.0f
                        ?DetailNoise(X,Y,Z,SurfaceSDF,CaveInfluence,FloorInfluence,
                            PassageInfluence)*Fade:0.0f;
                    const size_t FamilyIndex=static_cast<size_t>(Family);
                    FFamilyStats& F=Families[FamilyIndex];++F.Count;F.Sum+=Detail;F.SumSq+=Detail*Detail;
                    if(std::abs(Detail)<0.05f)++F.NearZero;
                    if(PassageInfluence>=0.5f)
                    {++PassageWalls.Count;PassageWalls.Sum+=Detail;PassageWalls.SumSq+=Detail*Detail;}
                    else if(Family==ESurfaceFamily::Cave&&PassageInfluence<0.1f)
                    {++OrdinaryCaveWalls.Count;OrdinaryCaveWalls.Sum+=Detail;OrdinaryCaveWalls.SumSq+=Detail*Detail;}
                    const FPatchKey Key{FloorDiv(X,16),FloorDiv(Y,16),FloorDiv(Z,16),
                        static_cast<uint8>(FamilyIndex)};
                    FPatchStats& P=Patches[Key];++P.Count;P.Sum+=Detail;P.SumSq+=Detail*Detail;
                }
            }
        }
        std::array<uint64,3> FlatCounts{};uint64 LargestFlatPatch=0;
        for(const auto& Entry:Patches)
        {
            const FPatchStats& P=Entry.second;if(P.Count<16)continue;
            const double Mean=P.Sum/P.Count;
            const double StdDev=std::sqrt(std::max(0.0,P.SumSq/P.Count-Mean*Mean));
            if(StdDev<0.10)
            {
                FlatCounts[Entry.first.Family]+=P.Count;
                LargestFlatPatch=std::max(LargestFlatPatch,P.Count);
            }
        }
        bool bPass=true;uint64 Tested=0,FlatTotal=0,Total=0;
        for(size_t I=0;I<Families.size();++I)
        {
            const FFamilyStats& F=Families[I];Total+=F.Count;FlatTotal+=FlatCounts[I];
            if(F.Count<16)continue;
            ++Tested;
            const double Mean=F.Sum/F.Count;
            const double StdDev=std::sqrt(std::max(0.0,F.SumSq/F.Count-Mean*Mean));
            const double ZeroShare=static_cast<double>(F.NearZero)/F.Count;
            const bool FamilyPass=StdDev>=0.15&&ZeroShare<0.60&&FlatCounts[I]<F.Count/2;
            bPass&=FamilyPass;
            const char* Name=I==0?"strata":I==1?"cave":"solid_overlay";
            std::printf("[SurfaceBandFamilyAudit] family=%s samples=%llu detail_stddev=%.4f near_zero_share=%.1f%% flat_patch_samples=%llu status=%s\n",
                Name,static_cast<unsigned long long>(F.Count),StdDev,ZeroShare*100.0,
                static_cast<unsigned long long>(FlatCounts[I]),FamilyPass?"PASS":"FAIL");
        }
        const double FlatShare=Total?100.0*static_cast<double>(FlatTotal)/Total:100.0;
        std::printf("[FlatPatchAudit] patch_width=16 vox min_patch_samples=16 flat_stddev_lt=0.10 flat_share=%.1f%% largest_flat_patch=%llu status=%s\n",
            FlatShare,static_cast<unsigned long long>(LargestFlatPatch),
            Tested>0&&FlatShare<20.0?"PASS":"FAIL");
        const double PassageRms=PassageWalls.Count
            ?std::sqrt(PassageWalls.SumSq/PassageWalls.Count):0.0;
        const double OrdinaryCaveRms=OrdinaryCaveWalls.Count
            ?std::sqrt(OrdinaryCaveWalls.SumSq/OrdinaryCaveWalls.Count):0.0;
        const double PassageRmsRatio=OrdinaryCaveRms>1.0e-9
            ?PassageRms/OrdinaryCaveRms:0.0;
        const bool bHasPassageSamples=PassageWalls.Count>0;
        const bool bRatioPass=PassageWalls.Count>=32&&OrdinaryCaveWalls.Count>=32
            &&PassageRmsRatio>=0.75&&PassageRmsRatio<=1.25;
        const bool bPassageDetail=bPassageOnly?bRatioPass:(!bHasPassageSamples||bRatioPass);
        const char* PassageStatus=!bHasPassageSamples
            ?(bPassageOnly?"FAIL":"SKIP"):(bPassageDetail?"PASS":"FAIL");
        std::printf("[PassageWallDetailAudit] passage_samples=%llu passage_rms=%.4f cave_samples=%llu cave_rms=%.4f ratio=%.3f range=(0.750,1.250) status=%s\n",
            static_cast<unsigned long long>(PassageWalls.Count),PassageRms,
            static_cast<unsigned long long>(OrdinaryCaveWalls.Count),OrdinaryCaveRms,
            PassageRmsRatio,PassageStatus);
        return bPassageOnly?bPassageDetail:(Tested>0&&FlatShare<20.0&&bPass&&bPassageDetail);
    }

    bool AuditGridStairIntegrity() const
    {
        uint64 CheckedEdges=0,MissingAny=0,MissingBoth=0;
        std::array<std::array<int32,4>,8> Examples{};
        size_t ExampleCount=0;
        const auto Record=[&](uint64 EdgeMask,uint64 CandidateA,uint64 CandidateB,
                              int32 X,int32 Y,int32 Z,int32 Axis)
        {
            CheckedEdges+=std::popcount(EdgeMask);
            const uint64 Missing=EdgeMask&~(CandidateA&CandidateB);
            uint64 AnyMissing=Missing;
            MissingAny+=std::popcount(Missing);
            MissingBoth+=std::popcount(EdgeMask&~(CandidateA|CandidateB));
            while(AnyMissing&&ExampleCount<Examples.size())
            {
                const uint32 Bit=std::countr_zero(AnyMissing);AnyMissing&=AnyMissing-1;
                Examples[ExampleCount++]={X,Y,Z+static_cast<int32>(Bit),Axis};
            }
        };

        const size_t Columns=static_cast<size_t>(Size[0])*Size[1];
        for(size_t Line=0;Line<Columns;++Line)
        {
            const int32 X=Min[0]+static_cast<int32>(Line%Size[0]);
            const int32 Y=Min[1]+static_cast<int32>(Line/Size[0]);
            const size_t Base=Line*WordsPerZ;
            for(size_t W=0;W<WordsPerZ;++W)
            {
                const size_t Word=Base+W;
                const uint64 Rock=RockWords[Word],Candidates=CandidateWords[Word];
                const uint64 PreviousRock=W?RockWords[Word-1]>>63:0;
                const uint64 PreviousCandidates=W?CandidateWords[Word-1]>>63:0;
                uint64 Valid=(Size[2]-W*64)>=64?~uint64{0}
                    :((uint64{1}<<(Size[2]-W*64))-1);
                if(W==0)Valid&=~uint64{1};
                const uint64 ShiftedRock=(Rock<<1)|PreviousRock;
                const uint64 ShiftedCandidates=(Candidates<<1)|PreviousCandidates;
                Record((Rock^ShiftedRock)&Valid,Candidates,ShiftedCandidates,
                    X,Y,Min[2]+static_cast<int32>(W*64),2);

                if(X+1<Max[0]+1)
                {
                    const size_t Other=Word+WordsPerZ;
                    Record(Rock^RockWords[Other],Candidates,CandidateWords[Other],
                        X,Y,Min[2]+static_cast<int32>(W*64),0);
                }
                if(Y+1<Max[1]+1)
                {
                    const size_t Other=Word+static_cast<size_t>(Size[0])*WordsPerZ;
                    Record(Rock^RockWords[Other],Candidates,CandidateWords[Other],
                        X,Y,Min[2]+static_cast<int32>(W*64),1);
                }
            }
        }
        std::printf("[GridStairDistanceAudit] region=(%d,%d,%d)..(%d,%d,%d) sign_edges=%llu candidate_fallback_edges=%llu both_fallback_edges=%llu status=%s\n",
            Min[0],Min[1],Min[2],Max[0],Max[1],Max[2],
            static_cast<unsigned long long>(CheckedEdges),
            static_cast<unsigned long long>(MissingAny),
            static_cast<unsigned long long>(MissingBoth),MissingAny==0?"PASS":"FAIL");
        const auto CandidateAt=[&](int32 X,int32 Y,int32 Z)
        {
            if(!Contains(X,Y,Z))return false;
            const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]+static_cast<size_t>(X-Min[0]);
            const size_t Zi=static_cast<size_t>(Z-Min[2]);
            return (CandidateWords[Column*WordsPerZ+(Zi>>6)]&(uint64{1}<<(Zi&63u)))!=0;
        };
        for(size_t I=0;I<ExampleCount;++I)
        {
            int32 AX=Examples[I][0],AY=Examples[I][1],AZ=Examples[I][2];
            int32 BX=AX,BY=AY,BZ=AZ;
            if(Examples[I][3]==0)++BX;else if(Examples[I][3]==1)++BY;else --BZ;
            const float AD=DensityAtLattice(AX,AY,AZ),BD=DensityAtLattice(BX,BY,BZ);
            const float AExact=AnalyticDensityAt(static_cast<float>(AX),static_cast<float>(AY),static_cast<float>(AZ));
            const float BExact=AnalyticDensityAt(static_cast<float>(BX),static_cast<float>(BY),static_cast<float>(BZ));
            std::printf("[GridStairDistanceCandidate] a=(%d,%d,%d) b=(%d,%d,%d) axis=%d candidate=(%d,%d) solid=(%d,%d) density=(%.4f,%.4f) exact=(%.4f,%.4f) critical_air=(%d,%d)\n",
                AX,AY,AZ,BX,BY,BZ,Examples[I][3],CandidateAt(AX,AY,AZ),CandidateAt(BX,BY,BZ),
                IsRock(AX,AY,AZ),IsRock(BX,BY,BZ),
                AD,BD,AExact,BExact,
                IsInsideCriticalAir(AX,AY,AZ),IsInsideCriticalAir(BX,BY,BZ));
        }
        return MissingAny==0;
    }

    bool AuditViewSurface(double CameraX,double CameraY,double CameraZ,
                          float Yaw,float Pitch) const
    {
        struct FFamilyStats
        {
            uint64 Hits=0,NearZero=0,AxisLocked=0;
            double Sum=0.0,SumSq=0.0;
        };
        std::array<FFamilyStats,3> FamilyStats{};
        constexpr std::array<float,13> YawOffsets={-36.0f,-30.0f,-24.0f,-18.0f,-12.0f,-6.0f,
            0.0f,6.0f,12.0f,18.0f,24.0f,30.0f,36.0f};
        constexpr std::array<float,11> PitchOffsets={-80.0f,-70.0f,-60.0f,-50.0f,-40.0f,
            -30.0f,-20.0f,-10.0f,0.0f,10.0f,20.0f};
        const double OX=CameraX*4.0,OY=CameraY*4.0,OZ=CameraZ*4.0;
        auto Distance=[&](double X,double Y,double Z,ESurfaceFamily* OutFamily=nullptr,
                          float* OutRaw=nullptr,float* OutDetail=nullptr,
                          bool* OutFloorSurface=nullptr,float* OutPassageInfluence=nullptr,
                          float* OutCaveInfluence=nullptr,float* OutFloorInfluence=nullptr,
                          float* OutSurfaceSDF=nullptr)
        {
            ESurfaceFamily Family=ESurfaceFamily::Strata;float SurfaceSDF=100000.0f;
            bool bFloorSurface=false;float CaveInfluence=0.0f,FloorInfluence=0.0f;
            float PassageInfluence=0.0f;
            float D=EffectiveRockDistance(X,Y,Z,&Family,&SurfaceSDF,
                &bFloorSurface,&CaveInfluence,&FloorInfluence,nullptr,nullptr,false,
                &PassageInfluence);
            float Detail=0.0f;
            const bool bInside=X>=Min[0]&&X<=Max[0]&&Y>=Min[1]&&Y<=Max[1]
                &&Z>=Min[2]&&Z<=Max[2];
            const bool bCriticalAir=IsInsideCriticalAir(X,Y,Z);
            if(bInside&&DetailVariant!=EDetailVariant::Smooth&&std::abs(D)<=DetailSupremum+0.125f)
            {
                const float Fade=DetailBandFadeAt(X,Y,Z,D,SurfaceSDF,CaveInfluence,FloorInfluence);
                if(Fade>0.0f)
                {Detail=DetailNoise(X,Y,Z,SurfaceSDF,CaveInfluence,FloorInfluence,
                    PassageInfluence)*Fade;D+=Detail;}
            }
            if(bCriticalAir)D=std::min(D,-1.0f/16.0f);
            if(OutFamily)*OutFamily=Family;
            if(OutRaw)*OutRaw=D-Detail;
            if(OutDetail)*OutDetail=Detail;
            if(OutFloorSurface)*OutFloorSurface=bFloorSurface;
            if(OutPassageInfluence)*OutPassageInfluence=PassageInfluence;
            if(OutCaveInfluence)*OutCaveInfluence=CaveInfluence;
            if(OutFloorInfluence)*OutFloorInfluence=FloorInfluence;
            if(OutSurfaceSDF)*OutSurfaceSDF=SurfaceSDF;
            return D;
        };
        uint64 TotalHits=0,TotalAxisLocked=0,TotalNearZero=0,FloorTaggedHits=0,FloorAxisLocked=0;
        uint64 FamilyTransitionPairs=0,StableFamilyPairs=0;
        uint64 ThinDetachedSheets=0;
        double ThinnestDetachedSheet=std::numeric_limits<double>::max();
        double FamilyTransitionGradientSq=0.0,StableFamilyGradientSq=0.0;
        for(float YawOffset:YawOffsets)for(float PitchOffset:PitchOffsets)
        {
            const double YawRad=Yaw+YawOffset*0.017453292519943295;
            const double PitchRad=Pitch+PitchOffset*0.017453292519943295;
            const double CP=std::cos(PitchRad),DX=std::sin(YawRad)*CP,
                DY=std::cos(YawRad)*CP,DZ=std::sin(PitchRad);
            double PreviousT=0.0;
            float PreviousD=Distance(OX,OY,OZ+0.001);
            bool bFound=false;
            double PrimaryHitT=-1.0;
            for(double T=0.5;T<=256.0;T+=0.5)
            {
                const double X=OX+DX*T,Y=OY+DY*T,Z=OZ+DZ*T;
                const float D=Distance(X,Y,Z);
                if(PreviousD<0.0f&&D>=0.0f)
                {
                    double Lo=PreviousT,Hi=T;
                    for(int32 It=0;It<10;++It)
                    {
                        const double Mid=(Lo+Hi)*0.5;
                        if(Distance(OX+DX*Mid,OY+DY*Mid,OZ+DZ*Mid)<0.0f)Lo=Mid;else Hi=Mid;
                    }
                    const double HitT=(Lo+Hi)*0.5;
                    PrimaryHitT=HitT;
                    const double XH=OX+DX*HitT,YH=OY+DY*HitT,ZH=OZ+DZ*HitT;
                    ESurfaceFamily Family=ESurfaceFamily::Strata;float Raw=0.0f,Detail=0.0f;
                    bool bFloorSurface=false;float PassageInfluence=0.0f;
                    float CaveInfluence=0.0f,FloorInfluence=0.0f,SurfaceSDF=100000.0f;
                    Distance(XH,YH,ZH,&Family,&Raw,&Detail,&bFloorSurface,&PassageInfluence,
                        &CaveInfluence,&FloorInfluence,&SurfaceSDF);
                    const double GX=Distance(XH+0.5,YH,ZH)-Distance(XH-0.5,YH,ZH);
                    const double GY=Distance(XH,YH+0.5,ZH)-Distance(XH,YH-0.5,ZH);
                    const double GZ=Distance(XH,YH,ZH+0.5)-Distance(XH,YH,ZH-0.5);
                    const double GL=std::sqrt(GX*GX+GY*GY+GZ*GZ);
                    const double AxisDot=GL>1.0e-8?std::max({std::abs(GX),std::abs(GY),std::abs(GZ)})/GL:1.0;
                    for(int32 Axis=0;Axis<3;++Axis)
                    {
                        double AP[3]={XH,YH,ZH},AM[3]={XH,YH,ZH};
                        AP[Axis]+=0.5;AM[Axis]-=0.5;
                        ESurfaceFamily FamilyP=ESurfaceFamily::Strata,FamilyM=ESurfaceFamily::Strata;
                        float DetailP=0.0f,DetailM=0.0f;bool bFloorP=false,bFloorM=false;
                        Distance(AP[0],AP[1],AP[2],&FamilyP,nullptr,&DetailP,&bFloorP);
                        Distance(AM[0],AM[1],AM[2],&FamilyM,nullptr,&DetailM,&bFloorM);
                        const double Gradient=static_cast<double>(DetailP-DetailM);
                        if(FamilyP!=FamilyM||bFloorP!=bFloorM)
                        {FamilyTransitionGradientSq+=Gradient*Gradient;++FamilyTransitionPairs;}
                        else
                        {StableFamilyGradientSq+=Gradient*Gradient;++StableFamilyPairs;}
                    }
                    constexpr double ScanRadius=16.0;
                    constexpr int32 ScanSteps=128;
                    double ScanT=std::max(0.0,HitT-ScanRadius);
                    ESurfaceFamily ScanFamily=ESurfaceFamily::Strata;
                    bool bScanFloor=false;float ScanRaw=0.0f,ScanDetail=0.0f;
                    Distance(OX+DX*ScanT,OY+DY*ScanT,OZ+DZ*ScanT,
                        &ScanFamily,&ScanRaw,&ScanDetail,&bScanFloor);
                    for(int32 Step=1;Step<=ScanSteps;++Step)
                    {
                        const double T=std::min(HitT+ScanRadius,ScanT+0.25);
                        ESurfaceFamily NextFamily=ESurfaceFamily::Strata;
                        bool bNextFloor=false;float NextRaw=0.0f,NextDetail=0.0f;
                        Distance(OX+DX*T,OY+DY*T,OZ+DZ*T,
                            &NextFamily,&NextRaw,&NextDetail,&bNextFloor);
                        if(std::abs(ScanRaw)<=5.0f&&std::abs(NextRaw)<=5.0f)
                        {
                            const double Gradient=static_cast<double>(NextDetail-ScanDetail);
                            if(ScanFamily!=NextFamily||bScanFloor!=bNextFloor)
                            {FamilyTransitionGradientSq+=Gradient*Gradient;++FamilyTransitionPairs;}
                            else
                            {StableFamilyGradientSq+=Gradient*Gradient;++StableFamilyPairs;}
                        }
                        ScanT=T;ScanFamily=NextFamily;bScanFloor=bNextFloor;
                        ScanRaw=NextRaw;ScanDetail=NextDetail;
                    }
                    FFamilyStats& S=FamilyStats[static_cast<size_t>(Family)];
                    ++S.Hits;++TotalHits;S.Sum+=Detail;S.SumSq+=Detail*Detail;
                    if(std::abs(Detail)<0.05f){++S.NearZero;++TotalNearZero;}
                    if(AxisDot>0.985){++S.AxisLocked;++TotalAxisLocked;}
                    if(bFloorSurface){++FloorTaggedHits;if(AxisDot>0.985)++FloorAxisLocked;}
                    if(YawOffset==0.0f&&PitchOffset==0.0f)
                    {
                        const char* Name=Family==ESurfaceFamily::Strata?"strata":
                            Family==ESurfaceFamily::Cave?"cave":"solid_overlay";
                        const FLayerField* Field=FindLayerField(ZH);
                        FOwnerNoiseLineContext OwnerNoise8,OwnerNoise2;
                        const float Owner8=Field?OwnerCaveRoughness(XH,YH,ZH,SurfaceSDF,
                            *Field,CaveInfluence,OwnerNoise8,nullptr,8):0.0f;
                        const float Owner2=Field?OwnerCaveRoughness(XH,YH,ZH,SurfaceSDF,
                            *Field,CaveInfluence,OwnerNoise2,nullptr,2):0.0f;
                        const float Relief=SurfaceRelief(static_cast<float>(XH),
                            static_cast<float>(YH),static_cast<float>(ZH),
                            static_cast<uint32>(Owner->Seed));
                        std::printf("[SurfaceRay] t=%.2f vox hit=(%.2f,%.2f,%.2f) family=%s floor_surface=%s cave_influence=%.3f floor_influence=%.3f passage_influence=%.3f surface_sdf=%.4f raw_sdf=%.4f detail=%.4f relief=%.4f owner8=%.4f owner2=%.4f axis_dot=%.4f\n",
                            HitT,XH,YH,ZH,Name,bFloorSurface?"yes":"no",CaveInfluence,
                            FloorInfluence,PassageInfluence,SurfaceSDF,Raw,Detail,Relief,
                            Owner8,Owner2,AxisDot);
                    }
                    bFound=true;break;
                }
                PreviousT=T;PreviousD=D;
            }
            if(PrimaryHitT>=0.0)
            {
                constexpr double SheetStep=0.25;
                constexpr double MinimumAirGap=3.0;
                constexpr double MaximumSheetThickness=1.0;
                double T=PrimaryHitT+SheetStep;
                float Prev=Distance(OX+DX*T,OY+DY*T,OZ+DZ*T);
                bool bInSolid=Prev>=0.0f;
                double SolidStart=T,LastSolidExit=PrimaryHitT;
                bool bSeparatedFromPrevious=false;
                for(T+=SheetStep;T<=256.0;T+=SheetStep)
                {
                    const float D=Distance(OX+DX*T,OY+DY*T,OZ+DZ*T);
                    if(!bInSolid&&Prev<0.0f&&D>=0.0f)
                    {
                        SolidStart=T;
                        bSeparatedFromPrevious=(T-LastSolidExit)>=MinimumAirGap;
                        bInSolid=true;
                    }
                    else if(bInSolid&&Prev>=0.0f&&D<0.0f)
                    {
                        const double Thickness=T-SolidStart;
                        if(bSeparatedFromPrevious&&Thickness<MaximumSheetThickness)
                        {
                            ++ThinDetachedSheets;
                            ThinnestDetachedSheet=std::min(ThinnestDetachedSheet,Thickness);
                            if(ThinDetachedSheets<=8)
                                std::printf("[ThinSheetCandidate] yaw_offset=%.0f pitch_offset=%.0f entry=%.2f vox thickness=%.3f vox air_gap=%.2f vox\n",
                                    YawOffset,PitchOffset,SolidStart,Thickness,SolidStart-LastSolidExit);
                        }
                        LastSolidExit=T;
                        bSeparatedFromPrevious=false;
                        bInSolid=false;
                    }
                    Prev=D;
                }
            }
            (void)bFound;
        }
        const double NearZeroShare=TotalHits?static_cast<double>(TotalNearZero)/TotalHits:1.0;
        const double AxisShare=TotalHits?static_cast<double>(TotalAxisLocked)/TotalHits:1.0;
        const double FloorAxisShare=FloorTaggedHits?static_cast<double>(FloorAxisLocked)/FloorTaggedHits:1.0;
        const double TransitionRMS=FamilyTransitionPairs
            ?std::sqrt(FamilyTransitionGradientSq/FamilyTransitionPairs):0.0;
        const double StableRMS=StableFamilyPairs
            ?std::sqrt(StableFamilyGradientSq/StableFamilyPairs):0.0;
        const double TransitionRatio=StableRMS>1.0e-6?TransitionRMS/StableRMS:1000000.0;
        double Sum=0.0,SumSq=0.0;
        for(const FFamilyStats& S:FamilyStats){Sum+=S.Sum;SumSq+=S.SumSq;}
        const double Mean=TotalHits?Sum/TotalHits:0.0;
        const double Variance=TotalHits?std::max(0.0,SumSq/TotalHits-Mean*Mean):0.0;
        const double SurfaceDetailRMS=std::sqrt(Variance);
        const double RelativeJoinStep=SurfaceDetailRMS>1.0e-6?TransitionRMS/SurfaceDetailRMS:1000000.0;
        const bool bDetailPass=TotalHits>=24&&std::sqrt(Variance)>=0.15&&NearZeroShare<0.50;
        constexpr double GridStairThreshold=0.40;
        const bool bJoinCoverage=FloorTaggedHits>=8
            &&(FamilyTransitionPairs==0||(FamilyTransitionPairs>=8&&RelativeJoinStep<GridStairThreshold));
        const bool bGridPass=TotalHits>=24&&AxisShare<0.60
            &&bJoinCoverage;
        const bool bThinSheetPass=ThinDetachedSheets==0;
        std::printf("[FlatSurfaceAudit] rays=%llu detail_stddev=%.4f vox near_zero_share=%.1f%% threshold=50.0%% status=%s\n",
            static_cast<unsigned long long>(TotalHits),std::sqrt(Variance),NearZeroShare*100.0,
            bDetailPass?"PASS":"FAIL");
        std::printf("[GridStairAudit] rays=%llu axis_locked_normals=%.1f%% threshold=60.0%% floor_tagged_hits=%llu floor_axis_locked=%.1f%% family_transition_pairs=%llu transition_rms=%.4f vox stable_rms=%.4f vox surface_detail_rms=%.4f vox relative_join_step=%.3f threshold=%.3f legacy_join_ratio=%.3f status=%s\n",
            static_cast<unsigned long long>(TotalHits),AxisShare*100.0,
            static_cast<unsigned long long>(FloorTaggedHits),FloorAxisShare*100.0,
            static_cast<unsigned long long>(FamilyTransitionPairs),TransitionRMS,StableRMS,
            SurfaceDetailRMS,RelativeJoinStep,GridStairThreshold,TransitionRatio,bGridPass?"PASS":"FAIL");
        std::printf("[ThinSheetAudit] rays=%llu isolated_sheets=%llu thickness_lt=1.000 vox air_gap_ge=3.000 vox thinnest=%.3f vox status=%s\n",
            static_cast<unsigned long long>(TotalHits),static_cast<unsigned long long>(ThinDetachedSheets),
            ThinDetachedSheets?ThinnestDetachedSheet:0.0,bThinSheetPass?"PASS":"FAIL");
        for(size_t I=0;I<FamilyStats.size();++I)
        {
            const char* Name=I==0?"strata":I==1?"cave":"solid_overlay";
            const FFamilyStats& S=FamilyStats[I];
            const double M=S.Hits?S.Sum/S.Hits:0.0;
            const double V=S.Hits?std::sqrt(std::max(0.0,S.SumSq/S.Hits-M*M)):0.0;
            std::printf("[SurfaceFamilyAudit] family=%s rays=%llu detail_mean=%.4f detail_stddev=%.4f near_zero=%llu axis_locked=%llu\n",
                Name,static_cast<unsigned long long>(S.Hits),M,V,
                static_cast<unsigned long long>(S.NearZero),static_cast<unsigned long long>(S.AxisLocked));
        }
        const bool bFloorProfilePass=Stats.MaxUnmarkedFloorSlopeDelta<=0.75
            &&Stats.MaxFloorProfileEndpointValueError<=0.01
            &&Stats.MaxFloorProfileEndpointSlopeError<=0.001
            &&Stats.FloorProfileEndpointStepControlDetected
            &&Stats.FloorProfileEndpointSlopeControlDetected;
        return bDetailPass&&bGridPass&&bThinSheetPass&&bFloorProfilePass;
    }

private:
    bool NativeOnlyContainsColumn(float X,float Y) const
    {
        return std::isfinite(X)&&std::isfinite(Y)
            &&X>=NativeOnlyMinimum.X&&X<=NativeOnlyMaximum.X
            &&Y>=NativeOnlyMinimum.Y&&Y<=NativeOnlyMaximum.Y;
    }

    bool NativeOnlyContains(float X,float Y,float Z) const
    {
        return std::isfinite(X)&&std::isfinite(Y)&&std::isfinite(Z)
            &&X>=NativeOnlyMinimum.X&&X<=NativeOnlyMaximum.X
            &&Y>=NativeOnlyMinimum.Y&&Y<=NativeOnlyMaximum.Y
            &&Z>=NativeOnlyMinimum.Z&&Z<=NativeOnlyMaximum.Z;
    }

    static FClassificationThreadStats& ThreadClassificationStats()
    {
        static thread_local FClassificationThreadStats Stats;
        return Stats;
    }

    const VoxelForgeCore::WorldAssemblyStratumPlanV1* FindWorldAssemblyStratum(
        int32 StrateIndex,int32 ChunkZ) const
    {
        if(!WorldAssembly||StrateIndex<0)return nullptr;
        const auto It=std::find_if(WorldAssembly->plan.strates.begin(),WorldAssembly->plan.strates.end(),
            [StrateIndex,ChunkZ](const auto& Entry)
            {return Entry.strateIndex==StrateIndex&&ChunkZ<=Entry.topChunkZ&&ChunkZ>=Entry.bottomChunkZ;});
        return It==WorldAssembly->plan.strates.end()?nullptr:&*It;
    }

    const VoxelForgeCore::WorldAssemblyFloatingIslandPlanV1* FindWorldAssemblyFloatingIslandStratum(
        int32 StrateIndex,int32 ChunkZ) const
    {
        if(!WorldAssembly||StrateIndex<0)return nullptr;
        const auto It=std::find_if(WorldAssembly->floatingIslands.begin(),
            WorldAssembly->floatingIslands.end(),[StrateIndex,ChunkZ](const auto& Entry)
            {return Entry.strateIndex==StrateIndex&&ChunkZ<=Entry.topChunkZ&&ChunkZ>=Entry.bottomChunkZ;});
        return It==WorldAssembly->floatingIslands.end()?nullptr:&*It;
    }

    bool NativeSurfaceDensityAt(float X,float Y,float Z,float& OutDensity) const
    {
        if(!bUseNativeManifestFields||!WorldAssembly||!ResolvedLayout||!Owner
            ||!Owner->Manager||!Owner->Generator||!std::isfinite(X)
            ||!std::isfinite(Y)||!std::isfinite(Z))return false;
        const float LayoutWidth=static_cast<float>(GetResolvedLayoutChunkWidthVoxels());
        if(!(LayoutWidth>0.0f))return false;
        const int32 ChunkZ=FMath::FloorToInt(Z/LayoutWidth);
        const FBoundStratumField* Bound=FindBoundStratumForChunk(ChunkZ);
        if(!Bound||Bound->Kind!=FBoundStratumField::EKind::SurfaceWorld
            ||!Bound->SurfacePlan||ChunkZ<Bound->SurfacePlan->bottomChunkZ
            ||ChunkZ>Bound->SurfacePlan->topChunkZ)return false;
        const auto* Field=std::get_if<FSurfaceWorldFieldAdapter>(&Bound->Evaluator);
        return Field&&Field->densityAt(X,Y,Z,OutDensity);
    }

    bool NativeFloatingIslandDensityAt(float X,float Y,float Z,float& OutDensity) const
    {
        if(!bUseNativeManifestFields||!WorldAssembly||!Owner||!Owner->Manager||!Owner->Generator
            ||!ResolvedLayout||!std::isfinite(X)||!std::isfinite(Y)||!std::isfinite(Z))
            return false;
        // Convert Core query Z back to the owner's legacy chunk coordinate.
        // Convertir Z du Core vers la coordonnee de chunk legacy du proprietaire.
        const double LayoutChunkWidth=GetResolvedLayoutChunkWidthVoxels();
        if(!(LayoutChunkWidth>0.0))return false;
        const int32 ChunkZ=FMath::FloorToInt(Z/static_cast<float>(LayoutChunkWidth));
        const FBoundStratumField* Bound=FindBoundStratumForChunk(ChunkZ);
        if(!Bound||Bound->Kind!=FBoundStratumField::EKind::FloatingIslands
            ||!Bound->IslandPlan||ChunkZ<Bound->IslandPlan->bottomChunkZ
            ||ChunkZ>Bound->IslandPlan->topChunkZ)return false;
        const int32 StrateIndex=Bound->StrateIndex;
        const auto* Plan=Bound->IslandPlan;
        const auto* FieldAdapter=std::get_if<FFloatingIslandFieldAdapter>(
            &Bound->Evaluator);
        if(!FieldAdapter||!FieldAdapter->Evaluator.isValid())return false;
        constexpr double Scale=static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel);
        constexpr double Maximum=1000000000000.0/Scale;
        if(std::abs(static_cast<double>(X))>Maximum||std::abs(static_cast<double>(Y))>Maximum
            ||std::abs(static_cast<double>(Z))>Maximum)return false;
        const auto ToFixed=[](float Value)
        {return static_cast<int64>(std::llround(static_cast<double>(Value)
            *VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel));};
        const std::int64_t qx=ToFixed(X),qy=ToFixed(Y),qz=ToFixed(Z);
        std::int64_t Density=FieldAdapter->densitySubvoxelsAt(qx,qy,qz);
        const std::int64_t NativeDensity=Density;
        // The anchor-root field keeps broad lobes, but its shortest authored noise
        // wavelength is below one metre. Filter that detail only around a FloatingIslands
        // passage mouth so Marching Cubes does not expose voxel-sized chips on the crater
        // wall. The broad root profile is unchanged outside this local mouth envelope.
        double mouthFilterWeight=0.0;
        const double qToMetres=static_cast<double>(ResolvedLayout->coreVoxelSizeMicrometres)
            /(static_cast<double>(VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel)*1000000.0);
        const double densityMetres=std::abs(static_cast<double>(Density))*qToMetres;
        if(densityMetres<4.0)
        {
            bool hasResolvedPassageMouth=false;
            for(const auto& passage:ResolvedLayout->passages)
            {
                if(passage.upperStrateIndex!=StrateIndex)continue;
                hasResolvedPassageMouth=true;
                const double dx=(static_cast<double>(qx)-passage.upperMouthSubvoxels[0])*qToMetres;
                const double dy=(static_cast<double>(qy)-passage.upperMouthSubvoxels[1])*qToMetres;
                const double dz=(static_cast<double>(qz)-passage.upperMouthSubvoxels[2])*qToMetres;
                const double distance=std::sqrt(dx*dx+dy*dy+dz*dz);
                constexpr double FilterCoreRadiusMetres=8.5;
                constexpr double FilterOuterRadiusMetres=12.5;
                const double fade=std::clamp((FilterOuterRadiusMetres-distance)
                    /(FilterOuterRadiusMetres-FilterCoreRadiusMetres),0.0,1.0);
                const double weight=fade*fade*(3.0-2.0*fade);
                mouthFilterWeight=std::max(mouthFilterWeight,weight);
            }
            if(!hasResolvedPassageMouth)
            {
                // The passage-free native control retains the stratum route anchors.
                // Use its terminal route point as the same local mouth filter origin so
                // both native and composed fields receive the same root smoothing.
                const auto stratum=std::find_if(ResolvedLayout->strates.begin(),
                    ResolvedLayout->strates.end(),[StrateIndex](const auto& value)
                        {return value.strateIndex==StrateIndex;});
                if(stratum!=ResolvedLayout->strates.end())
                {
                    const VoxelForgeCore::ResolvedLayoutAnchorV2* terminal=nullptr;
                    for(const auto& anchor:stratum->anchors)
                        if(anchor.kind=="route_point"&&anchor.values.size()>=3)
                            terminal=&anchor;
                    if(terminal)
                    {
                        const double dx=static_cast<double>(qx-terminal->values[0])*qToMetres;
                        const double dy=static_cast<double>(qy-terminal->values[1])*qToMetres;
                        const double dz=static_cast<double>(qz-terminal->values[2])*qToMetres;
                        const double distance=std::sqrt(dx*dx+dy*dy+dz*dz);
                        constexpr double FilterCoreRadiusMetres=8.5;
                        constexpr double FilterOuterRadiusMetres=12.5;
                        const double fade=std::clamp((FilterOuterRadiusMetres-distance)
                            /(FilterOuterRadiusMetres-FilterCoreRadiusMetres),0.0,1.0);
                        mouthFilterWeight=fade*fade*(3.0-2.0*fade);
                    }
                }
            }
        }
        double routeNativeBlend=0.0;
        const auto mouthPassage=std::find_if(ResolvedLayout->passages.begin(),
            ResolvedLayout->passages.end(),[StrateIndex](const auto& passage)
                {return passage.upperStrateIndex==StrateIndex;});
        const double queryX=static_cast<double>(qx)*qToMetres;
        const double queryY=static_cast<double>(qy)*qToMetres;
        const double queryZ=static_cast<double>(qz)*qToMetres;
        const bool outsideCraterMouth=mouthPassage==ResolvedLayout->passages.end()
            ||std::hypot(queryX-mouthPassage->upperMouthSubvoxels[0]*qToMetres,
                queryY-mouthPassage->upperMouthSubvoxels[1]*qToMetres)>5.5;
        if(mouthFilterWeight>0.0&&outsideCraterMouth)
        {
            // Retain the native route only on the outer approach. The crater-mouth
            // interior stays with the filtered ground field and cannot become a bridge.
            const auto stratum=std::find_if(ResolvedLayout->strates.begin(),
                ResolvedLayout->strates.end(),[StrateIndex](const auto& value)
                    {return value.strateIndex==StrateIndex;});
            if(stratum!=ResolvedLayout->strates.end())
            {
                const VoxelForgeCore::ResolvedLayoutAnchorV2* previous=nullptr;
                for(const auto& anchor:stratum->anchors)
                {
                    if(anchor.kind!="route_point"||anchor.values.size()<3)continue;
                    if(previous)
                    {
                        const double ax=static_cast<double>(previous->values[0])*qToMetres;
                        const double ay=static_cast<double>(previous->values[1])*qToMetres;
                        const double az=static_cast<double>(previous->values[2])*qToMetres;
                        const double dx=(static_cast<double>(anchor.values[0])
                            -previous->values[0])*qToMetres;
                        const double dy=(static_cast<double>(anchor.values[1])
                            -previous->values[1])*qToMetres;
                        const double lengthSquared=dx*dx+dy*dy;
                        const double t=lengthSquared>0.0?std::clamp(
                            ((queryX-ax)*dx+(queryY-ay)*dy)/lengthSquared,0.0,1.0):0.0;
                        const double centerX=ax+t*dx,centerY=ay+t*dy;
                        const double centerZ=az+t*(static_cast<double>(anchor.values[2])
                            -previous->values[2])*qToMetres;
                        const double supportRadius=previous->values.size()>=4
                            ?static_cast<double>(previous->values[3])*qToMetres:0.75;
                        const double floorZ=centerZ-1.20;
                        constexpr double WalkCoreRadiusMetres=0.45;
                        constexpr double WearShoulderMetres=0.80;
                        const double protectedRadius=std::min(WalkCoreRadiusMetres,
                            supportRadius+0.10);
                        const double routeDistance=std::hypot(queryX-centerX,queryY-centerY);
                        const double radialT=std::clamp(
                            (protectedRadius+WearShoulderMetres-routeDistance)
                                /WearShoulderMetres,0.0,1.0);
                        const double verticalT=std::clamp(
                            (3.25-std::abs(queryZ-floorZ))/2.0,0.0,1.0);
                        const double radialSmooth=radialT*radialT*(3.0-2.0*radialT);
                        const double verticalSmooth=verticalT*verticalT*(3.0-2.0*verticalT);
                        routeNativeBlend=std::max(routeNativeBlend,
                            radialSmooth*verticalSmooth);
                    }
                    previous=&anchor;
                }
            }
        }
        if(mouthFilterWeight>0.0)
        {
            constexpr std::int64_t FilterStep=8*VoxelForgeCore::WorldAssemblySubvoxelsPerVoxel;
            std::int64_t weightedSum=0;
            for(int dz=-1;dz<=1;++dz)
                for(int dy=-1;dy<=1;++dy)
                    for(int dx=-1;dx<=1;++dx)
                    {
                        const std::int64_t weight=(dx==0?2:1)*(dy==0?2:1)*(dz==0?2:1);
                        const std::int64_t sample=(dx==0&&dy==0&&dz==0)?Density:
                            FieldAdapter->densitySubvoxelsAt(qx+dx*FilterStep,qy+dy*FilterStep,
                                qz+dz*FilterStep);
                        weightedSum+=sample*weight;
                    }
            // A separable [1,2,1]^3 kernel over a 2 m footprint filters sub-voxel
            // root detail while retaining the signed field on both sides of the surface.
            const double filtered=static_cast<double>(weightedSum)/64.0;
            std::int64_t filteredDensity=static_cast<std::int64_t>(std::llround(
                std::lerp(static_cast<double>(Density),filtered,mouthFilterWeight)));
            // Filtering detail at an open mouth may soften the surface, but it cannot
            // turn native air into a new solid shelf over the crater.
            if(NativeDensity>=0&&filteredDensity<0)filteredDensity=0;
            Density=filteredDensity;
            if(routeNativeBlend>0.0&&NativeDensity<0)
            {
                const double routePreserved=std::lerp(static_cast<double>(Density),
                    static_cast<double>(std::min(Density,NativeDensity)),
                    routeNativeBlend*0.60);
                Density=static_cast<std::int64_t>(std::llround(routePreserved));
            }
            // Marching Cubes can retain an isolated solid with no two-metre axis
            // thickness as a handful of disconnected triangles. Remove only shallow
            // negative samples surrounded by air at a one-metre probe distance; a
            // walk floor or wall has solid material on at least one side of this test.
            constexpr double FragmentProbeMetres=1.0;
            const std::int64_t fragmentStep=static_cast<std::int64_t>(std::llround(
                FragmentProbeMetres/qToMetres));
            if(mouthFilterWeight>=0.25&&Density<0
                &&static_cast<double>(-Density)*qToMetres<FragmentProbeMetres)
            {
                bool surroundedByAir=true;
                std::int64_t minimumAirDensity=std::numeric_limits<std::int64_t>::max();
                for(std::size_t axis=0;axis<3&&surroundedByAir;++axis)
                    for(const int sign:{-1,1})
                    {
                        std::array<std::int64_t,3> sample{qx,qy,qz};
                        sample[axis]+=sign*fragmentStep;
                        const std::int64_t neighbor=FieldAdapter->densitySubvoxelsAt(
                            sample[0],sample[1],sample[2]);
                        if(neighbor<=0)
                        {
                            surroundedByAir=false;
                            break;
                        }
                        minimumAirDensity=std::min(minimumAirDensity,neighbor);
                    }
                if(surroundedByAir)Density=std::max(Density,minimumAirDensity);
            }
        }
        const std::int64_t Bottom=Plan->manifest.recipe.layoutMinimumZSubvoxels;
        const std::int64_t Top=Plan->manifest.recipe.layoutMaximumZSubvoxels;
        const std::int64_t Seal=Plan->manifest.recipe.boundarySealSubvoxels;
        const std::int64_t Zq=ToFixed(Z);
        if(Plan->manifest.recipe.geometryVersion<3)
        {
            if(Zq>=Bottom&&Zq<Bottom+Seal)
                Density=std::min(Density,-std::max<std::int64_t>(1,Zq-Bottom));
            if(Zq<=Top&&Zq>Top-Seal)
                Density=std::min(Density,-std::max<std::int64_t>(1,Top-Zq));
            OutDensity=static_cast<float>(static_cast<double>(Density)/Scale);
        }
        else if(Plan->manifest.recipe.geometryVersion<4)
        {
            OutDensity=static_cast<float>(static_cast<double>(Density)/Scale);
            FResolvedStratumBounds Bounds;
            if(!MakeResolvedStratumBounds(static_cast<double>(Bottom)/Scale,
                static_cast<double>(Top)/Scale,static_cast<double>(Seal)/Scale,Bounds))
                return false;
            const FFloatingIslandParams* Params=FieldAdapter->legacyBoundaryParamsAt(ChunkZ);
            if(!Params)return false;
            float InternalDensity=-OutDensity;
            VF_ApplyUpperBoundarySeal(InternalDensity,Z,static_cast<float>(Bounds.TopZ),
                static_cast<float>(Bounds.SealThickness),Params->BaseDensity);
            OutDensity=-InternalDensity;
        }
        else OutDensity=static_cast<float>(static_cast<double>(Density)/Scale);
        return std::isfinite(OutDensity);
    }

    bool UsesLegacySurfaceField(float X,float Y,float Z) const
    {
        const FBoundStratumField* Bound=FindBoundStratumForZ(Z);
        return Bound&&Bound->Kind==FBoundStratumField::EKind::SurfaceWorld;
    }

    bool LegacyGeneratorDensityAt(float X,float Y,float Z,float& OutDensity) const
    {
        const FBoundStratumField* Bound=FindBoundStratumForZ(Z);
        const auto* Legacy=Bound?std::get_if<FLegacyGeneratorFieldAdapter>(
            &Bound->Evaluator):nullptr;
        return Legacy&&Legacy->densityAt(X,Y,Z,OutDensity);
    }

    float LegacySurfaceDensityAt(float X,float Y,float Z) const
    {
        // SurfaceWorld consumes biome overrides, terrain ops, water level and its sky cap in
        // the legacy stack. Reuse that immutable evaluator as an exact temporary bridge.
        // SurfaceWorld lit biomes, ops de terrain, niveau d'eau et plafond; reutiliser ce champ.
        float density=0.0f;
        if(!LegacyGeneratorDensityAt(X,Y,Z,density))
            density=Owner->Generator->GetDensityAt(X,Y,Z);
        density=ApplyResolvedStrateComposition(density,X,Y,Z);
        return ApplyEditBrushes(density,X,Y,Z);
    }

    float ApplyEditBrushes(float Density,double X,double Y,double Z) const
    {
        if(EditBrushes.empty()||X<EditBoundsMin.X||X>EditBoundsMax.X
            ||Y<EditBoundsMin.Y||Y>EditBoundsMax.Y||Z<EditBoundsMin.Z||Z>EditBoundsMax.Z)
            return Density;
        const double P[3]={X,Y,Z};
        for(const FEditBrush& Brush:EditBrushes)
        {
            double Distance=0.0;
            if(Brush.Shape==FEditBrush::EShape::Sphere)
            {
                const double DX=X-Brush.A[0],DY=Y-Brush.A[1],DZ=Z-Brush.A[2];
                Distance=DeterministicSqrt(DX*DX+DY*DY+DZ*DZ)-Brush.Radius;
            }
            else if(Brush.Shape==FEditBrush::EShape::Capsule)
            {
                double AB[3]{},AP[3]{},LengthSq=0.0,Dot=0.0;
                for(int32 Axis=0;Axis<3;++Axis)
                {AB[Axis]=Brush.B[Axis]-Brush.A[Axis];AP[Axis]=P[Axis]-Brush.A[Axis];LengthSq+=AB[Axis]*AB[Axis];Dot+=AB[Axis]*AP[Axis];}
                const double T=LengthSq>1.0e-12?std::clamp(Dot/LengthSq,0.0,1.0):0.0;
                double D2=0.0;
                for(int32 Axis=0;Axis<3;++Axis)
                {const double D=AP[Axis]-T*AB[Axis];D2+=D*D;}
                Distance=DeterministicSqrt(D2)-Brush.Radius;
            }
            else
            {
                double OutsideSq=0.0,MaxQ=-std::numeric_limits<double>::infinity();
                for(int32 Axis=0;Axis<3;++Axis)
                {
                    const double Q=std::abs(P[Axis]-Brush.A[Axis])-Brush.HalfExtent[Axis];
                    const double Outside=std::max(Q,0.0);
                    OutsideSq+=Outside*Outside;MaxQ=std::max(MaxQ,Q);
                }
                Distance=DeterministicSqrt(OutsideSq)+std::min(MaxQ,0.0)-Brush.Rounding;
            }
            if(Brush.Operation==FEditBrush::EOperation::DensityOffset)
            {
                double Influence=0.0;
                if(Brush.Shape==FEditBrush::EShape::Sphere)
                {
                    const double Radius=std::max(Brush.Radius,1.0e-12);
                    const double T=std::clamp((Distance+Brush.Radius)/Radius,0.0,1.0);
                    if(Distance+Brush.Radius>=Brush.Radius)continue;
                    Influence=1.0-T*T*(3.0-2.0*T);
                }
                else
                {
                    const double Band=std::max(static_cast<double>(Brush.Falloff),0.01);
                    if(Distance>=Band)continue;
                    const double T=std::clamp(std::max(Distance,0.0)/Band,0.0,1.0);
                    Influence=1.0-T*T*(3.0-2.0*T);
                }
                Density+=Brush.Strength*static_cast<float>(Influence);
                continue;
            }
            if(Brush.Operation==FEditBrush::EOperation::Carve)
                Density=std::max(Density,static_cast<float>(-Distance));
            else
                Density=std::min(Density,static_cast<float>(Distance));
        }
        return Density;
    }

    struct FAxisBins { int32 MinA=0,MinB=0,CountA=0,CountB=0; std::vector<std::vector<uint32>> Items; };
    struct FLayerField
    {
        int32 Lo=0,Hi=-1;
        int32 StrateIndex=INDEX_NONE;
        FStrateGenerationParams Params;
    };
    enum class ESurfaceFamily : uint8 { Strata, Cave, SolidOverlay };

    static bool NearInteger(float V,int32& Out)
    {
        const float R=std::round(V);
        if(std::abs(V-R)>0.0001f||R<static_cast<float>(MIN_int32)||R>static_cast<float>(MAX_int32))return false;
        Out=static_cast<int32>(R);return true;
    }

    static double DeterministicSqrt(double Value)
    {
        if(!(Value>0.0))return 0.0;
        return _mm_cvtsd_f64(_mm_sqrt_sd(_mm_setzero_pd(),_mm_set_sd(Value)));
    }

    bool Contains(int32 X,int32 Y,int32 Z) const
    {return X>=Min[0]&&X<=Max[0]&&Y>=Min[1]&&Y<=Max[1]&&Z>=Min[2]&&Z<=Max[2];}

    static int32 FloorDiv(int32 A,int32 B)
    {int32 Q=A/B,R=A%B;return Q-((R!=0&&R<0)?1:0);}

    static int64 RoundDiv(int64 N,int64 D)
    {return N>=0?(N+D/2)/D:-((-N+D/2)/D);}
    static float SmoothMinDistance(float A,float B,float Width)
    {
        if(Width<=0.0f)return std::min(A,B);
        const float H=std::max(Width-std::abs(A-B),0.0f)/Width;
        return std::min(A,B)-(H*H*H)*(Width/6.0f);
    }
    static float SmoothMaxDistance(float A,float B,float Width)
    {return -SmoothMinDistance(-A,-B,Width);}
    static std::uint64_t StampMix64(std::uint64_t value)
    {
        value^=value>>30;value*=0xbf58476d1ce4e5b9ull;
        value^=value>>27;value*=0x94d049bb133111ebull;
        return value^(value>>31);
    }
    static float StampLatticeValue(std::uint64_t seed,std::int64_t x,
        std::int64_t y,std::int64_t z)
    {
        std::uint64_t hash=StampMix64(seed^StampMix64(static_cast<std::uint64_t>(x)));
        hash=StampMix64(hash^StampMix64(static_cast<std::uint64_t>(y)));
        hash=StampMix64(hash^StampMix64(static_cast<std::uint64_t>(z)));
        const double unit=static_cast<double>(hash>>11)
            /static_cast<double>((std::uint64_t{1}<<53)-1);
        return static_cast<float>(unit*2.0-1.0);
    }
    static float StampValueNoise(float x,float y,float z,float wavelength,
        std::uint64_t seed)
    {
        if(!(wavelength>0.0f))return 0.0f;
        const double sx=static_cast<double>(x)/wavelength;
        const double sy=static_cast<double>(y)/wavelength;
        const double sz=static_cast<double>(z)/wavelength;
        const std::int64_t ix=static_cast<std::int64_t>(std::floor(sx));
        const std::int64_t iy=static_cast<std::int64_t>(std::floor(sy));
        const std::int64_t iz=static_cast<std::int64_t>(std::floor(sz));
        const auto smooth=[](float t){return t*t*(3.0f-2.0f*t);};
        const float tx=smooth(static_cast<float>(sx-ix));
        const float ty=smooth(static_cast<float>(sy-iy));
        const float tz=smooth(static_cast<float>(sz-iz));
        const auto lerp=[](float a,float b,float t){return a+(b-a)*t;};
        const float z0=lerp(lerp(StampLatticeValue(seed,ix,iy,iz),
                StampLatticeValue(seed,ix+1,iy,iz),tx),
            lerp(StampLatticeValue(seed,ix,iy+1,iz),
                StampLatticeValue(seed,ix+1,iy+1,iz),tx),ty);
        const float z1=lerp(lerp(StampLatticeValue(seed,ix,iy,iz+1),
                StampLatticeValue(seed,ix+1,iy,iz+1),tx),
            lerp(StampLatticeValue(seed,ix,iy+1,iz+1),
                StampLatticeValue(seed,ix+1,iy+1,iz+1),tx),ty);
        return lerp(z0,z1,tz);
    }
    static float StampEllipsoidSdf(float x,float y,float z,
        const std::array<float,3>& radius)
    {
        const float minimum=std::min({radius[0],radius[1],radius[2]});
        if(!(minimum>0.0f))return std::numeric_limits<float>::infinity();
        const float k0=std::sqrt((x/radius[0])*(x/radius[0])
            +(y/radius[1])*(y/radius[1])+(z/radius[2])*(z/radius[2]));
        const float k1=std::sqrt((x/(radius[0]*radius[0]))*(x/(radius[0]*radius[0]))
            +(y/(radius[1]*radius[1]))*(y/(radius[1]*radius[1]))
            +(z/(radius[2]*radius[2]))*(z/(radius[2]*radius[2])));
        return k1>1.0e-8f?k0*(k0-1.0f)/k1:-minimum;
    }
    static float StampRoundedBoxSdf(float x,float y,float z,
        const std::array<float,3>& halfSize,float rounding)
    {
        const float qx=std::abs(x)-halfSize[0]+rounding;
        const float qy=std::abs(y)-halfSize[1]+rounding;
        const float qz=std::abs(z)-halfSize[2]+rounding;
        const float outside=std::sqrt(std::max(qx,0.0f)*std::max(qx,0.0f)
            +std::max(qy,0.0f)*std::max(qy,0.0f)
            +std::max(qz,0.0f)*std::max(qz,0.0f));
        return outside+std::min(std::max({qx,qy,qz}),0.0f)-rounding;
    }
    static float StampPillarSdf(float x,float y,float z,
        const std::array<float,3>& halfSize)
    {
        const float radial=(std::sqrt((x/halfSize[0])*(x/halfSize[0])
            +(y/halfSize[1])*(y/halfSize[1]))-1.0f)
            *std::min(halfSize[0],halfSize[1]);
        const float vertical=std::abs(z)-halfSize[2];
        const float outside=std::sqrt(std::max(radial,0.0f)*std::max(radial,0.0f)
            +std::max(vertical,0.0f)*std::max(vertical,0.0f));
        return outside+std::min(std::max(radial,vertical),0.0f);
    }
    static float StampArchSdf(float x,float y,float z,
        const std::array<float,3>& halfSize)
    {
        const float round=std::min(0.25f,std::min(halfSize[0],halfSize[1])*0.08f);
        const float lower=StampRoundedBoxSdf(x,y,z+halfSize[2]*0.5f,
            {halfSize[0],halfSize[1],halfSize[2]*0.5f},round);
        const float top=std::max(StampEllipsoidSdf(x,y,z,halfSize),-z);
        return SmoothMinDistance(lower,top,round*2.0f);
    }
    float StampSdf(const FStampRuntime& stamp,float x,float y,float z) const
    {
        float localX=x-stamp.positionVoxels[0];
        float localY=y-stamp.positionVoxels[1];
        const float localZ=z-stamp.positionVoxels[2];
        switch(stamp.quarterTurns&3u)
        {
        case 1:{const float oldX=localX;localX=localY;localY=-oldX;break;}
        case 2:localX=-localX;localY=-localY;break;
        case 3:{const float oldX=localX;localX=-localY;localY=oldX;break;}
        default:break;
        }
        float distance=0.0f;
        switch(stamp.record->kind)
        {
        case VoxelForgeCore::ResolvedSdfStampKindV1::carveEllipsoid:
            distance=StampEllipsoidSdf(localX,localY,localZ,stamp.halfExtentsVoxels);break;
        case VoxelForgeCore::ResolvedSdfStampKindV1::carveArch:
            distance=StampArchSdf(localX,localY,localZ,stamp.halfExtentsVoxels);break;
        case VoxelForgeCore::ResolvedSdfStampKindV1::fillPillar:
            distance=StampPillarSdf(localX,localY,localZ,stamp.halfExtentsVoxels);break;
        case VoxelForgeCore::ResolvedSdfStampKindV1::fillDais:
            if(ResolvedLayout&&ResolvedLayout->stampVocabularyVersion
                >=VoxelForgeCore::ResolvedLayoutStampVocabularyVersionV2)
                distance=StampEllipsoidSdf(localX,localY,localZ,stamp.halfExtentsVoxels);
            else
                distance=StampRoundedBoxSdf(localX,localY,localZ,stamp.halfExtentsVoxels,
                    std::min(0.35f,std::min({stamp.halfExtentsVoxels[0],
                        stamp.halfExtentsVoxels[1],stamp.halfExtentsVoxels[2]})*0.15f));
            break;
        default:return std::numeric_limits<float>::infinity();
        }
        if(stamp.irregularityAmplitudeVoxels>0.0f)
            distance+=StampValueNoise(localX,localY,localZ,
                stamp.irregularityWavelengthVoxels,stamp.irregularitySeed)
                    *stamp.irregularityAmplitudeVoxels;
        return distance;
    }
    float ApplyResolvedSdfStamps(float density,float X,float Y,float Z) const
    {
        if(StampRuntime.empty()||!Owner||Owner->CoreVoxelSizeMicrons==0)return density;
        const auto* tileQueries=ActivePassageTileQueries;
        const bool scoped=tileQueries&&tileQueries->matches(*this);
        if(scoped&&!tileQueries->hasStampCandidates())return density;
        const auto* bound=FindBoundStratumForManagerZ(Z);
        if(!bound)return density;
        const double micronsPerVoxel=Owner->CoreVoxelSizeMicrons;
        const std::array<double,3> worldMicrometres={X*micronsPerVoxel,
            Y*micronsPerVoxel,Z*micronsPerVoxel};
        float composed=density;
        const auto apply=[&](std::uint32_t index)
        {
            if(index>=StampRuntime.size())return;
            const auto& runtime=StampRuntime[index];const auto& record=*runtime.record;
            if(record.strateIndex!=bound->StrateIndex)return;
            for(std::size_t axis=0;axis<3;++axis)
                if(worldMicrometres[axis]<record.boundsMinimumMicrometres[axis]
                    ||worldMicrometres[axis]>record.boundsMaximumMicrometres[axis])return;
            const float distance=StampSdf(runtime,X,Y,Z);
            if(record.kind==VoxelForgeCore::ResolvedSdfStampKindV1::carveEllipsoid
                ||record.kind==VoxelForgeCore::ResolvedSdfStampKindV1::carveArch)
                composed=SmoothMaxDistance(composed,-distance,runtime.smoothWidthVoxels);
            else
                composed=SmoothMinDistance(composed,distance,runtime.smoothWidthVoxels);
        };
        if(scoped)
            for(const auto index:tileQueries->stampCandidates())apply(index);
        else
            for(std::size_t index=0;index<StampRuntime.size();++index)
                apply(static_cast<std::uint32_t>(index));
        return composed;
    }
    float ApplyResolvedCavernGraph(float density,float X,float Y,float Z) const
    {
        if(CavernRuntime.empty()||!Owner||Owner->CoreVoxelSizeMicrons==0)return density;
        const auto* tileQueries=ActivePassageTileQueries;
        const bool scoped=tileQueries&&tileQueries->matches(*this);
        if(scoped&&!tileQueries->hasCavernCandidates())return density;
        const auto* bound=FindBoundStratumForManagerZ(Z);
        if(!bound)return density;
        const double micronsPerVoxel=Owner->CoreVoxelSizeMicrons;
        const std::array<double,3> worldMicrometres={X*micronsPerVoxel,
            Y*micronsPerVoxel,Z*micronsPerVoxel};
        float composed=density;
        const auto apply=[&](std::uint32_t index)
        {
            if(index>=CavernRuntime.size())return;
            const auto& feature=CavernRuntime[index];
            const std::int32_t strateIndex=feature.room?feature.room->strateIndex
                :feature.edge?feature.edge->strateIndex:-1;
            if(strateIndex!=bound->StrateIndex)return;
            for(std::size_t axis=0;axis<3;++axis)
                if(worldMicrometres[axis]<feature.boundsMinimumMicrometres[axis]
                    ||worldMicrometres[axis]>feature.boundsMaximumMicrometres[axis])return;
            if(feature.room)
            {
                const float localX=X-feature.centerVoxels[0];
                const float localY=Y-feature.centerVoxels[1];
                const float localZ=Z-feature.centerVoxels[2];
                if(Z<feature.floorVoxels)return;
                float distance=StampEllipsoidSdf(localX,localY,localZ,
                    feature.halfExtentsVoxels);
                if(feature.irregularityAmplitudeVoxels>0.0f)
                {
                    const float fade=SmoothUnit((Z-feature.floorVoxels)/0.8f);
                    distance+=StampValueNoise(localX,localY,localZ,
                        feature.irregularityWavelengthVoxels,feature.irregularitySeed)
                            *feature.irregularityAmplitudeVoxels*fade;
                }
                composed=SmoothMaxDistance(composed,-distance,feature.smoothWidthVoxels);
                const float horizontal=std::sqrt(
                    (localX*localX)/(feature.halfExtentsVoxels[0]
                        *feature.halfExtentsVoxels[0])
                    +(localY*localY)/(feature.halfExtentsVoxels[1]
                        *feature.halfExtentsVoxels[1]));
                if(horizontal<=1.0f)
                    composed=std::min(composed,Z-feature.floorVoxels);
                return;
            }
            if(!feature.edge)return;
            const auto bezier=[&](float t,std::size_t axis)
            {
                const float one=1.0f-t;
                return one*one*one*feature.controlPointsVoxels[0][axis]
                    +3.0f*one*one*t*feature.controlPointsVoxels[1][axis]
                    +3.0f*one*t*t*feature.controlPointsVoxels[2][axis]
                    +t*t*t*feature.controlPointsVoxels[3][axis];
            };
            const auto derivative=[&](float t,std::size_t axis)
            {
                const float one=1.0f-t;
                return 3.0f*one*one*(feature.controlPointsVoxels[1][axis]
                        -feature.controlPointsVoxels[0][axis])
                    +6.0f*one*t*(feature.controlPointsVoxels[2][axis]
                        -feature.controlPointsVoxels[1][axis])
                    +3.0f*t*t*(feature.controlPointsVoxels[3][axis]
                        -feature.controlPointsVoxels[2][axis]);
            };
            const auto secondDerivative=[&](float t,std::size_t axis)
            {
                return 6.0f*(1.0f-t)*(feature.controlPointsVoxels[2][axis]
                        -2.0f*feature.controlPointsVoxels[1][axis]
                        +feature.controlPointsVoxels[0][axis])
                    +6.0f*t*(feature.controlPointsVoxels[3][axis]
                        -2.0f*feature.controlPointsVoxels[2][axis]
                        +feature.controlPointsVoxels[1][axis]);
            };
            float t=0.0f,bestDistanceSquared=std::numeric_limits<float>::infinity();
            for(int sample=0;sample<=16;++sample)
            {
                const float candidate=static_cast<float>(sample)/16.0f;
                const float dx=X-bezier(candidate,0),dy=Y-bezier(candidate,1);
                const float distanceSquared=dx*dx+dy*dy;
                if(distanceSquared<bestDistanceSquared)
                {bestDistanceSquared=distanceSquared;t=candidate;}
            }
            for(int iteration=0;iteration<5;++iteration)
            {
                const float dx=bezier(t,0)-X,dy=bezier(t,1)-Y;
                const float vx=derivative(t,0),vy=derivative(t,1);
                const float ax=secondDerivative(t,0),ay=secondDerivative(t,1);
                const float denominator=vx*vx+vy*vy+dx*ax+dy*ay;
                if(std::abs(denominator)<1.0e-5f)break;
                t=std::clamp(t-(dx*vx+dy*vy)/denominator,0.0f,1.0f);
            }
            const float centerX=bezier(t,0),centerY=bezier(t,1);
            const float floorZ=bezier(t,2);
            const float radial=std::hypot(X-centerX,Y-centerY);
            const float radius=feature.boreRadiusVoxels;
            const float vertical=(Z-floorZ)/feature.boreHeightVoxels;
            const float normalized=std::sqrt((radial/radius)*(radial/radius)
                +vertical*vertical);
            float distance=(normalized-1.0f)*std::min(radius,feature.boreHeightVoxels);
            if(feature.irregularityAmplitudeVoxels>0.0f)
            {
                const float fade=SmoothUnit((Z-floorZ)/0.8f);
                distance+=StampValueNoise(X-feature.controlPointsVoxels[0][0],
                    Y-feature.controlPointsVoxels[0][1],Z-floorZ,
                    feature.irregularityWavelengthVoxels,feature.irregularitySeed)
                        *feature.irregularityAmplitudeVoxels*fade;
            }
            if(Z<floorZ)
            {
                if(composed>0.0f&&feature.floorSupportDepthVoxels>0.0f
                    &&Z>=floorZ-feature.floorSupportDepthVoxels
                    &&radial<radius-0.12f)
                {
                    const float supportDistance=std::max(radial-(radius-0.12f),
                        std::max(floorZ-feature.floorSupportDepthVoxels-Z,Z-floorZ));
                    composed=std::min(composed,supportDistance);
                }
                return;
            }
            composed=SmoothMaxDistance(composed,-distance,feature.smoothWidthVoxels);
            // The hard profile cap is deliberately applied after the smooth union and
            // relief. Below it, native rock remains untouched; the narrow support above
            // fills only baseline air.
            if(radial<=radius)
                composed=std::min(composed,Z-floorZ);
        };
        if(scoped)
            for(const auto index:tileQueries->cavernFeatureCandidates())apply(index);
        else
            for(std::size_t index=0;index<CavernRuntime.size();++index)
                apply(static_cast<std::uint32_t>(index));
        return composed;
    }

    float ApplyResolvedCavernFloorCaps(float density,float X,float Y,float Z) const
    {
        if(CavernRuntime.empty()||!Owner||Owner->CoreVoxelSizeMicrons==0)return density;
        const auto* tileQueries=ActivePassageTileQueries;
        const bool scoped=tileQueries&&tileQueries->matches(*this);
        if(scoped&&!tileQueries->hasCavernCandidates())return density;
        const auto* bound=FindBoundStratumForManagerZ(Z);
        if(!bound)return density;
        const double micronsPerVoxel=Owner->CoreVoxelSizeMicrons;
        const std::array<double,3> worldMicrometres={X*micronsPerVoxel,
            Y*micronsPerVoxel,Z*micronsPerVoxel};
        float capped=density;
        const auto apply=[&](std::uint32_t index)
        {
            if(index>=CavernRuntime.size())return;
            const auto& feature=CavernRuntime[index];
            const std::int32_t strateIndex=feature.room?feature.room->strateIndex
                :feature.edge?feature.edge->strateIndex:-1;
            if(strateIndex!=bound->StrateIndex)return;
            for(std::size_t axis=0;axis<3;++axis)
                if(worldMicrometres[axis]<feature.boundsMinimumMicrometres[axis]
                    ||worldMicrometres[axis]>feature.boundsMaximumMicrometres[axis])return;
            if(feature.room)
            {
                if(Z<feature.floorVoxels)return;
                const float localX=X-feature.centerVoxels[0];
                const float localY=Y-feature.centerVoxels[1];
                const float horizontal=std::sqrt(
                    (localX*localX)/(feature.halfExtentsVoxels[0]
                        *feature.halfExtentsVoxels[0])
                    +(localY*localY)/(feature.halfExtentsVoxels[1]
                        *feature.halfExtentsVoxels[1]));
                if(horizontal<=1.0f)
                    capped=std::min(capped,Z-feature.floorVoxels);
                return;
            }
            if(!feature.edge)return;
            const auto bezier=[&](float t,std::size_t axis)
            {
                const float one=1.0f-t;
                return one*one*one*feature.controlPointsVoxels[0][axis]
                    +3.0f*one*one*t*feature.controlPointsVoxels[1][axis]
                    +3.0f*one*t*t*feature.controlPointsVoxels[2][axis]
                    +t*t*t*feature.controlPointsVoxels[3][axis];
            };
            const auto derivative=[&](float t,std::size_t axis)
            {
                const float one=1.0f-t;
                return 3.0f*one*one*(feature.controlPointsVoxels[1][axis]
                        -feature.controlPointsVoxels[0][axis])
                    +6.0f*one*t*(feature.controlPointsVoxels[2][axis]
                        -feature.controlPointsVoxels[1][axis])
                    +3.0f*t*t*(feature.controlPointsVoxels[3][axis]
                        -feature.controlPointsVoxels[2][axis]);
            };
            const auto secondDerivative=[&](float t,std::size_t axis)
            {
                return 6.0f*(1.0f-t)*(feature.controlPointsVoxels[2][axis]
                        -2.0f*feature.controlPointsVoxels[1][axis]
                        +feature.controlPointsVoxels[0][axis])
                    +6.0f*t*(feature.controlPointsVoxels[3][axis]
                        -2.0f*feature.controlPointsVoxels[2][axis]
                        +feature.controlPointsVoxels[1][axis]);
            };
            float t=0.0f,bestDistanceSquared=std::numeric_limits<float>::infinity();
            for(int sample=0;sample<=16;++sample)
            {
                const float candidate=static_cast<float>(sample)/16.0f;
                const float dx=X-bezier(candidate,0),dy=Y-bezier(candidate,1);
                const float distanceSquared=dx*dx+dy*dy;
                if(distanceSquared<bestDistanceSquared)
                {bestDistanceSquared=distanceSquared;t=candidate;}
            }
            for(int iteration=0;iteration<5;++iteration)
            {
                const float dx=bezier(t,0)-X,dy=bezier(t,1)-Y;
                const float vx=derivative(t,0),vy=derivative(t,1);
                const float ax=secondDerivative(t,0),ay=secondDerivative(t,1);
                const float denominator=vx*vx+vy*vy+dx*ax+dy*ay;
                if(std::abs(denominator)<1.0e-5f)break;
                t=std::clamp(t-(dx*vx+dy*vy)/denominator,0.0f,1.0f);
            }
            const float floorZ=bezier(t,2);
            const float radial=std::hypot(X-bezier(t,0),Y-bezier(t,1));
            if(Z<floorZ)
            {
                // Re-evaluate the narrow fallback after passages and stamps, since
                // those later operations may open air beneath an otherwise native
                // floor. Negative native density is preserved by the min operation.
                if(capped>0.0f&&feature.floorSupportDepthVoxels>0.0f
                    &&Z>=floorZ-feature.floorSupportDepthVoxels
                    &&radial<feature.boreRadiusVoxels-0.12f)
                {
                    const float supportDistance=std::max(radial-
                        (feature.boreRadiusVoxels-0.12f),
                        std::max(floorZ-feature.floorSupportDepthVoxels-Z,Z-floorZ));
                    capped=std::min(capped,supportDistance);
                }
                return;
            }
            if(radial<=feature.boreRadiusVoxels)
                capped=std::min(capped,Z-floorZ);
        };
        if(scoped)
            for(const auto index:tileQueries->cavernFeatureCandidates())apply(index);
        else
            for(std::size_t index=0;index<CavernRuntime.size();++index)
                apply(static_cast<std::uint32_t>(index));
        return capped;
    }
    static float SmoothUnit(float V)
    {
        V=std::clamp(V,0.0f,1.0f);
        return V*V*(3.0f-2.0f*V);
    }
    static float DetailBandFade(float SignedDistance)
    {
        // Keep the larger candidate mask conservative around smooth family unions;
        // visible relief still fades to zero beyond its 4.125-voxel support radius.
        constexpr float Edge=DetailSupremum+0.125f;
        constexpr float Width=1.5f;
        return SmoothUnit((Edge-std::abs(SignedDistance))/Width);
    }
    static float DetailContrast(float CaveInfluence,float FloorInfluence)
    {
        const float Cave=std::clamp(CaveInfluence,0.0f,1.0f);
        const float Floor=std::min(Cave,std::clamp(FloorInfluence,0.0f,1.0f));
        const float StrataWeight=1.0f-Cave;
        const float CaveWeight=Cave-Floor;
        const float FloorWeight=Floor;
        // The three influences are a partition of unity. Cave floors blend at the
        // cave family's amplitude instead of multiplying both family contributions.
        return 1.35f*StrataWeight+1.00f*CaveWeight+0.55f*FloorWeight;
    }
    static float BlendDetailFamilies(float Relief,float PassageBandRelief,float OwnerRelief,
        float CaveInfluence,float FloorInfluence,float PassageInfluence)
    {
        const float Cave=std::clamp(CaveInfluence,0.0f,1.0f);
        const float Floor=std::min(Cave,std::clamp(FloorInfluence,0.0f,1.0f));
        const float Passage=std::clamp(PassageInfluence,0.0f,1.0f);
        const float NonPassageWeight=1.0f-Passage;
        const float StrataWeight=NonPassageWeight*(1.0f-Cave);
        const float CaveWeight=NonPassageWeight*(Cave-Floor);
        const float FloorWeight=NonPassageWeight*Floor;
        const float StrataRelief=1.35f*(Relief+0.5f*OwnerRelief);
        const float CaveRelief=1.00f*Relief;
        const float FloorRelief=0.55f*Relief;
        // The shared passage sweep supplies its own irregular relief. Keep only a
        // small trace of the terrain value-noise bands so their cell edges cannot
        // dominate the passage wall and read as repeated rings.
        const float PassageRelief=0.10f*PassageBandRelief;
        return StrataWeight*StrataRelief+CaveWeight*CaveRelief
            +FloorWeight*FloorRelief+Passage*PassageRelief;
    }
    static constexpr float DetailBandInnerRadius=1.5f;
    static float DetailBandFade(float SignedDistance,float Edge)
    {
        const float Distance=std::abs(SignedDistance);
        if(Distance<=DetailBandInnerRadius)return 1.0f;
        const float Width=Edge-DetailBandInnerRadius;
        return Width>0.0f?SmoothUnit((Edge-Distance)/Width):0.0f;
    }
    static float LocalDetailBandEdge(float MacroValue,float SurfaceSDF,
        float CaveInfluence,float FloorInfluence,const FLayerField* Field)
    {
        float OwnerBound=0.0f;
        if(Field)
        {
            const FStrateGenerationParams& Params=Field->Params;
            const float Depth=Params.SurfaceRoughness*2.0f;
            if(Depth>0.0f&&std::abs(SurfaceSDF)<Depth&&Params.RoughnessFrequency>0.0f)
            {
                const float Fade=1.0f-std::abs(SurfaceSDF)/Depth;
                // Perlin is bounded by 2; the squared ridged fold by 2.25. This
                // uses the largest type bound and remains valid under domain warp.
                OwnerBound=3.15f*VOXEL_NOISE_SCALE*Params.SurfaceRoughness*Fade*Fade;
            }
        }
        const float ReliefBound=1.20f*std::abs(MacroValue)
            +(0.80f+0.25f*MacroValue)*(0.40f+0.60f);
        const float Contrast=DetailContrast(CaveInfluence,FloorInfluence);
        const float LocalSupremum=std::min(3.9f,(ReliefBound+0.5f*OwnerBound)*Contrast);
        return std::clamp(LocalSupremum+0.125f,DetailBandInnerRadius,DetailSupremum+0.125f);
    }

    float DetailBandFadeAt(double X,double Y,double Z,float SignedDistance,float SurfaceSDF,
        float CaveInfluence,float FloorInfluence) const
    {
        if(DetailVariant!=EDetailVariant::Coherent
            ||std::abs(SignedDistance)<=DetailBandInnerRadius)
            return DetailBandFade(SignedDistance);
        const float MacroValue=FStandaloneResearchTunnels::ValueNoise(
            static_cast<float>(X),static_cast<float>(Y),static_cast<float>(Z),32,
            static_cast<uint32>(Owner->Seed)^0xB5297A4Du);
        const FLayerField* Field=FindLayerField(Z);
        return DetailBandFade(SignedDistance,LocalDetailBandEdge(MacroValue,SurfaceSDF,
            CaveInfluence,FloorInfluence,Field));
    }

    void BuildLayerBounds()
    {
        LayerRanges.clear();LayerFields.clear();
        const auto& Layout=Owner->Manager->GetLayout();
        int32 Top=MIN_int32,Bottom=MAX_int32;
        for(const FStrateSlot& Slot:Layout)
        {
            FResolvedStratumBounds Bounds;
            if(!GetResolvedStratumBounds(Slot,Bounds))continue;
            const int32 ResolvedBottom=FMath::FloorToInt(static_cast<float>(Bounds.BottomZ));
            const int32 ResolvedTop=FMath::CeilToInt(static_cast<float>(Bounds.TopZ));
            Top=std::max(Top,ResolvedTop);Bottom=std::min(Bottom,ResolvedBottom);
            if(!Slot.Definition)continue;
            const int32 MidChunkZ=(Slot.TopChunkZ+Slot.BottomChunkZ)/2;
            FLayerField Field;
            Field.Lo=ResolvedBottom;
            Field.Hi=ResolvedTop;
            Field.StrateIndex=Slot.StrateIndex;
            Field.Params=Owner->Manager->GetGenerationParams(FIntVector(0,0,MidChunkZ));
            LayerFields.push_back(std::move(Field));
        }
        if(Top>=Bottom)
        {
            LayerRanges.push_back({Bottom,Top});
        }
    }

    static std::array<double,3> V3(const FVector& V){return {V.X,V.Y,V.Z};}
    static double Dot(const std::array<double,3>& A,const std::array<double,3>& B)
    {return A[0]*B[0]+A[1]*B[1]+A[2]*B[2];}
    static std::array<double,3> Sub(const FVector& A,const FVector& B)
    {return {A.X-B.X,A.Y-B.Y,A.Z-B.Z};}
    static std::array<double,3> Normalize(std::array<double,3> V)
    {
        const double L=std::sqrt(std::max(1.0e-24,Dot(V,V)));
        for(double& C:V)C/=L;return V;
    }
    static std::array<double,3> Cross(const std::array<double,3>& A,const std::array<double,3>& B)
    {return {A[1]*B[2]-A[2]*B[1],A[2]*B[0]-A[0]*B[2],A[0]*B[1]-A[1]*B[0]};}

    static VF_FieldPrimitive MakeSharedFieldPrimitive(const FPrimitive& P)
    {
        VF_FieldPrimitive Out{};
        if(P.bCapsule)Out.flags|=VF_FIELD_PRIMITIVE_CAPSULE;
        if(P.bSmoothCapsuleRadius)Out.flags|=VF_FIELD_PRIMITIVE_SMOOTH_CAPSULE;
        if(P.bRoundedBox)Out.flags|=VF_FIELD_PRIMITIVE_ROUNDED_BOX;
        if(P.bHasFloorClip)Out.flags|=VF_FIELD_PRIMITIVE_HAS_FLOOR;
        if(P.bCurvedFloorClip)Out.flags|=VF_FIELD_PRIMITIVE_CURVED_FLOOR;
        if(P.bCarve)Out.flags|=VF_FIELD_PRIMITIVE_CARVE;
        if(P.bCritical)Out.flags|=VF_FIELD_PRIMITIVE_CRITICAL;
        if(P.bPassageSurface)Out.flags|=VF_FIELD_PRIMITIVE_PASSAGE;
        for(int32 A=0;A<3;++A)
        {
            Out.minVoxel[A]=P.Min[A];Out.maxVoxel[A]=P.Max[A];
            Out.center[A]=P.CenterSub[A]/16.0;
            Out.capsuleStart[A]=P.CapsuleStartWorld[A];
            Out.capsuleDelta[A]=P.CapsuleAxisDelta[A];
            Out.roundedHalfExtent[A]=P.RoundedHalfExtent[A];
        }
        for(int32 I=0;I<3;++I)for(int32 J=0;J<3;++J)
            Out.q[I*3+J]=static_cast<double>(P.Q[I][J])/QScale;
        Out.minRadius=P.MinRadius;
        Out.capsuleAxisLengthSquared=P.CapsuleAxisLengthSquared;
        Out.capsuleAxisLength=P.CapsuleAxisLength;
        Out.capsuleStartRadius=P.CapsuleStartRadius;
        Out.capsuleEndRadius=P.CapsuleEndRadius;
        Out.profileStartT=P.CapsuleProfileStartT;
        Out.profileEndT=P.CapsuleProfileEndT;
        Out.profileStartRadius=P.CapsuleProfileStartRadius;
        Out.profileEndRadius=P.CapsuleProfileEndRadius;
        Out.radiusSlopeStart=P.CapsuleRadiusSlopeStart;
        Out.radiusSlopeEnd=P.CapsuleRadiusSlopeEnd;
        Out.rounding=P.Rounding;
        Out.blendRadius=P.BlendRadius;
        Out.floorBlendRadius=P.FloorBlendRadius;
        Out.floorCenterZ=P.FloorCenterZ;
        Out.floorSlopeX=P.FloorSlopeX;
        Out.floorSlopeY=P.FloorSlopeY;
        Out.floorCurveOriginX=P.FloorCurveOriginX;
        Out.floorCurveOriginY=P.FloorCurveOriginY;
        Out.floorCurveDeltaX=P.FloorCurveDeltaX;
        Out.floorCurveDeltaY=P.FloorCurveDeltaY;
        Out.floorCurveLength=P.FloorCurveLength;
        Out.floorCurveStartZ=P.FloorCurveStartZ;
        Out.floorCurveEndZ=P.FloorCurveEndZ;
        Out.floorCurveTangentStart=P.FloorCurveTangentStart;
        Out.floorCurveTangentEnd=P.FloorCurveTangentEnd;
        Out.floorCurveStartBlend=P.FloorCurveStartBlend;
        Out.floorCurveEndBlend=P.FloorCurveEndBlend;
        return Out;
    }

    void RebuildSharedFieldPrimitives()
    {
        InvalidateFarFieldGpuInput();
        SharedFieldPrimitives.clear();SharedFieldPrimitives.reserve(Primitives.size());
        for(const FPrimitive& P:Primitives)
            SharedFieldPrimitives.push_back(MakeSharedFieldPrimitive(P));
    }

    void AddEllipsoid(const FVector& Center,const std::array<double,3>& Radii,
                      const std::array<double,3>& Axis0={1,0,0},
                      const std::array<double,3>& Axis1={0,1,0},
                      const std::array<double,3>& Axis2={0,0,1},bool bCarve=true)
    {
        FPrimitive P;const auto C=V3(Center);
        for(int32 A=0;A<3;++A)P.CenterSub[A]=static_cast<int32>(std::llround(C[A]*SubPerVoxel));
        const std::array<std::array<double,3>,3> Axes={Axis0,Axis1,Axis2};
        int32 RSub[3];
        for(int32 K=0;K<3;++K)RSub[K]=std::max(16,static_cast<int32>(std::llround(std::max(1.0,Radii[K])*SubPerVoxel)));
        for(int32 I=0;I<3;++I)for(int32 J=0;J<3;++J)
        {
            int64 Sum=0;
            for(int32 K=0;K<3;++K)
            {
                const int64 RI=static_cast<int64>(std::llround(Axes[K][I]*32768.0));
                const int64 RJ=static_cast<int64>(std::llround(Axes[K][J]*32768.0));
                const int64 Den=static_cast<int64>(32768)*32768*RSub[K]*RSub[K];
                Sum+=RoundDiv(RI*RJ*QScale,Den);
            }
            P.Q[I][J]=Sum;
        }
        for(int32 A=0;A<3;++A)
        {
            double E=0.0;for(int32 K=0;K<3;++K)E+=std::abs(Axes[K][A])*Radii[K];
            P.Min[A]=static_cast<int32>(std::floor(C[A]-E))-1;
            P.Max[A]=static_cast<int32>(std::ceil(C[A]+E))+1;
        }
        P.MinRadius=static_cast<float>(std::min({Radii[0],Radii[1],Radii[2]}));
        P.BlendRadius=ActiveBlendRadius;
        P.bCarve=bCarve;Primitives.push_back(P);
    }

    void AddRoundedBox(const FVector& Center,const std::array<double,3>& HalfExtent,
                       double Rounding,bool bCarve=true)
    {
        const std::array<double,3> Outer={HalfExtent[0]+Rounding,HalfExtent[1]+Rounding,HalfExtent[2]+Rounding};
        AddEllipsoid(Center,Outer,{1,0,0},{0,1,0},{0,0,1},bCarve);
        FPrimitive& P=Primitives.back();P.bRoundedBox=true;P.Rounding=Rounding;
        for(int32 A=0;A<3;++A)P.RoundedHalfExtent[A]=HalfExtent[A];
    }

    static void ApplyFloorClip(FPrimitive& P,double FloorCenterZ,double SlopeX=0.0,double SlopeY=0.0,
                               double FloorBlendRadius=0.0)
    {
        P.bHasFloorClip=true;P.FloorCenterZ=FloorCenterZ-0.5;
        P.FloorSlopeX=SlopeX;P.FloorSlopeY=SlopeY;P.FloorBlendRadius=FloorBlendRadius;
    }

    void AddCapsule(const FVector& A,const FVector& B,float Radius,bool bCarve=true,bool bCritical=false,
                    bool bFloorClip=false,double FloorA=0.0,double FloorB=0.0)
    {
        AddLegacyEllipsoidCapsule(A,B,Radius,bCarve,bCritical,bFloorClip,FloorA,FloorB);
    }

    static FVector ApproximateUnwarp(const FVector& Target,const FStrateGenerationParams& Params,
                                     uint32 Seed)
    {
        FVector WorldPoint=Target;
        const float ZScale=Params.VerticalScale>0.0f?Params.VerticalScale:1.0f;
        if(ZScale!=1.0f)WorldPoint.Z*=ZScale;
        if(Params.CaveWarpStrength<=0.0f)return WorldPoint;
        for(int32 Iteration=0;Iteration<8;++Iteration)
        {
            const FVector Mapped=VoxelCaveMorphology::ApplyCaveWarp(WorldPoint,Params,Seed);
            const FVector Error=Target-Mapped;
            if(!Error.ContainsNaN()&&VoxelMath::IsFinite(Error.X)
                &&VoxelMath::IsFinite(Error.Y)&&VoxelMath::IsFinite(Error.Z))
            {
                WorldPoint.X+=Error.X;WorldPoint.Y+=Error.Y;WorldPoint.Z+=Error.Z*ZScale;
            }
        }
        return WorldPoint;
    }

    void AddLegacyEllipsoidCapsule(const FVector& A,const FVector& B,float Radius,bool bCarve,
                                   bool bCritical,bool bFloorClip,double FloorA,double FloorB)
    {
        const auto D=Sub(B,A);const double Length=std::sqrt(Dot(D,D));
        const double PreviousBlendRadius=ActiveBlendRadius;ActiveBlendRadius=0.0;
        if(!(Length>1.0e-4))
        {
            const size_t Before=Primitives.size();
            AddEllipsoid(A,{Radius,Radius,Radius},{1,0,0},{0,1,0},{0,0,1},bCarve);
            if(bFloorClip)ApplyFloorClip(Primitives.back(),std::min(FloorA,FloorB),0.0,0.0,
                0.0);
            if(bCritical)for(size_t I=Before;I<Primitives.size();++I)Primitives[I].bCritical=true;
            ActiveBlendRadius=PreviousBlendRadius;return;
        }
        const auto U=Normalize(D);
        const std::array<double,3> Ref=std::abs(U[2])<0.90?std::array<double,3>{0,0,1}:std::array<double,3>{0,1,0};
        const auto V=Normalize(Cross(U,Ref));const auto W=Normalize(Cross(U,V));
        const double SegmentStep=std::max(8.0,static_cast<double>(Radius)*2.0);
        const int32 Segments=std::max(1,static_cast<int32>(std::ceil(Length/SegmentStep)));
        for(int32 I=0;I<Segments;++I)
        {
            const double T0=static_cast<double>(I)/Segments,T1=static_cast<double>(I+1)/Segments;
            const FVector P0(A.X+D[0]*T0,A.Y+D[1]*T0,A.Z+D[2]*T0);
            const FVector P1(A.X+D[0]*T1,A.Y+D[1]*T1,A.Z+D[2]*T1);
            const FVector C((P0.X+P1.X)*0.5,(P0.Y+P1.Y)*0.5,(P0.Z+P1.Z)*0.5);
            const double Half=Length*(T1-T0)*0.5+Radius;
            const size_t Before=Primitives.size();AddEllipsoid(C,{Half,Radius,Radius},U,V,W,bCarve);
            if(bFloorClip)
            {
                const double Mid=(T0+T1)*0.5;
                const double Floor=(1.0-Mid)*FloorA+Mid*FloorB;
                const double DX=P1.X-P0.X,DY=P1.Y-P0.Y,HorizontalSq=DX*DX+DY*DY;
                const double FloorStep=(FloorB-FloorA)*(T1-T0);
                if(HorizontalSq>1.0e-6)
                    ApplyFloorClip(Primitives.back(),Floor,FloorStep*DX/HorizontalSq,
                        FloorStep*DY/HorizontalSq,0.0);
                else ApplyFloorClip(Primitives.back(),std::min(FloorA,FloorB),0.0,0.0,
                    0.0);
            }
            if(bCritical)for(size_t J=Before;J<Primitives.size();++J)Primitives[J].bCritical=true;
        }
        ActiveBlendRadius=PreviousBlendRadius;
    }

    void AddTaperedCapsule(const FVector& A,const FVector& B,float RadiusA,float RadiusB,
                           bool bCarve=true,bool bCritical=false,bool bFloorClip=false,
                           double FloorA=0.0,double FloorB=0.0,
                           double ExtendStart=0.0,double ExtendEnd=0.0)
    {
        RadiusA=std::max(1.0f,RadiusA);RadiusB=std::max(1.0f,RadiusB);
        const auto D=Sub(B,A);const double Length=std::sqrt(Dot(D,D));
        if(!(Length>1.0e-4))
        {
            AddEllipsoid(A,{RadiusA,RadiusA,RadiusA},{1,0,0},{0,1,0},{0,0,1},bCarve);
            Primitives.back().bCritical=bCritical;
            if(bFloorClip)ApplyFloorClip(Primitives.back(),std::min(FloorA,FloorB),0.0,0.0,
                ActiveFloorBlendRadius);
            return;
        }
        ExtendStart=std::clamp(ExtendStart,0.0,Length*0.4);
        ExtendEnd=std::clamp(ExtendEnd,0.0,Length*0.4);
        const double RadiusSlope=(static_cast<double>(RadiusB)-RadiusA)/Length;
        const float ExtendedRadiusA=static_cast<float>(std::max(1.0,RadiusA-RadiusSlope*ExtendStart));
        const float ExtendedRadiusB=static_cast<float>(std::max(1.0,RadiusB+RadiusSlope*ExtendEnd));
        const double Start[3]={A.X-D[0]*(ExtendStart/Length),A.Y-D[1]*(ExtendStart/Length),A.Z-D[2]*(ExtendStart/Length)};
        const double End[3]={B.X+D[0]*(ExtendEnd/Length),B.Y+D[1]*(ExtendEnd/Length),B.Z+D[2]*(ExtendEnd/Length)};
        FPrimitive P;
        P.bCapsule=true;P.bCarve=bCarve;P.bCritical=bCritical;
        P.CapsuleStartRadius=ExtendedRadiusA;P.CapsuleEndRadius=ExtendedRadiusB;
        P.MinRadius=std::min(ExtendedRadiusA,ExtendedRadiusB);P.BlendRadius=ActiveBlendRadius;
        const double R=std::max(ExtendedRadiusA,ExtendedRadiusB);
        double AxisLengthSquared=0.0;
        for(int32 Axis=0;Axis<3;++Axis)
        {
            P.CapsuleStartSub[Axis]=static_cast<int32>(std::llround(Start[Axis]*SubPerVoxel));
            P.CapsuleEndSub[Axis]=static_cast<int32>(std::llround(End[Axis]*SubPerVoxel));
            P.CapsuleStartWorld[Axis]=P.CapsuleStartSub[Axis]/static_cast<double>(SubPerVoxel);
            const double CapsuleEndWorld=P.CapsuleEndSub[Axis]/static_cast<double>(SubPerVoxel);
            P.CapsuleAxisDelta[Axis]=CapsuleEndWorld-P.CapsuleStartWorld[Axis];
            AxisLengthSquared+=P.CapsuleAxisDelta[Axis]*P.CapsuleAxisDelta[Axis];
            P.CenterSub[Axis]=static_cast<int32>(std::llround((Start[Axis]+End[Axis])*0.5*SubPerVoxel));
            P.Min[Axis]=static_cast<int32>(std::floor(std::min(Start[Axis],End[Axis])-R))-1;
            P.Max[Axis]=static_cast<int32>(std::ceil(std::max(Start[Axis],End[Axis])+R))+1;
        }
        P.CapsuleAxisLengthSquared=AxisLengthSquared;
        P.CapsuleAxisLength=std::sqrt(std::max(0.0,AxisLengthSquared));
        if(bFloorClip)
        {
            const double FloorSlope=(FloorB-FloorA)/Length;
            const double ExtendedFloorA=FloorA-FloorSlope*ExtendStart;
            const double ExtendedFloorB=FloorB+FloorSlope*ExtendEnd;
            const double ExtendedD[3]={End[0]-Start[0],End[1]-Start[1],End[2]-Start[2]};
            const double HorizontalSq=ExtendedD[0]*ExtendedD[0]+ExtendedD[1]*ExtendedD[1];
            if(HorizontalSq>1.0e-6)
                ApplyFloorClip(P,(ExtendedFloorA+ExtendedFloorB)*0.5,
                    (ExtendedFloorB-ExtendedFloorA)*ExtendedD[0]/HorizontalSq,
                    (ExtendedFloorB-ExtendedFloorA)*ExtendedD[1]/HorizontalSq,ActiveFloorBlendRadius);
            else ApplyFloorClip(P,std::min(ExtendedFloorA,ExtendedFloorB),0.0,0.0,ActiveFloorBlendRadius);
        }
        Primitives.push_back(P);
    }

    static double ContinuousJoinExtension(float RadiusA,float RadiusB,double SegmentLength)
    {
        return std::min(std::max(0.0,SegmentLength*0.35),
            JoinBlendRadius+0.5*static_cast<double>(std::max(RadiusA,RadiusB)));
    }

    static float CapsuleRadiusAt(const FPrimitive& P,const FVector& Point)
    {
        if(!P.bCapsule)return P.MinRadius;
        const double Start[3]={P.CapsuleStartSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[2]/static_cast<double>(SubPerVoxel)};
        const double End[3]={P.CapsuleEndSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[2]/static_cast<double>(SubPerVoxel)};
        const double V[3]={Point.X-Start[0],Point.Y-Start[1],Point.Z-Start[2]};
        const double D[3]={End[0]-Start[0],End[1]-Start[1],End[2]-Start[2]};
        const double D2=D[0]*D[0]+D[1]*D[1]+D[2]*D[2];
        const double T=D2>1.0e-12?(V[0]*D[0]+V[1]*D[1]+V[2]*D[2])/D2:0.0;
        return CapsuleRadiusAtT(P,T,std::sqrt(std::max(0.0,D2)));
    }

    static void FitCapsuleRadiiAtEndpoints(FPrimitive& P,const FVector& PointA,float RadiusA,
                                            const FVector& PointB,float RadiusB)
    {
        const double Start[3]={P.CapsuleStartSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[2]/static_cast<double>(SubPerVoxel)};
        const double End[3]={P.CapsuleEndSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[2]/static_cast<double>(SubPerVoxel)};
        const double D[3]={End[0]-Start[0],End[1]-Start[1],End[2]-Start[2]};
        const double D2=D[0]*D[0]+D[1]*D[1]+D[2]*D[2];
        if(D2<=1.0e-12)return;
        const auto Parameter=[&](const FVector& Point)
        {
            const double V[3]={Point.X-Start[0],Point.Y-Start[1],Point.Z-Start[2]};
            return (V[0]*D[0]+V[1]*D[1]+V[2]*D[2])/D2;
        };
        const double TA=Parameter(PointA),TB=Parameter(PointB);
        if(std::abs(TB-TA)<=1.0e-9)return;
        const double Slope=(RadiusB-RadiusA)/(TB-TA);
        P.CapsuleStartRadius=static_cast<float>(RadiusA-Slope*TA);
        P.CapsuleEndRadius=static_cast<float>(P.CapsuleStartRadius+Slope);
        P.MinRadius=std::min(P.CapsuleStartRadius,P.CapsuleEndRadius);
    }

    static void SetCapsuleRadiusProfile(FPrimitive& P,const FVector& PointA,float RadiusA,
        double SlopeA,const FVector& PointB,float RadiusB,double SlopeB)
    {
        const double Start[3]={P.CapsuleStartSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleStartSub[2]/static_cast<double>(SubPerVoxel)};
        const double End[3]={P.CapsuleEndSub[0]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[1]/static_cast<double>(SubPerVoxel),
            P.CapsuleEndSub[2]/static_cast<double>(SubPerVoxel)};
        const double D[3]={End[0]-Start[0],End[1]-Start[1],End[2]-Start[2]};
        const double D2=D[0]*D[0]+D[1]*D[1]+D[2]*D[2];
        if(D2<=1.0e-12)return;
        const auto Parameter=[&](const FVector& Point)
        {
            const double V[3]={Point.X-Start[0],Point.Y-Start[1],Point.Z-Start[2]};
            return std::clamp((V[0]*D[0]+V[1]*D[1]+V[2]*D[2])/D2,0.0,1.0);
        };
        P.CapsuleProfileStartT=Parameter(PointA);
        P.CapsuleProfileEndT=Parameter(PointB);
        P.CapsuleProfileStartRadius=RadiusA;
        P.CapsuleProfileEndRadius=RadiusB;
        P.CapsuleRadiusSlopeStart=SlopeA;
        P.CapsuleRadiusSlopeEnd=SlopeB;
        P.bSmoothCapsuleRadius=P.CapsuleProfileEndT-P.CapsuleProfileStartT>1.0e-6;
    }

    static float SmoothedControlRadius(const TArray<float>& Radii,int32 Index,float Fallback,
                                        float Minimum)
    {
        const int32 Count=Radii.Num();
        const float Current=std::max(Minimum,Radii.IsValidIndex(Index)?Radii[Index]:Fallback);
        if(Index<=0||Index+1>=Count)return Current;
        const auto At=[&](int32 I)
        {return std::max(Minimum,Radii[std::clamp(I,0,Count-1)]);};
        return (At(Index-4)+8.0f*At(Index-3)+28.0f*At(Index-2)+56.0f*At(Index-1)
            +70.0f*Current+56.0f*At(Index+1)+28.0f*At(Index+2)+8.0f*At(Index+3)
            +At(Index+4))*(1.0f/256.0f);
    }

    static double ControlRadiusSlopeAt(const TArray<FVector>& Points,const TArray<float>& Radii,
        int32 Index,float Fallback,float Minimum)
    {
        if(Points.Num()<2||Index<0||Index>=Points.Num())return 0.0;
        const auto RadiusAt=[&](int32 I)
        {return static_cast<double>(SmoothedControlRadius(Radii,I,Fallback,Minimum));};
        const auto LengthAt=[&](int32 I)
        {
            const FVector& A=Points[I];const FVector& B=Points[I+1];
            const double DX=B.X-A.X,DY=B.Y-A.Y,DZ=B.Z-A.Z;
            return std::sqrt(DX*DX+DY*DY+DZ*DZ);
        };
        if(Index==0)
        {
            const double Length=LengthAt(0);
            return Length>1.0e-9?(RadiusAt(1)-RadiusAt(0))/Length:0.0;
        }
        if(Index+1==Points.Num())
        {
            const double Length=LengthAt(Index-1);
            return Length>1.0e-9?(RadiusAt(Index)-RadiusAt(Index-1))/Length:0.0;
        }
        const double PrevLength=LengthAt(Index-1),NextLength=LengthAt(Index);
        if(PrevLength<=1.0e-9||NextLength<=1.0e-9)return 0.0;
        const double PrevSlope=(RadiusAt(Index)-RadiusAt(Index-1))/PrevLength;
        const double NextSlope=(RadiusAt(Index+1)-RadiusAt(Index))/NextLength;
        if(PrevSlope*NextSlope<=0.0)return 0.0;
        const double W1=2.0*NextLength+PrevLength,W2=NextLength+2.0*PrevLength;
        const double Harmonic=(W1+W2)/(W1/PrevSlope+W2/NextSlope);
        const double Limit=3.0*std::min(std::abs(PrevSlope),std::abs(NextSlope));
        return std::copysign(std::min(std::abs(Harmonic),Limit),Harmonic);
    }

    static double EvaluateFloorProfile(double A,double B,double TangentA,double TangentB,
        double Length,double StartBlend,double EndBlend,double S)
    {
        const double Secant=(B-A)/Length;
        if(S<0.0)return A+TangentA*S;
        if(S>Length)return B+TangentB*(S-Length);
        double Result=std::lerp(A,B,S/Length);
        const auto Correction=[](double DeltaSlope,double Span,double T)
        {
            if(!(Span>0.0)||T<0.0||T>=1.0)return 0.0;
            return DeltaSlope*Span*(T-2.0*T*T+T*T*T);
        };
        if(S<StartBlend)
            Result+=Correction(TangentA-Secant,StartBlend,S/StartBlend);
        if(Length-S<EndBlend)
            Result-=Correction(TangentB-Secant,EndBlend,(Length-S)/EndBlend);
        return Result;
    }

    static double EvaluateFloorProfileSlope(double A,double B,double TangentA,double TangentB,
        double Length,double StartBlend,double EndBlend,double S)
    {
        if(S<0.0)return TangentA;
        if(S>Length)return TangentB;
        const double Secant=(B-A)/Length;
        double Result=Secant;
        const auto CorrectionSlope=[](double DeltaSlope,double T)
        {return DeltaSlope*(1.0-4.0*T+3.0*T*T);};
        if(S<StartBlend)
            Result+=CorrectionSlope(TangentA-Secant,S/StartBlend);
        if(Length-S<EndBlend)
            Result+=CorrectionSlope(TangentB-Secant,(Length-S)/EndBlend);
        return Result;
    }

    void AuditFloorProfileBlendNegativeControls()
    {
        constexpr double A=2.0,B=11.0,TangentA=0.35,TangentB=-0.20;
        constexpr double Length=20.0,StartBlend=7.0,EndBlend=7.0;
        constexpr double Step=3.0,SlopeStep=0.25;
        constexpr double ValueThreshold=0.01,SlopeThreshold=0.001;
        const double endValue=EvaluateFloorProfile(A,B,TangentA,TangentB,
            Length,StartBlend,EndBlend,Length);
        const double startSlope=EvaluateFloorProfileSlope(A,B,TangentA,TangentB,
            Length,StartBlend,EndBlend,0.0);
        Stats.FloorProfileEndpointStepControlDetected=
            std::abs((endValue+Step)-B)>ValueThreshold;
        Stats.FloorProfileEndpointSlopeControlDetected=
            std::abs((startSlope+SlopeStep)-TangentA)>SlopeThreshold;
        std::printf("[FloorProfileBlendNegativeControls] endpoint_step=%.3f_vox tangent_step=%.3f_vox_per_m detected=%s/%s status=%s\n",
            Step,SlopeStep,
            Stats.FloorProfileEndpointStepControlDetected?"true":"false",
            Stats.FloorProfileEndpointSlopeControlDetected?"true":"false",
            Stats.FloorProfileEndpointStepControlDetected
                &&Stats.FloorProfileEndpointSlopeControlDetected?"PASS":"FAIL");
    }

    static double FloorSurfaceRelief(double X,double Y,uint32 Seed)
    {
        // A shared XY field keeps independently authored floor clips from ending on
        // separate flat planes. Its peak displacement stays under 1.2 voxels.
        const float Broad=FStandaloneResearchTunnels::ValueNoise(
            static_cast<float>(X),static_cast<float>(Y),0.0f,32,Seed^0x7F4A7C15u);
        const float Mid=FStandaloneResearchTunnels::ValueNoise(
            static_cast<float>(X),static_cast<float>(Y),0.0f,16,Seed^0x94D049BBu);
        return 0.80*Broad+0.35*Mid;
    }

    static std::vector<double> BuildFloorTangents(const TArray<FVector>& Points,
        const std::vector<float>& Floor,const std::vector<uint8_t>& MarkedSegments)
    {
        const size_t Count=Floor.size();std::vector<double> Tangent(Count,0.0);
        if(Count<2||Count!=static_cast<size_t>(Points.Num())||MarkedSegments.size()+1!=Count)return Tangent;
        std::vector<double> Length(Count-1,0.0),Slope(Count-1,0.0);
        for(size_t I=0;I+1<Count;++I)
        {
            const FVector& A=Points[static_cast<int32>(I)];const FVector& B=Points[static_cast<int32>(I+1)];
            Length[I]=std::hypot(B.X-A.X,B.Y-A.Y);
            if(Length[I]>1.0e-6)Slope[I]=(Floor[I+1]-Floor[I])/Length[I];
        }
        for(size_t I=0;I<Count;++I)
        {
            const bool bHasPrev=I>0&&Length[I-1]>1.0e-6;
            const bool bHasNext=I+1<Count&&Length[I]>1.0e-6;
            if(I==0){Tangent[I]=MarkedSegments[0]?0.0:Slope[0];continue;}
            if(I+1==Count){Tangent[I]=MarkedSegments[I-1]?0.0:Slope[I-1];continue;}
            const bool bPrevMarked=MarkedSegments[I-1]!=0,bNextMarked=MarkedSegments[I]!=0;
            if(bPrevMarked||bNextMarked)
            {
                if(!bPrevMarked&&bHasPrev)Tangent[I]=Slope[I-1];
                else if(!bNextMarked&&bHasNext)Tangent[I]=Slope[I];
                continue;
            }
            if(!bHasPrev||!bHasNext||Slope[I-1]*Slope[I]<=0.0)continue;
            const double W0=2.0*Length[I]+Length[I-1],W1=Length[I]+2.0*Length[I-1];
            const double Denominator=W0/Slope[I-1]+W1/Slope[I];
            if(std::abs(Denominator)>1.0e-12)
                Tangent[I]=(W0+W1)/Denominator;
        }
        return Tangent;
    }

    static void SetCurvedFloorClip(FPrimitive& P,const FVector& A,const FVector& B,
        double FloorA,double FloorB,double TangentA,double TangentB)
    {
        if(!P.bHasFloorClip)return;
        const double DX=B.X-A.X,DY=B.Y-A.Y,Length=std::hypot(DX,DY);
        if(Length<=1.0e-6)return;
        P.bCurvedFloorClip=true;P.FloorCurveOriginX=A.X;P.FloorCurveOriginY=A.Y;
        P.FloorCurveDeltaX=DX;P.FloorCurveDeltaY=DY;P.FloorCurveLength=Length;
        P.FloorCurveStartZ=FloorA;P.FloorCurveEndZ=FloorB;
        P.FloorCurveTangentStart=TangentA;P.FloorCurveTangentEnd=TangentB;
        P.FloorCurveStartBlend=std::min(8.0,Length*0.35);
        P.FloorCurveEndBlend=std::min(8.0,Length*0.35);
        for(int32 I=1;I<64;++I)
        {
            const double T=I/64.0;
            const double Curve=EvaluateFloorProfile(FloorA,FloorB,TangentA,TangentB,
                Length,P.FloorCurveStartBlend,P.FloorCurveEndBlend,Length*T);
            const double Linear=std::lerp(FloorA,FloorB,T);
            P.FloorCurveMaxDeviation=std::max(P.FloorCurveMaxDeviation,std::abs(Curve-Linear));
        }
        P.FloorCurveEndpointValueError=std::max(
            std::abs(EvaluateFloorProfile(FloorA,FloorB,TangentA,TangentB,Length,
                P.FloorCurveStartBlend,P.FloorCurveEndBlend,0.0)-FloorA),
            std::abs(EvaluateFloorProfile(FloorA,FloorB,TangentA,TangentB,Length,
                P.FloorCurveStartBlend,P.FloorCurveEndBlend,Length)-FloorB));
        P.FloorCurveEndpointSlopeError=std::max(
            std::abs(EvaluateFloorProfileSlope(FloorA,FloorB,TangentA,TangentB,Length,
                P.FloorCurveStartBlend,P.FloorCurveEndBlend,0.0)-TangentA),
            std::abs(EvaluateFloorProfileSlope(FloorA,FloorB,TangentA,TangentB,Length,
                P.FloorCurveStartBlend,P.FloorCurveEndBlend,Length)-TangentB));
    }

    double FloorAt(const FPrimitive& P,double X,double Y) const
    {
        double Base=0.0;
        if(P.bCurvedFloorClip)
        {
            const double T=((X-P.FloorCurveOriginX)*P.FloorCurveDeltaX
                +(Y-P.FloorCurveOriginY)*P.FloorCurveDeltaY)
                /(P.FloorCurveLength*P.FloorCurveLength);
            Base=EvaluateFloorProfile(P.FloorCurveStartZ,P.FloorCurveEndZ,
                P.FloorCurveTangentStart,P.FloorCurveTangentEnd,P.FloorCurveLength,
                P.FloorCurveStartBlend,P.FloorCurveEndBlend,T*P.FloorCurveLength);
        }
        else
            Base=P.FloorCenterZ+P.FloorSlopeX*(X-P.CenterSub[0]/16.0)
                +P.FloorSlopeY*(Y-P.CenterSub[1]/16.0);
        return Base;
    }

    double FloorSlopeAtEndpoint(const FPrimitive& P,bool bEnd) const
    {
        const double DX=P.bCurvedFloorClip?P.FloorCurveDeltaX
            :P.CapsuleEndSub[0]-P.CapsuleStartSub[0];
        const double DY=P.bCurvedFloorClip?P.FloorCurveDeltaY
            :P.CapsuleEndSub[1]-P.CapsuleStartSub[1];
        const double Length=P.bCurvedFloorClip?P.FloorCurveLength
            :std::hypot(DX,DY)/SubPerVoxel;
        if(Length<=1.0e-9)return 0.0;
        const double OriginX=P.bCurvedFloorClip?P.FloorCurveOriginX
            :P.CapsuleStartSub[0]/static_cast<double>(SubPerVoxel);
        const double OriginY=P.bCurvedFloorClip?P.FloorCurveOriginY
            :P.CapsuleStartSub[1]/static_cast<double>(SubPerVoxel);
        const double X=OriginX+(bEnd?DX/(P.bCurvedFloorClip?1.0:SubPerVoxel):0.0);
        const double Y=OriginY+(bEnd?DY/(P.bCurvedFloorClip?1.0:SubPerVoxel):0.0);
        constexpr double Epsilon=0.125;
        const double UX=DX/(Length*(P.bCurvedFloorClip?1.0:SubPerVoxel));
        const double UY=DY/(Length*(P.bCurvedFloorClip?1.0:SubPerVoxel));
        return (FloorAt(P,X+UX*Epsilon,Y+UY*Epsilon)
            -FloorAt(P,X-UX*Epsilon,Y-UY*Epsilon))/(2.0*Epsilon);
    }

    void BuildOwnerPrimitives()
    {
        const auto& Layout=Owner->Manager->GetLayout();
        const float MinX=static_cast<float>(Min[0]-256),MinY=static_cast<float>(Min[1]-256);
        const float MaxX=static_cast<float>(Max[0]+256),MaxY=static_cast<float>(Max[1]+256);
        for(const FStrateSlot& Slot:Layout)
        {
            if(!Slot.Definition)continue;
            const FIntVector MidChunk(0,0,(Slot.TopChunkZ+Slot.BottomChunkZ)/2);
            const FStrateGenerationParams Params=Owner->Manager->GetGenerationParams(MidChunk);
            ActiveBlendRadius=0.0;
            ActiveFloorBlendRadius=0.0;
            FChunkSDFCache Cache;
            VoxelCaveMorphology::BuildChunkCache(Cache,MinX,MinY,MaxX,MaxY,Params,
                static_cast<uint32>(Owner->Seed),
                Slot.StrateIndex,&Slot.Definition->TerrainOperations,ERoomGraphBuildSite::Unknown);
            for(const FCachedRoom& R:Cache.Rooms)
            {
                ++Stats.RoomCount;
                const size_t RoomPrimitiveStart=Primitives.size();
                const FVector RoomCenter=ApproximateUnwarp(R.Center,Params,
                    static_cast<uint32>(Owner->Seed));
                if(R.ShapeType==2)
                    AddCapsule(ApproximateUnwarp(R.ShapeA,Params,static_cast<uint32>(Owner->Seed)),
                        ApproximateUnwarp(R.ShapeB,Params,static_cast<uint32>(Owner->Seed)),
                        std::max(1.0f,R.ShapeR),true);
                else if(R.ShapeType==1)
                {
                    AddRoundedBox(RoomCenter,{std::abs(R.ShapeA.X),std::abs(R.ShapeA.Y),std::abs(R.ShapeA.Z)},
                        std::max(0.0f,R.ShapeR),true);
                }
                else
                    AddEllipsoid(RoomCenter,{std::abs(R.ShapeA.X),std::abs(R.ShapeA.Y),std::abs(R.ShapeA.Z)},
                        {1,0,0},{0,1,0},{0,0,1},true);
                if(R.FloorCutZ>-FLT_MAX*0.5f)
                {
                    const double Relief=std::max(0.0f,R.FloorReliefStrength);
                    const double FloorZ=ApproximateUnwarp(
                        FVector(R.Center.X,R.Center.Y,R.FloorCutZ-Relief),Params,
                        static_cast<uint32>(Owner->Seed)).Z;
                    for(size_t I=RoomPrimitiveStart;I<Primitives.size();++I)
                        if(Primitives[I].bCarve)ApplyFloorClip(Primitives[I],FloorZ,0.0,0.0,
                            FloorClipBlendRadius);
                }
                // The packed signs still union room intervals exactly. Blend only
                // the analytic cave field where neighboring authored rooms meet;
                // this rounds the room-to-room edge without touching tunnel radii.
                for(size_t I=RoomPrimitiveStart;I<Primitives.size();++I)
                    if(Primitives[I].bCarve)Primitives[I].BlendRadius=RoomUnionBlendRadius;
            }
            // Do not turn automatic room-overlap joins into thin positive ellipsoids.
            // Their 2.5-voxel support plates can sit above the lower room floor and render as
            // disconnected shards. Each room already carries its own clipped floor; the join
            // metadata remains available to the owner generator and is audited here.
            Stats.RoomFloorJoinCount+=static_cast<uint64>(Cache.RoomFloorJoins.Num());
            const double RoomBlendRadius=ActiveBlendRadius;
            ActiveBlendRadius=JoinBlendRadius;
            ActiveFloorBlendRadius=FloorClipBlendRadius;
            for(const FCachedTunnel& T:Cache.Tunnels)
            {
                ++Stats.TunnelCount;
                const bool bHasWorldChain=T.WorldControlPoints.Num()>1
                    &&T.WorldControlRadii.Num()==T.WorldControlPoints.Num();
                const TArray<FVector>& Points=bHasWorldChain?T.WorldControlPoints:T.ControlPoints;
                const TArray<float>& Radii=bHasWorldChain?T.WorldControlRadii:T.ControlRadii;
                const TArray<FTunnelFloorSegmentProfile>& FloorProfiles=bHasWorldChain
                    &&T.WorldFloorProfiles.Num()==Points.Num()-1?T.WorldFloorProfiles:T.FloorProfiles;
                std::vector<float> RawFloor(static_cast<size_t>(Points.Num()));
                std::vector<uint8_t> MarkedFloorSegments(Points.Num()>0?static_cast<size_t>(Points.Num()-1):0,0);
                for(int32 I=0;I<Points.Num();++I)
                    RawFloor[static_cast<size_t>(I)]=static_cast<float>(Points[I].Z
                        -SmoothedControlRadius(Radii,I,T.RadiusA,2.0f));
                if(FloorProfiles.Num()==Points.Num()-1)
                {
                    for(int32 I=0;I+1<Points.Num();++I)
                    {
                        const FTunnelFloorSegmentProfile& Profile=FloorProfiles[I];
                        if(I==0)RawFloor[0]=Profile.StartFloorZ;
                        else RawFloor[static_cast<size_t>(I)]=0.5f*(FloorProfiles[I-1].EndFloorZ+Profile.StartFloorZ);
                        RawFloor[static_cast<size_t>(I+1)]=Profile.EndFloorZ;
                        MarkedFloorSegments[static_cast<size_t>(I)]=Profile.bLedgeTransition?1:0;
                    }
                }
                for(int32 I=0;I<Points.Num();++I)
                {
                    const bool bPreviousUnmarked=I==0
                        ||!MarkedFloorSegments[static_cast<size_t>(I-1)];
                    const bool bNextUnmarked=I+1>=Points.Num()
                        ||!MarkedFloorSegments[static_cast<size_t>(I)];
                    if(bPreviousUnmarked&&bNextUnmarked)
                        RawFloor[static_cast<size_t>(I)]+=static_cast<float>(FloorSurfaceRelief(
                            Points[I].X,Points[I].Y,static_cast<uint32>(Owner->Seed)));
                }
                const std::vector<double> FloorTangents=BuildFloorTangents(
                    Points,RawFloor,MarkedFloorSegments);
                for(int32 Join=1;Join+1<Points.Num();++Join)
                {
                    const FVector A=Points[Join]-Points[Join-1],B=Points[Join+1]-Points[Join];
                    const double AL=std::sqrt(A.X*A.X+A.Y*A.Y+A.Z*A.Z);
                    const double BL=std::sqrt(B.X*B.X+B.Y*B.Y+B.Z*B.Z);
                    if(AL>1.0e-6&&BL>1.0e-6)
                    {
                        const double Dot=(A.X*B.X+A.Y*B.Y+A.Z*B.Z)/(AL*BL);
                        const double Angle=std::acos(std::clamp(Dot,-1.0,1.0))*57.29577951308232;
                        if(Angle>Stats.MaxTunnelBendDegrees)
                        {
                            Stats.MaxTunnelBendDegrees=Angle;Stats.MaxTunnelBendVoxels=Points[Join];
                            const double DX=A.X/AL+B.X/BL,DY=A.Y/AL+B.Y/BL,DZ=A.Z/AL+B.Z/BL;
                            const double DL=std::sqrt(DX*DX+DY*DY+DZ*DZ);
                            if(DL>1.0e-6)Stats.MaxTunnelBendDirection=FVector(DX/DL,DY/DL,DZ/DL);
                        }
                    }
                    const float RPrev=std::max(2.0f,Radii.IsValidIndex(Join-1)?Radii[Join-1]:T.RadiusA);
                    const float RHere=std::max(2.0f,Radii.IsValidIndex(Join)?Radii[Join]:T.RadiusA);
                    const float RNext=std::max(2.0f,Radii.IsValidIndex(Join+1)?Radii[Join+1]:T.RadiusB);
                    Stats.LegacySegmentRadiusStep=std::max(Stats.LegacySegmentRadiusStep,
                        static_cast<double>(std::abs(std::max(RPrev,RHere)-std::max(RHere,RNext))));
                    if(FloorProfiles.IsValidIndex(Join-1)&&FloorProfiles.IsValidIndex(Join))
                    {
                        Stats.MaxCapsuleJoinFloorDelta=std::max(Stats.MaxCapsuleJoinFloorDelta,
                            static_cast<double>(std::abs(FloorProfiles[Join-1].EndFloorZ
                                -FloorProfiles[Join].StartFloorZ)));
                        const FVector PrevD=Points[Join]-Points[Join-1];
                        const FVector NextD=Points[Join+1]-Points[Join];
                        const double PrevXY=std::sqrt(PrevD.X*PrevD.X+PrevD.Y*PrevD.Y);
                        const double NextXY=std::sqrt(NextD.X*NextD.X+NextD.Y*NextD.Y);
                        const double RawPrevSlope=PrevXY>1.0e-6
                            ?(FloorProfiles[Join-1].EndFloorZ-FloorProfiles[Join-1].StartFloorZ)/PrevXY:0.0;
                        const double RawNextSlope=NextXY>1.0e-6
                            ?(FloorProfiles[Join].EndFloorZ-FloorProfiles[Join].StartFloorZ)/NextXY:0.0;
                        const double RawSlopeDelta=std::abs(RawPrevSlope-RawNextSlope);
                        if(FloorProfiles[Join-1].bLedgeTransition||FloorProfiles[Join].bLedgeTransition)
                        {
                            ++Stats.MarkedFloorSlopeJoins;
                            Stats.MaxMarkedFloorSlopeDelta=std::max(Stats.MaxMarkedFloorSlopeDelta,RawSlopeDelta);
                        }
                        else
                        {
                            Stats.MaxRawUnmarkedFloorSlopeDelta=std::max(Stats.MaxRawUnmarkedFloorSlopeDelta,RawSlopeDelta);
                        }
                    }
                    ++Stats.CapsuleJoinCount;
                }
                if(Points.Num()>1)
                {
                    const size_t SegmentPrimitiveStart=Primitives.size();
                    for(int32 I=0;I+1<Points.Num();++I)
                    {
                        const float R0=SmoothedControlRadius(Radii,I,T.RadiusA,2.0f);
                        const float R1=SmoothedControlRadius(Radii,I+1,T.RadiusB,2.0f);
                        const double RadiusSlope0=ControlRadiusSlopeAt(Points,Radii,I,T.RadiusA,2.0f);
                        const double RadiusSlope1=ControlRadiusSlopeAt(Points,Radii,I+1,T.RadiusB,2.0f);
                        Stats.SmoothedProfileRadiusStep=std::max(Stats.SmoothedProfileRadiusStep,
                            static_cast<double>(std::abs(R1-R0)));
                        const FVector Segment=Points[I+1]-Points[I];
                        const double SegmentLength=std::sqrt(Segment.X*Segment.X+Segment.Y*Segment.Y+Segment.Z*Segment.Z);
                        const double Extension=ContinuousJoinExtension(R0,R1,SegmentLength);
                        const float ZA=RawFloor[static_cast<size_t>(I)];
                        const float ZB=RawFloor[static_cast<size_t>(I+1)];
                        AddTaperedCapsule(Points[I],Points[I+1],R0,R1,true,false,true,ZA,ZB,
                            I>0?Extension:0.0,I+2<Points.Num()?Extension:0.0);
                        if(!MarkedFloorSegments[static_cast<size_t>(I)])
                        {
                            SetCurvedFloorClip(Primitives.back(),Points[I],Points[I+1],ZA,ZB,
                                FloorTangents[static_cast<size_t>(I)],FloorTangents[static_cast<size_t>(I+1)]);
                            ++Stats.CurvedFloorSegments;
                            Stats.MaxFloorCurveDeviation=std::max(Stats.MaxFloorCurveDeviation,
                                Primitives.back().FloorCurveMaxDeviation);
                            Stats.MaxFloorProfileEndpointValueError=std::max(
                                Stats.MaxFloorProfileEndpointValueError,
                                Primitives.back().FloorCurveEndpointValueError);
                            Stats.MaxFloorProfileEndpointSlopeError=std::max(
                                Stats.MaxFloorProfileEndpointSlopeError,
                                Primitives.back().FloorCurveEndpointSlopeError);
                        }
                        FitCapsuleRadiiAtEndpoints(Primitives.back(),Points[I],R0,Points[I+1],R1);
                        SetCapsuleRadiusProfile(Primitives.back(),Points[I],R0,RadiusSlope0,
                            Points[I+1],R1,RadiusSlope1);
                    }
                    for(int32 Join=1;Join+1<Points.Num();++Join)
                    {
                        const FPrimitive& Previous=Primitives[SegmentPrimitiveStart+static_cast<size_t>(Join-1)];
                        const FPrimitive& Next=Primitives[SegmentPrimitiveStart+static_cast<size_t>(Join)];
                        const float PreviousEnd=CapsuleRadiusAt(Previous,Points[Join]);
                        const float NextStart=CapsuleRadiusAt(Next,Points[Join]);
                        Stats.MaxCapsuleJoinRadiusDelta=std::max(Stats.MaxCapsuleJoinRadiusDelta,
                            static_cast<double>(std::abs(PreviousEnd-NextStart)));
                        Stats.MaxCapsuleJoinRadiusSlopeDelta=std::max(
                            Stats.MaxCapsuleJoinRadiusSlopeDelta,
                            std::abs(Previous.CapsuleRadiusSlopeEnd-Next.CapsuleRadiusSlopeStart));
                        if(!MarkedFloorSegments[static_cast<size_t>(Join-1)]
                            &&!MarkedFloorSegments[static_cast<size_t>(Join)])
                        {
                            const double TangentDelta=Previous.bCurvedFloorClip&&Next.bCurvedFloorClip
                                ?std::abs(Previous.FloorCurveTangentEnd-Next.FloorCurveTangentStart)
                                :std::abs(FloorSlopeAtEndpoint(Previous,true)-FloorSlopeAtEndpoint(Next,false));
                            const double DirectionalSlopeChange=std::abs(FloorSlopeAtEndpoint(Previous,true)
                                -FloorSlopeAtEndpoint(Next,false));
                            Stats.MaxCapsuleJoinFloorSlopeDelta=std::max(
                                Stats.MaxCapsuleJoinFloorSlopeDelta,TangentDelta);
                            Stats.MaxUnmarkedFloorSlopeDelta=std::max(
                                Stats.MaxUnmarkedFloorSlopeDelta,TangentDelta);
                            Stats.MaxUnmarkedFloorDirectionSlopeDelta=std::max(
                                Stats.MaxUnmarkedFloorDirectionSlopeDelta,DirectionalSlopeChange);
                        }
                    }
                }
                else AddCapsule(T.EndpointA,T.EndpointB,std::max(T.RadiusA,T.RadiusB),true);
            }
            ActiveBlendRadius=RoomBlendRadius;
            ActiveFloorBlendRadius=0.0;
            for(const FCachedPit& P:Cache.Pits)
                AddCapsule(FVector(P.CenterX,P.CenterY,P.TopZ-P.Depth),
                    FVector(P.CenterX,P.CenterY,P.TopZ),std::max(2.0f,P.Radius),true);
            for(const FCachedChimney& C:Cache.Chimneys)
                AddCapsule(FVector(C.CenterX,C.CenterY,C.BottomZ),
                    FVector(C.CenterX,C.CenterY,C.BottomZ+C.Height),std::max(2.0f,C.Radius),true);
            for(const FCachedColumn& C:Cache.Columns)
            {
                FVector Center(C.CenterX,C.CenterY,(LayerRanges[0].Lo+LayerRanges[0].Hi)*0.5);
                const double HalfZ=std::max(8.0,(LayerRanges[0].Hi-LayerRanges[0].Lo)*0.48);
                AddEllipsoid(Center,{std::max(2.0f,C.Radius),std::max(2.0f,C.Radius),HalfZ},
                    {1,0,0},{0,1,0},{0,0,1},false);
            }

            // Reproduce the owner's finite, top-anchored origin room in every strate.
            // Reproduire dans chaque strate la salle d'origine finie et ancrée en haut.
            AddOriginLandingRoom(FieldForStrate(Slot.StrateIndex));
        }
        const double PassageJoinBlend=ActiveBlendRadius;ActiveBlendRadius=JoinBlendRadius;
        ActiveFloorBlendRadius=FloorClipBlendRadius;
        for(const FVoxelPassage& P:Owner->Manager->GetPassages())
        {
            ++Stats.PassageCount;
            const TArray<FVector>& Points=P.ControlPoints;
            const TArray<float>& Radii=P.ControlRadii;
            const size_t PassagePrimitiveStart=Primitives.size();
            std::vector<float> RawFloor(static_cast<size_t>(Points.Num()));
            std::vector<uint8_t> MarkedFloorSegments(Points.Num()>0?static_cast<size_t>(Points.Num()-1):0,0);
            for(int32 I=0;I<Points.Num();++I)
                RawFloor[static_cast<size_t>(I)]=static_cast<float>(Points[I].Z
                    -SmoothedControlRadius(Radii,I,P.Radius,6.0f));
            if(P.NativeFloorProfileZ.Num()==Points.Num())
                for(int32 I=0;I<Points.Num();++I)RawFloor[static_cast<size_t>(I)]=P.NativeFloorProfileZ[I];
            for(int32 I=0;I<Points.Num();++I)
                RawFloor[static_cast<size_t>(I)]+=static_cast<float>(FloorSurfaceRelief(
                    Points[I].X,Points[I].Y,static_cast<uint32>(Owner->Seed)));
            const std::vector<double> FloorTangents=BuildFloorTangents(
                Points,RawFloor,MarkedFloorSegments);
            for(int32 Join=1;Join+1<Points.Num();++Join)
            {
                const float RPrev=std::max(6.0f,Radii.IsValidIndex(Join-1)?Radii[Join-1]:P.Radius);
                const float RHere=std::max(6.0f,Radii.IsValidIndex(Join)?Radii[Join]:P.Radius);
                const float RNext=std::max(6.0f,Radii.IsValidIndex(Join+1)?Radii[Join+1]:P.Radius);
                Stats.LegacySegmentRadiusStep=std::max(Stats.LegacySegmentRadiusStep,
                    static_cast<double>(std::abs(std::max(RPrev,RHere)-std::max(RHere,RNext))));
                if(P.NativeFloorProfileZ.IsValidIndex(Join-1)&&P.NativeFloorProfileZ.IsValidIndex(Join))
                {
                    const FVector PrevD=Points[Join]-Points[Join-1];
                    const FVector NextD=Points[Join+1]-Points[Join];
                    const double PrevXY=std::sqrt(PrevD.X*PrevD.X+PrevD.Y*PrevD.Y);
                    const double NextXY=std::sqrt(NextD.X*NextD.X+NextD.Y*NextD.Y);
                    const double PrevSlope=PrevXY>1.0e-6
                        ?(P.NativeFloorProfileZ[Join]-P.NativeFloorProfileZ[Join-1])/PrevXY:0.0;
                    const double NextSlope=NextXY>1.0e-6
                        ?(P.NativeFloorProfileZ[Join+1]-P.NativeFloorProfileZ[Join])/NextXY:0.0;
                    const double RawSlopeDelta=std::abs(PrevSlope-NextSlope);
                    Stats.MaxRawUnmarkedFloorSlopeDelta=std::max(Stats.MaxRawUnmarkedFloorSlopeDelta,RawSlopeDelta);
                }
                ++Stats.CapsuleJoinCount;
            }
            if(Points.Num()>1)
            {
                for(int32 I=0;I+1<Points.Num();++I)
                {
                    const float RadiusA=SmoothedControlRadius(Radii,I,P.Radius,6.0f);
                    const float RadiusB=SmoothedControlRadius(Radii,I+1,P.Radius,6.0f);
                    const double RadiusSlopeA=ControlRadiusSlopeAt(Points,Radii,I,P.Radius,6.0f);
                    const double RadiusSlopeB=ControlRadiusSlopeAt(Points,Radii,I+1,P.Radius,6.0f);
                    Stats.SmoothedProfileRadiusStep=std::max(Stats.SmoothedProfileRadiusStep,
                        static_cast<double>(std::abs(RadiusB-RadiusA)));
                    const FVector Segment=Points[I+1]-Points[I];
                    const double SegmentLength=std::sqrt(Segment.X*Segment.X+Segment.Y*Segment.Y+Segment.Z*Segment.Z);
                    const float ZA=RawFloor[static_cast<size_t>(I)];
                    const float ZB=RawFloor[static_cast<size_t>(I+1)];
                    const double Extension=ContinuousJoinExtension(RadiusA,RadiusB,SegmentLength);
                    const double CoreExtension=ContinuousJoinExtension(std::min(2.5f,RadiusA*0.45f),
                        std::min(2.5f,RadiusB*0.45f),SegmentLength);
                    const double ExtendStart=I>0?Extension:0.0,ExtendEnd=I+2<Points.Num()?Extension:0.0;
                    const double CoreExtendStart=I>0?CoreExtension:0.0,CoreExtendEnd=I+2<Points.Num()?CoreExtension:0.0;
                    AddTaperedCapsule(Points[I],Points[I+1],RadiusA,RadiusB,true,false,true,ZA,ZB,
                        ExtendStart,ExtendEnd);
                    Primitives.back().bPassageSurface=true;
                    SetCurvedFloorClip(Primitives.back(),Points[I],Points[I+1],ZA,ZB,
                        FloorTangents[static_cast<size_t>(I)],FloorTangents[static_cast<size_t>(I+1)]);
                    ++Stats.CurvedFloorSegments;
                    Stats.MaxFloorCurveDeviation=std::max(Stats.MaxFloorCurveDeviation,
                        Primitives.back().FloorCurveMaxDeviation);
                    Stats.MaxFloorProfileEndpointValueError=std::max(
                        Stats.MaxFloorProfileEndpointValueError,
                        Primitives.back().FloorCurveEndpointValueError);
                    Stats.MaxFloorProfileEndpointSlopeError=std::max(
                        Stats.MaxFloorProfileEndpointSlopeError,
                        Primitives.back().FloorCurveEndpointSlopeError);
                    FitCapsuleRadiiAtEndpoints(Primitives.back(),Points[I],RadiusA,Points[I+1],RadiusB);
                    SetCapsuleRadiusProfile(Primitives.back(),Points[I],RadiusA,RadiusSlopeA,
                        Points[I+1],RadiusB,RadiusSlopeB);
                    const float CoreRadiusA=std::min(2.5f,RadiusA*0.45f);
                    const float CoreRadiusB=std::min(2.5f,RadiusB*0.45f);
                    const double CoreSlopeA=CoreRadiusA<2.5f-1.0e-4?RadiusSlopeA*0.45:0.0;
                    const double CoreSlopeB=CoreRadiusB<2.5f-1.0e-4?RadiusSlopeB*0.45:0.0;
                    // Keep a narrow, un-clipped air core through every authored control segment.
                    // The larger outer tube owns the D-section floor; its interpolated floor curve
                    // can bow above the path on sharp drops, so clipping this safety bore would
                    // close the passage precisely where Cascading/Worm need the continuity repair.
                    // Garder un petit noyau d'air sans coupe de plancher dans chaque segment.
                    // Le tube large porte le plancher en D; sa courbe peut depasser l'axe dans les
                    // chutes brusques et fermer la route si ce noyau herite de la meme coupe.
                    AddTaperedCapsule(Points[I],Points[I+1],CoreRadiusA,
                        CoreRadiusB,true,true,false,ZA,ZB,
                        CoreExtendStart,CoreExtendEnd);
                    FitCapsuleRadiiAtEndpoints(Primitives.back(),Points[I],CoreRadiusA,
                        Points[I+1],CoreRadiusB);
                    SetCapsuleRadiusProfile(Primitives.back(),Points[I],CoreRadiusA,CoreSlopeA,
                        Points[I+1],CoreRadiusB,CoreSlopeB);
                }
                for(int32 Join=1;Join+1<Points.Num();++Join)
                {
                    const size_t PreviousBase=PassagePrimitiveStart+static_cast<size_t>(Join-1)*2;
                    const size_t NextBase=PassagePrimitiveStart+static_cast<size_t>(Join)*2;
                    for(size_t Tube=0;Tube<2;++Tube)
                    {
                        const FPrimitive& Previous=Primitives[PreviousBase+Tube];
                        const FPrimitive& Next=Primitives[NextBase+Tube];
                        const float PreviousEnd=CapsuleRadiusAt(Previous,Points[Join]);
                        const float NextStart=CapsuleRadiusAt(Next,Points[Join]);
                        Stats.MaxCapsuleJoinRadiusDelta=std::max(Stats.MaxCapsuleJoinRadiusDelta,
                            static_cast<double>(std::abs(PreviousEnd-NextStart)));
                        Stats.MaxCapsuleJoinRadiusSlopeDelta=std::max(
                            Stats.MaxCapsuleJoinRadiusSlopeDelta,
                            std::abs(Previous.CapsuleRadiusSlopeEnd-Next.CapsuleRadiusSlopeStart));
                        if(Tube==0)
                        {
                            const double TangentDelta=Previous.bCurvedFloorClip&&Next.bCurvedFloorClip
                                ?std::abs(Previous.FloorCurveTangentEnd-Next.FloorCurveTangentStart)
                                :std::abs(FloorSlopeAtEndpoint(Previous,true)-FloorSlopeAtEndpoint(Next,false));
                            const double DirectionalSlopeChange=std::abs(FloorSlopeAtEndpoint(Previous,true)
                                -FloorSlopeAtEndpoint(Next,false));
                            Stats.MaxCapsuleJoinFloorSlopeDelta=std::max(
                                Stats.MaxCapsuleJoinFloorSlopeDelta,TangentDelta);
                            Stats.MaxUnmarkedFloorSlopeDelta=std::max(
                                Stats.MaxUnmarkedFloorSlopeDelta,TangentDelta);
                            Stats.MaxUnmarkedFloorDirectionSlopeDelta=std::max(
                                Stats.MaxUnmarkedFloorDirectionSlopeDelta,DirectionalSlopeChange);
                        }
                    }
                }
            }
            else
            {
                AddCapsule(P.UpperPoint,P.LowerPoint,std::max(6.0f,P.Radius),true,true);
                Primitives.back().bPassageSurface=true;
            }
            AddLanding(P.UpperLanding,true);
            AddLanding(P.LowerLanding,true);
        }
        ActiveBlendRadius=PassageJoinBlend;ActiveFloorBlendRadius=0.0;
    }

    const FLayerField* FieldForStrate(int32 StrateIndex) const
    {
        for(const FLayerField& Field:LayerFields)
            if(Field.StrateIndex==StrateIndex)return &Field;
        return nullptr;
    }

    void AddOriginLandingRoom(const FLayerField* Field)
    {
        if(Field==nullptr||Owner==nullptr||Owner->Settings==nullptr)return;
        const double Radius=Owner->Settings->OriginSpineRadius;
        if(!(Radius>0.0)||!std::isfinite(Radius))return;

        // These constants mirror VoxelPassageGeometry in legacy voxel units.
        // Ces constantes reprennent VoxelPassageGeometry en voxels historiques.
        constexpr double MinimumHalfWidth=12.0;
        constexpr double MinimumRoomHeight=24.0;
        constexpr double PlayerHeight=14.08;
        constexpr double Headroom=8.0;
        constexpr double FloorThickness=6.0;
        constexpr double SealSafetyMargin=8.0;
        constexpr double RoomRounding=3.0;
        constexpr double ShaftFloorClearance=8.0;

        const double SafeRadius=std::max(std::abs(Radius),2.0);
        const double HalfWidth=std::max({MinimumHalfWidth,SafeRadius+4.0,
            SafeRadius+ShaftFloorClearance});
        const double DesiredHeight=std::max({MinimumRoomHeight,PlayerHeight+Headroom,
            2.0*SafeRadius+4.0});
        const double Seal=std::max(0.0,static_cast<double>(Field->Params.BoundarySealThickness));
        const double InnerBottom=static_cast<double>(Field->Lo)+Seal;
        const double InnerTop=static_cast<double>(Field->Hi)-Seal;
        const double MinimumFloor=InnerBottom+FloorThickness+SealSafetyMargin;
        const double MaximumFloor=InnerTop-DesiredHeight-SealSafetyMargin;
        if(!(InnerTop>InnerBottom)||MaximumFloor<MinimumFloor)return;

        const double FloorZ=MaximumFloor;
        const double CeilingZ=FloorZ+DesiredHeight;
        const double HalfZ=(CeilingZ-FloorZ)*0.5;
        const double HalfExtent=std::max(HalfWidth-RoomRounding,0.5);
        const double RoundedHalfZ=std::max(HalfZ-RoomRounding,0.5);
        const size_t Before=Primitives.size();
        AddRoundedBox(FVector(0,0,(FloorZ+CeilingZ)*0.5),
            {HalfExtent,HalfExtent,RoundedHalfZ},RoomRounding,true);
        for(size_t I=Before;I<Primitives.size();++I)
        {
            // Keep the authored room floor hard and level while leaving all lower seal rock intact.
            // Garder un sol horizontal net et préserver la roche du joint inférieur.
            ApplyFloorClip(Primitives[I],FloorZ+0.5,0.0,0.0,0.0);
        }
    }

    void AddLanding(const FVoxelPassageLanding& L,bool bCritical=false)
    {
        if(!(L.HalfWidth>0.0f)||!(L.CeilingZ>L.FloorZ))return;
        const double HalfZ=std::max(2.0,(L.CeilingZ-L.FloorZ)*0.5);
        const FVector Center(L.StandingPoint.X,L.StandingPoint.Y,(L.CeilingZ+L.FloorZ)*0.5);
        const double Width=std::max(6.0f,L.HalfWidth);
        AddRoundedBox(Center,{Width,Width,HalfZ},2.0,true);
        if(bCritical)
        {
            const size_t Before=Primitives.size();
            AddEllipsoid(Center,{2.5,2.5,HalfZ},{1,0,0},{0,1,0},{0,0,1},true);
            for(size_t I=Before;I<Primitives.size();++I)Primitives[I].bCritical=true;
        }
        // The rounded landing carve and native floor already provide support.
        // A shallow positive ellipsoid under this floor creates a broad shaft/floor plate.
    }

    void BuildRoundTunnelPrimitives()
    {
        const double PreviousBlendRadius=ActiveBlendRadius;ActiveBlendRadius=0.0;
        constexpr double Pitch=144.0,RadiusBase=28.0,HalfHeight=26.0;
        const int32 CX0=FloorDiv(Min[0],144)-1,CY0=FloorDiv(Min[1],144)-1;
        const int32 CX1=FloorDiv(Max[0],144)+1,CY1=FloorDiv(Max[1],144)+1;
        const uint32 Seed=static_cast<uint32>(Owner->Seed);
        auto Unit=[](uint32 H){return static_cast<double>(FStandaloneResearchTunnels::Unit(H));};
        for(int32 CY=CY0;CY<=CY1;++CY)for(int32 CX=CX0;CX<=CX1;++CX)
        for(int32 Axis=0;Axis<2;++Axis)
        {
            const uint32 H=FStandaloneResearchTunnels::EdgeHash(CX,CY,Axis,Seed);
            if(Unit(H^0x68E31DA4u)>0.56)continue;
            const int32 NX=CX+(Axis==0?1:0),NY=CY+(Axis==1?1:0);
            auto Cell=[&](int32 X,int32 Y,double& OX,double& OY)
            {
                const uint32 CH=FStandaloneResearchTunnels::EdgeHash(X,Y,3,Seed);
                OX=(X+0.5)*Pitch+(Unit(CH^0xA511E9B3u)-0.5)*Pitch*0.18;
                OY=(Y+0.5)*Pitch+(Unit(CH^0x63D83595u)-0.5)*Pitch*0.18;
            };
            double AX,AY,BX,BY;Cell(CX,CY,AX,AY);Cell(NX,NY,BX,BY);
            const double DX=BX-AX,DY=BY-AY,L2=DX*DX+DY*DY,L=std::sqrt(std::max(1.0e-8,L2));
            const double NXrm=-DY/L,NYrm=DX/L;
            const double BA=(Unit(H^0xB5297A4Du)*2.0-1.0)*Pitch*0.16;
            const double BB=(Unit(H^0x1B56C4E9u)*2.0-1.0)*Pitch*0.16;
            const std::array<double,3> P0={AX,AY,FStandaloneResearchTunnels::WorldCenterZVoxels};
            const std::array<double,3> C1={AX+DX/3.0+NXrm*BA,AY+DY/3.0+NYrm*BA,-80.0};
            const std::array<double,3> C2={AX+DX*2.0/3.0+NXrm*BB,AY+DY*2.0/3.0+NYrm*BB,-80.0};
            const std::array<double,3> P3={BX,BY,FStandaloneResearchTunnels::WorldCenterZVoxels};
            const uint32 PhaseHash=H^0xA511E9B3u;
            const double Phase=Unit(PhaseHash)*6.2831853071795864769;
            auto Bezier=[&](double T)
            {
                const double O=1.0-T;
                std::array<double,3> P{};
                for(int32 A=0;A<3;++A)
                    P[A]=O*O*O*P0[A]+3*O*O*T*C1[A]+3*O*T*T*C2[A]+T*T*T*P3[A];
                const double R=RadiusBase*(0.82+0.36*Unit(H^0x63D83595u))
                    *(1.0+0.22*VoxelMath::DetSin(static_cast<float>(6.2831853071795864769*T+Phase)));
                const double VW=4.0*VoxelMath::DetSin(static_cast<float>(3.141592653589793*T))
                    *VoxelMath::DetSin(static_cast<float>(6.2831853071795864769*T+Phase));
                P[2]+=VW;
                return std::pair{P,R};
            };
            constexpr int32 Segments=12;
            auto Last=Bezier(0.0);
            for(int32 I=1;I<=Segments;++I)
            {
                const auto Next=Bezier(static_cast<double>(I)/Segments);
                const FVector A(Last.first[0],Last.first[1],Last.first[2]);
                const FVector B(Next.first[0],Next.first[1],Next.first[2]);
                const FVector Segment=B-A;
                const double SegmentLength=std::sqrt(Segment.X*Segment.X+Segment.Y*Segment.Y+Segment.Z*Segment.Z);
                const double Extension=ContinuousJoinExtension(static_cast<float>(Last.second),
                    static_cast<float>(Next.second),SegmentLength);
                AddTaperedCapsule(A,B,static_cast<float>(Last.second),static_cast<float>(Next.second),
                    true,false,false,0.0,0.0,I>1?Extension:0.0,I<Segments?Extension:0.0);
                Last=Next;
            }
        }
        ActiveBlendRadius=PreviousBlendRadius;
    }

    void BuildSpatialBins(int32 BinResolution,bool bBuildAxisBins=true)
    {
        InvalidateFarFieldGpuInput();
        SpatialBins.clear();
        CriticalAirBins.clear();
        ActiveSpatialBinSize=BinResolution;
        // Primitive bounds overlap multiple cells. Reserve from the measured bins-per-primitive
        // density for each grid instead of repeatedly rehashing from a 2x primitive guess.
          const size_t BinsPerPrimitive=bBuildAxisBins?96u:24u;
        SpatialBins.reserve(std::max<size_t>(Primitives.size()*BinsPerPrimitive,1u));
        if(!bBuildAxisBins)
        {
            CriticalAirBins.reserve(Primitives.size()/16+1);
        }
        if(bBuildAxisBins)for(int32 Axis=0;Axis<3;++Axis)
        {
            FAxisBins& B=AxisBins[Axis];
            const int32 A=(Axis+1)%3,C=(Axis+2)%3;
            B.MinA=FloorDiv(Min[A],LineBinSize);B.MinB=FloorDiv(Min[C],LineBinSize);
            const int32 MaxA=FloorDiv(Max[A],LineBinSize),MaxB=FloorDiv(Max[C],LineBinSize);
            B.CountA=MaxA-B.MinA+1;B.CountB=MaxB-B.MinB+1;
            B.Items.resize(static_cast<size_t>(B.CountA)*B.CountB);
            for(uint32 Id=0;Id<Primitives.size();++Id)
            {
                const FPrimitive& P=Primitives[Id];
                const int32 A0=std::max(B.MinA,FloorDiv(P.Min[A],LineBinSize));
                const int32 A1=std::min(MaxA,FloorDiv(P.Max[A],LineBinSize));
                const int32 B0=std::max(B.MinB,FloorDiv(P.Min[C],LineBinSize));
                const int32 B1=std::min(MaxB,FloorDiv(P.Max[C],LineBinSize));
                if(A0>A1||B0>B1)continue;
                for(int32 IB=B0;IB<=B1;++IB)for(int32 IA=A0;IA<=A1;++IA)
                    B.Items[static_cast<size_t>(IB-B.MinB)*B.CountA+(IA-B.MinA)].push_back(Id);
            }
        }
        for(uint32 Id=0;Id<Primitives.size();++Id)
        {
            const FPrimitive& P=Primitives[Id];
            const bool bCriticalAir=P.bCarve&&P.bCritical;
            const int32 X0=FloorDiv(P.Min[0]-DetailBand,BinResolution),X1=FloorDiv(P.Max[0]+DetailBand,BinResolution);
            const int32 Y0=FloorDiv(P.Min[1]-DetailBand,BinResolution),Y1=FloorDiv(P.Max[1]+DetailBand,BinResolution);
            const int32 Z0=FloorDiv(P.Min[2]-DetailBand,BinResolution),Z1=FloorDiv(P.Max[2]+DetailBand,BinResolution);
            const int64 BoundingBinCount=static_cast<int64>(X1-X0+1)*(Y1-Y0+1)*(Z1-Z0+1);
            if(BoundingBinCount>100000)
            {
                // Long diagonal passages have a huge AABB even though their capsule is narrow.
                // Rasterize the centerline with a conservative bin halo instead of dropping the
                // primitive from analytic queries outside the packed near region.
                // Les longues galeries diagonales ont une grande AABB mais un tube fin.
                // Echantillonner l'axe avec une marge prudente garde les requetes analytiques.
                if(!P.bCapsule)continue;
                const double BinWidth=static_cast<double>(BinResolution);
                const double AxisStep=std::max(1.0,BinWidth*0.5);
                const int32 AxisSamples=std::max(1,static_cast<int32>(std::ceil(
                    P.CapsuleAxisLength/AxisStep)));
                const double CapsuleRadius=std::max(P.CapsuleStartRadius,P.CapsuleEndRadius);
                const int32 Halo=std::clamp(static_cast<int32>(std::ceil(
                    (CapsuleRadius+DetailBand)/BinWidth))+1,1,8);
                std::vector<FBinKey> PrimitiveBins;
                const int64 HaloWidth=2*Halo+1;
                const uint64 Reserve=std::min<uint64>(
                    static_cast<uint64>(AxisSamples+1)*HaloWidth*HaloWidth*HaloWidth,
                    1000000ull);
                PrimitiveBins.reserve(static_cast<size_t>(Reserve));
                for(int32 Sample=0;Sample<=AxisSamples;++Sample)
                {
                    const double T=static_cast<double>(Sample)/AxisSamples;
                    const int32 CX=static_cast<int32>(std::floor(P.CapsuleStartWorld[0]
                        +P.CapsuleAxisDelta[0]*T));
                    const int32 CY=static_cast<int32>(std::floor(P.CapsuleStartWorld[1]
                        +P.CapsuleAxisDelta[1]*T));
                    const int32 CZ=static_cast<int32>(std::floor(P.CapsuleStartWorld[2]
                        +P.CapsuleAxisDelta[2]*T));
                    const int32 BX=FloorDiv(CX,BinResolution),BY=FloorDiv(CY,BinResolution);
                    const int32 BZ=FloorDiv(CZ,BinResolution);
                    for(int32 DZ=-Halo;DZ<=Halo;++DZ)
                        for(int32 DY=-Halo;DY<=Halo;++DY)
                            for(int32 DX=-Halo;DX<=Halo;++DX)
                                PrimitiveBins.push_back({BX+DX,BY+DY,BZ+DZ});
                }
                std::sort(PrimitiveBins.begin(),PrimitiveBins.end(),[](const FBinKey& A,const FBinKey& B)
                {
                    if(A.X!=B.X)return A.X<B.X;
                    if(A.Y!=B.Y)return A.Y<B.Y;
                    return A.Z<B.Z;
                });
                PrimitiveBins.erase(std::unique(PrimitiveBins.begin(),PrimitiveBins.end()),
                    PrimitiveBins.end());
                for(const FBinKey& Key:PrimitiveBins)
                {
                    SpatialBins[Key].push_back(Id);
                    if(bCriticalAir)CriticalAirBins[Key].push_back(Id);
                }
                continue;
            }
            for(int32 Z=Z0;Z<=Z1;++Z)for(int32 Y=Y0;Y<=Y1;++Y)for(int32 X=X0;X<=X1;++X)
            {
                const FBinKey Key{X,Y,Z};
                SpatialBins[Key].push_back(Id);
                if(bCriticalAir)CriticalAirBins[Key].push_back(Id);
            }
        }
    }

    void BuildFarParentShapes()
    {
        constexpr int32 ParentPitch=2048;
        FarConnectorSegments.clear();
        struct FParent { int32 GX=0,GY=0,Strate=0; FVector Center; double Rx=0,Ry=0,Rz=0; };
        const int32 GX0=FloorDiv(ClipMin[0],ParentPitch)-1,GY0=FloorDiv(ClipMin[1],ParentPitch)-1;
        const int32 GX1=FloorDiv(ClipMax[0],ParentPitch)+1,GY1=FloorDiv(ClipMax[1],ParentPitch)+1;
        std::vector<FParent> Parents;
        std::unordered_map<uint64,size_t> ByCell;
        const auto& Layout=Owner->Manager->GetLayout();
        const uint32 Seed=static_cast<uint32>(Owner->Seed);
        const auto Key=[](int32 GX,int32 GY,int32 Strate)
        {return (static_cast<uint64>(static_cast<uint32>(GX+524288)&0xFFFFFu)<<44)
            |(static_cast<uint64>(static_cast<uint32>(GY+524288)&0xFFFFFu)<<24)
            |(static_cast<uint64>(static_cast<uint32>(Strate)&0xFFFFu)<<8);};
        auto Hash=[](uint32 X)
        {X^=X>>16;X*=0x7FEB352Du;X^=X>>15;X*=0x846CA68Bu;X^=X>>16;return X;};
        auto Unit=[&](uint32 H){return static_cast<double>(Hash(H)>>8)*(1.0/16777216.0);};
        for(const FStrateSlot& Slot:Layout)
        {
        const double LayoutChunkWidth=GetResolvedLayoutChunkWidthVoxels();
        const double ZBottom=static_cast<double>(Slot.BottomChunkZ)*LayoutChunkWidth;
        const double ZTop=static_cast<double>(Slot.TopChunkZ+1)*LayoutChunkWidth;
            for(int32 GY=GY0;GY<=GY1;++GY)for(int32 GX=GX0;GX<=GX1;++GX)
            {
                uint32 H=Hash(Seed^static_cast<uint32>(GX)*0x9E3779B9u
                    ^static_cast<uint32>(GY)*0x85EBCA6Bu
                    ^static_cast<uint32>(Slot.StrateIndex)*0xC2B2AE35u);
                const double X=GX*static_cast<double>(ParentPitch)+ParentPitch*0.5
                    +(Unit(H^0xA511E9B3u)-0.5)*192.0;
                const double Y=GY*static_cast<double>(ParentPitch)+ParentPitch*0.5
                    +(Unit(H^0x63D83595u)-0.5)*192.0;
                const double Rx=300.0+Unit(H^0xB5297A4Du)*100.0;
                const double Ry=280.0+Unit(H^0x1B56C4E9u)*120.0;
                const double Rz=100.0+Unit(H^0x68E31DA4u)*60.0;
                if(X+Rx>=Min[0]&&X-Rx<=Max[0]&&Y+Ry>=Min[1]&&Y-Ry<=Max[1])continue;
                const double Z=ZBottom+(ZTop-ZBottom)*(0.35+0.30*Unit(H^0x27D4EB2Fu));
                FParent P{GX,GY,Slot.StrateIndex,FVector(X,Y,Z),Rx,Ry,Rz};
                const size_t Index=Parents.size();Parents.push_back(P);
                ByCell.emplace(Key(GX,GY,Slot.StrateIndex),Index);
                const std::array<double,3> Axis0={1,0,0},Axis1={0,1,0},Axis2={0,0,1};
                AddEllipsoid(P.Center,{P.Rx,P.Ry,P.Rz},Axis0,Axis1,Axis2,true);
            }
        }
        for(const FParent& P:Parents)
        {
            for(const auto [DX,DY]:std::array<std::pair<int32,int32>,2>{{{1,0},{0,1}}})
            {
                const auto It=ByCell.find(Key(P.GX+DX,P.GY+DY,P.Strate));
                if(It==ByCell.end())continue;
                const FVector A(P.Center.X,P.Center.Y,P.Center.Z);
                const FVector B=Parents[It->second].Center;
                const int32 MinX=static_cast<int32>(std::floor(std::min(A.X,B.X)-64.0));
                const int32 MaxX=static_cast<int32>(std::ceil(std::max(A.X,B.X)+64.0));
                const int32 MinY=static_cast<int32>(std::floor(std::min(A.Y,B.Y)-64.0));
                const int32 MaxY=static_cast<int32>(std::ceil(std::max(A.Y,B.Y)+64.0));
                if(MaxX>=Min[0]&&MinX<=Max[0]&&MaxY>=Min[1]&&MinY<=Max[1])continue;
                AddTaperedCapsule(A,B,64.0f,64.0f,true);
                Primitives.back().BlendRadius=0.0;
                FarConnectorSegments.push_back({A,B,64.0f});
            }
        }
        BuildFarConnectorSpatialBins();
        if(!Parents.empty())
            std::printf("[FarParents] pitch=%d rooms=%zu links=%llu clip=(%d,%d)..(%d,%d)\n",
                ParentPitch,Parents.size(),static_cast<unsigned long long>(Primitives.size()),
                ClipMin[0],ClipMin[1],ClipMax[0],ClipMax[1]);
    }

    void BuildFarConnectorSpatialBins()
    {
        constexpr int32 BinSize=2048;
        FarConnectorSpatialBins.clear();
        FarConnectorSpatialBins.reserve(FarConnectorSegments.size());
        for(uint32 Index=0;Index<FarConnectorSegments.size();++Index)
        {
            const FFarConnectorSegment& Connector=FarConnectorSegments[Index];
            const int32 MinX=static_cast<int32>(std::floor(
                (std::min(Connector.Start.X,Connector.End.X)-Connector.Radius)/BinSize));
            const int32 MaxX=static_cast<int32>(std::floor(
                (std::max(Connector.Start.X,Connector.End.X)+Connector.Radius)/BinSize));
            const int32 MinY=static_cast<int32>(std::floor(
                (std::min(Connector.Start.Y,Connector.End.Y)-Connector.Radius)/BinSize));
            const int32 MaxY=static_cast<int32>(std::floor(
                (std::max(Connector.Start.Y,Connector.End.Y)+Connector.Radius)/BinSize));
            const int32 MinZ=static_cast<int32>(std::floor(
                (std::min(Connector.Start.Z,Connector.End.Z)-Connector.Radius)/BinSize));
            const int32 MaxZ=static_cast<int32>(std::floor(
                (std::max(Connector.Start.Z,Connector.End.Z)+Connector.Radius)/BinSize));
            for(int32 Z=MinZ;Z<=MaxZ;++Z)for(int32 Y=MinY;Y<=MaxY;++Y)
            for(int32 X=MinX;X<=MaxX;++X)
                FarConnectorSpatialBins[{X,Y,Z}].push_back(Index);
        }
    }

    const std::vector<uint32>& GetLineCandidates(int32 Axis,int32 A,int32 B) const
    {
        static const std::vector<uint32> Empty;
        const FAxisBins& G=AxisBins[Axis];
        const int32 IA=FloorDiv(A,LineBinSize)-G.MinA,IB=FloorDiv(B,LineBinSize)-G.MinB;
        if(IA<0||IB<0||IA>=G.CountA||IB>=G.CountB)return Empty;
        return G.Items[static_cast<size_t>(IB)*G.CountA+IA];
    }

    FBinKey PointBin(double X,double Y,double Z) const
    {return {FloorDiv(static_cast<int32>(std::floor(X)),ActiveSpatialBinSize),FloorDiv(static_cast<int32>(std::floor(Y)),ActiveSpatialBinSize),FloorDiv(static_cast<int32>(std::floor(Z)),ActiveSpatialBinSize)};}

    bool ShapeContains(const FPrimitive& P,int32 X,int32 Y,int32 Z) const
    {
        bool bInside=false;
        if(P.bCapsule)
        {
            const double Position[3]={static_cast<double>(X),static_cast<double>(Y),static_cast<double>(Z)};
            double V[3],D[3];double D2=0.0,VD=0.0,V2=0.0;
            for(int32 A=0;A<3;++A)
            {
                const double Start=P.CapsuleStartSub[A]/static_cast<double>(SubPerVoxel);
                const double End=P.CapsuleEndSub[A]/static_cast<double>(SubPerVoxel);
                V[A]=Position[A]-Start;D[A]=End-Start;
                D2+=D[A]*D[A];VD+=V[A]*D[A];V2+=V[A]*V[A];
            }
            const double R0=P.CapsuleStartRadius,R1=P.CapsuleEndRadius,DR=R1-R0;
            const double QA=D2-DR*DR,QB=-2.0*(VD+R0*DR),QC=V2-R0*R0;
            double Minimum=std::min(QC,QA+QB+QC);
            if(QA>1.0e-12)
            {
                const double T=std::clamp(-QB/(2.0*QA),0.0,1.0);
                Minimum=std::min(Minimum,(QA*T+QB)*T+QC);
            }
            bInside=Minimum<=0.0;
        }
        else if(P.bRoundedBox)
        {
            const double D[3]={std::abs(X-P.CenterSub[0]/16.0)-P.RoundedHalfExtent[0],
                std::abs(Y-P.CenterSub[1]/16.0)-P.RoundedHalfExtent[1],
                std::abs(Z-P.CenterSub[2]/16.0)-P.RoundedHalfExtent[2]};
            const double Ox=std::max(D[0],0.0),Oy=std::max(D[1],0.0),Oz=std::max(D[2],0.0);
            const double Outside=std::sqrt(Ox*Ox+Oy*Oy+Oz*Oz);
            const double Inside=std::min(std::max({D[0],D[1],D[2]}),0.0);
            bInside=Outside+Inside-P.Rounding<=0.0;
        }
        else
        {
            const int32 World[3]={X,Y,Z};int64 D[3];
            for(int32 A=0;A<3;++A)D[A]=static_cast<int64>(World[A])*SubPerVoxel-P.CenterSub[A];
            int64 Q=0;
            for(int32 I=0;I<3;++I)for(int32 J=0;J<3;++J)Q+=P.Q[I][J]*D[I]*D[J];
            bInside=Q<=static_cast<int64>(QScale);
        }
        if(!bInside)return false;
        if(P.bHasFloorClip)
        {
            const double Floor=FloorAt(P,X,Y);
            if(P.FloorBlendRadius<=0.0)return Z>=Floor;
            return SmoothMaxDistance(ShapeDistance(P,X,Y,Z),static_cast<float>(Floor-Z),
                static_cast<float>(P.FloorBlendRadius))<=0.0f;
        }
        return true;
    }

    static float CapsuleRadiusAtT(const FPrimitive& P,double T,double AxisLength)
    {
        T=std::clamp(T,0.0,1.0);
        if(!P.bSmoothCapsuleRadius)
            return static_cast<float>(P.CapsuleStartRadius
                +(P.CapsuleEndRadius-P.CapsuleStartRadius)*T);
        const double T0=P.CapsuleProfileStartT,T1=P.CapsuleProfileEndT;
        if(T<T0)return static_cast<float>(P.CapsuleProfileStartRadius
            +P.CapsuleRadiusSlopeStart*AxisLength*(T-T0));
        if(T>T1)return static_cast<float>(P.CapsuleProfileEndRadius
            +P.CapsuleRadiusSlopeEnd*AxisLength*(T-T1));
        const double SpanT=std::max(1.0e-9,T1-T0);
        const double U=std::clamp((T-T0)/SpanT,0.0,1.0),U2=U*U,U3=U2*U;
        const double SpanDistance=AxisLength*SpanT;
        const double H00=2.0*U3-3.0*U2+1.0;
        const double H10=U3-2.0*U2+U;
        const double H01=-2.0*U3+3.0*U2;
        const double H11=U3-U2;
        return static_cast<float>(H00*P.CapsuleProfileStartRadius
            +H10*SpanDistance*P.CapsuleRadiusSlopeStart
            +H01*P.CapsuleProfileEndRadius
            +H11*SpanDistance*P.CapsuleRadiusSlopeEnd);
    }

    float ShapeDistance(const FPrimitive& P,double X,double Y,double Z) const
    {
        if(P.bCapsule)
        {
            const double Position[3]={X,Y,Z};
            double V[3],D[3],D2=0.0,VD=0.0;
            for(int32 A=0;A<3;++A)
            {
                V[A]=Position[A]-P.CapsuleStartWorld[A];
                D[A]=P.CapsuleAxisDelta[A];
                VD+=V[A]*D[A];
            }
            D2=P.CapsuleAxisLengthSquared;
            const double T=D2>1.0e-12?std::clamp(VD/D2,0.0,1.0):0.0;
            double DistanceSquared=0.0;
            for(int32 A=0;A<3;++A)
            {const double E=V[A]-T*D[A];DistanceSquared+=E*E;}
            const double Radius=CapsuleRadiusAtT(P,T,P.CapsuleAxisLength);
            return static_cast<float>(std::sqrt(DistanceSquared)-Radius);
        }
        if(P.bRoundedBox)
        {
            const double D[3]={std::abs(X-P.CenterSub[0]/16.0)-P.RoundedHalfExtent[0],
                std::abs(Y-P.CenterSub[1]/16.0)-P.RoundedHalfExtent[1],
                std::abs(Z-P.CenterSub[2]/16.0)-P.RoundedHalfExtent[2]};
            const double Ox=std::max(D[0],0.0),Oy=std::max(D[1],0.0),Oz=std::max(D[2],0.0);
            const double Outside=std::sqrt(Ox*Ox+Oy*Oy+Oz*Oz);
            const double Inside=std::min(std::max({D[0],D[1],D[2]}),0.0);
            return static_cast<float>(Outside+Inside-P.Rounding);
        }
        const double D[3]={X-P.CenterSub[0]/16.0,Y-P.CenterSub[1]/16.0,Z-P.CenterSub[2]/16.0};
        double Q=0.0;
        for(int32 I=0;I<3;++I)for(int32 J=0;J<3;++J)Q+=static_cast<double>(P.Q[I][J])/QScale*D[I]*D[J]*256.0;
        return static_cast<float>((std::sqrt(std::max(0.0,Q))-1.0)*P.MinRadius);
    }

    bool SolveLine(const FPrimitive& P,int32 Axis,const int32 Fixed[3],FInterval& Out) const
    {
        const int32 A=(Axis+1)%3,B=(Axis+2)%3;
        const int32 Lo=P.Min[Axis],Hi=P.Max[Axis];
        if(Fixed[A]<P.Min[A]||Fixed[A]>P.Max[A]||Fixed[B]<P.Min[B]||Fixed[B]>P.Max[B])return false;
        int32 L=Lo,H=Hi;
        if(!P.bRoundedBox&&!P.bCapsule)
        {
            double CoefA=static_cast<double>(P.Q[Axis][Axis]);
            double CoefB=0.0,CoefC=-static_cast<double>(QScale);
            int64 D[3];D[Axis]=0;
            for(int32 J=0;J<3;++J)if(J!=Axis)D[J]=static_cast<int64>(Fixed[J])*SubPerVoxel-P.CenterSub[J];
            for(int32 J=0;J<3;++J)if(J!=Axis)
            {
                CoefB+=2.0*P.Q[Axis][J]*D[J];
                for(int32 K=0;K<3;++K)if(K!=Axis)CoefC+=static_cast<double>(P.Q[J][K])*D[J]*D[K];
            }
            if(!(CoefA>0.0))return false;
            const double Disc=CoefB*CoefB-4.0*CoefA*CoefC;
            if(Disc<0.0)return false;
            const double S=std::sqrt(Disc);
            const double U0=(-CoefB-S)/(2.0*CoefA),U1=(-CoefB+S)/(2.0*CoefA);
            const double T0=(U0+P.CenterSub[Axis])/SubPerVoxel;
            const double T1=(U1+P.CenterSub[Axis])/SubPerVoxel;
            L=std::max(Lo,static_cast<int32>(std::floor(T0))-1);
            H=std::min(Hi,static_cast<int32>(std::ceil(T1))+1);
        }
        if(L>H)return false;
        if(P.bCarve&&P.bHasFloorClip&&(!P.bCurvedFloorClip||Axis==2))
        {
            double X0=Fixed[0],Y0=Fixed[1],Z0=Fixed[2];
            if(Axis==0)X0=0.0;else if(Axis==1)Y0=0.0;else Z0=0.0;
            const double Floor0=FloorAt(P,X0,Y0);
            const double SmoothAllowance=P.FloorBlendRadius>0.0?P.FloorBlendRadius/6.0:0.0;
            const double Margin0=Z0-(Floor0-SmoothAllowance);
            const double MarginSlope=Axis==0?-P.FloorSlopeX:Axis==1?-P.FloorSlopeY:1.0;
            if(std::abs(MarginSlope)<1.0e-12)
            {if(Margin0<0.0)return false;}
            else
            {
                const double Boundary=-Margin0/MarginSlope;
                if(MarginSlope>0.0)L=std::max(L,static_cast<int32>(std::ceil(Boundary)));
                else H=std::min(H,static_cast<int32>(std::floor(Boundary)));
            }
        }
        if(L>H)return false;
        int32 Mid=L+(H-L)/2;
        if(P.bCapsule)
        {
            double V2=0.0,VD=0.0,D2=0.0;
            for(int32 J=0;J<3;++J)if(J!=Axis)
            {
                const double Start=P.CapsuleStartSub[J]/static_cast<double>(SubPerVoxel);
                const double End=P.CapsuleEndSub[J]/static_cast<double>(SubPerVoxel);
                const double V=Fixed[J]-Start,D=End-Start;
                V2+=V*V;VD+=V*D;D2+=D*D;
            }
            const double R0=P.CapsuleStartRadius,DR=P.CapsuleEndRadius-R0;
            const double QA=D2-DR*DR,QB=-2.0*(VD+R0*DR),QC=V2-R0*R0;
            const auto Value=[&](double T){return (QA*T+QB)*T+QC;};
            double TBest=Value(1.0)<Value(0.0)?1.0:0.0;
            if(QA>1.0e-12)
            {
                const double T=std::clamp(-QB/(2.0*QA),0.0,1.0);
                if(Value(T)<Value(TBest))TBest=T;
            }
            if(Value(TBest)>0.0)return false;
            const double Start=P.CapsuleStartSub[Axis]/static_cast<double>(SubPerVoxel);
            const double End=P.CapsuleEndSub[Axis]/static_cast<double>(SubPerVoxel);
            Mid=std::clamp(static_cast<int32>(std::llround(Start+(End-Start)*TBest)),L,H);
        }
        if(!ShapeContains(P,Axis==0?Mid:Fixed[0],Axis==1?Mid:Fixed[1],Axis==2?Mid:Fixed[2]))
        {
            bool Found=false;
            const int32 SearchLimit=P.bCapsule?std::min(H-L,8):2;
            for(int32 Delta=1;Delta<=SearchLimit&&!Found;++Delta)
            {
                if(Mid-Delta>=L&&ShapeContains(P,Axis==0?Mid-Delta:Fixed[0],Axis==1?Mid-Delta:Fixed[1],Axis==2?Mid-Delta:Fixed[2])){Mid-=Delta;Found=true;}
                else if(Mid+Delta<=H&&ShapeContains(P,Axis==0?Mid+Delta:Fixed[0],Axis==1?Mid+Delta:Fixed[1],Axis==2?Mid+Delta:Fixed[2])){Mid+=Delta;Found=true;}
            }
            if(!Found&&P.bCapsule)
            {
                for(int32 Sample=L;Sample<=H;Sample+=2)
                    if(ShapeContains(P,Axis==0?Sample:Fixed[0],Axis==1?Sample:Fixed[1],Axis==2?Sample:Fixed[2]))
                    {Mid=Sample;Found=true;break;}
                if(!Found&&((H-L)&1)
                    &&ShapeContains(P,Axis==0?H:Fixed[0],Axis==1?H:Fixed[1],Axis==2?H:Fixed[2]))
                {Mid=H;Found=true;}
            }
            if(!Found)return false;
        }
        int32 Left=L,Right=Mid;
        while(Left<Right)
        {
            const int32 M=Left+(Right-Left)/2;
            const bool Inside=ShapeContains(P,Axis==0?M:Fixed[0],Axis==1?M:Fixed[1],Axis==2?M:Fixed[2]);
            if(Inside)Right=M;else Left=M+1;
        }
        const int32 First=Left;Left=Mid;Right=H;
        while(Left<Right)
        {
            const int32 M=Left+(Right-Left+1)/2;
            const bool Inside=ShapeContains(P,Axis==0?M:Fixed[0],Axis==1?M:Fixed[1],Axis==2?M:Fixed[2]);
            if(Inside)Left=M;else Right=M-1;
        }
        Out={First,Left};return true;
    }

    static void MergeIntervals(std::vector<FInterval>& Ranges)
    {
        if(Ranges.size()<2)return;
        std::sort(Ranges.begin(),Ranges.end(),[](const FInterval& A,const FInterval& B){return A.Lo==B.Lo?A.Hi<B.Hi:A.Lo<B.Lo;});
        size_t Out=0;
        for(size_t I=1;I<Ranges.size();++I)
        {
            if(Ranges[I].Lo<=Ranges[Out].Hi+1)Ranges[Out].Hi=std::max(Ranges[Out].Hi,Ranges[I].Hi);
            else Ranges[++Out]=Ranges[I];
        }
        Ranges.resize(Out+1);
    }

    static void FillBits(std::vector<uint64>& Words,size_t Base,int32 Lo,int32 Hi,bool bSet)
    {
        if(Lo>Hi)return;
        const size_t First=static_cast<size_t>(Lo)>>6,Last=static_cast<size_t>(Hi)>>6;
        for(size_t W=First;W<=Last;++W)
        {
            const uint32 Bit0=W==First?(static_cast<uint32>(Lo)&63u):0u;
            const uint32 Bit1=W==Last?(static_cast<uint32>(Hi)&63u):63u;
            const uint64 Mask=(~uint64{0}<<Bit0)&(~uint64{0}>>(63u-Bit1));
            if(bSet)Words[Base+W]|=Mask;else Words[Base+W]&=~Mask;
        }
    }

    void BuildPackedRockIntervals(FParallelTiming& Timing)
    {
        const int32 NX=Size[0],NY=Size[1],NZ=Size[2];
        CandidateAxisWords[2].assign(static_cast<size_t>(NX)*NY*WordsPerZ,0);
        struct FIntervalScratch
        {
            std::vector<FInterval> Carve,Solid,ProtectedAir;
        };
        std::array<FIntervalScratch,16> WorkerScratch;
        for(int32 Worker=0;Worker<WorkerCount;++Worker)
        {
            WorkerScratch[static_cast<size_t>(Worker)].Carve.reserve(24);
            WorkerScratch[static_cast<size_t>(Worker)].Solid.reserve(8);
            WorkerScratch[static_cast<size_t>(Worker)].ProtectedAir.reserve(4);
        }
        ParallelLines(static_cast<size_t>(NX)*NY,[&](size_t Line,int32 Worker)
        {
            const int32 X=Min[0]+static_cast<int32>(Line%NX),Y=Min[1]+static_cast<int32>(Line/NX);
            FIntervalScratch& Scratch=WorkerScratch[static_cast<size_t>(Worker)];
            std::vector<FInterval>& Carve=Scratch.Carve;
            std::vector<FInterval>& Solid=Scratch.Solid;
            std::vector<FInterval>& ProtectedAir=Scratch.ProtectedAir;
            Carve.clear();Solid.clear();ProtectedAir.clear();
            const int32 Fixed[3]={X,Y,0};
            for(uint32 Id:GetLineCandidates(2,X,Y))
            {
                const FPrimitive& P=Primitives[Id];FInterval R;
                if(SolveLine(P,2,Fixed,R))
                {
                    if(!P.bCritical)
                    {
                        const size_t CandidateBase=Line*WordsPerZ;
                        const int32 CandidateLo=std::max(Min[2],R.Lo-DetailBand);
                        const int32 CandidateHi=std::min(Max[2],R.Lo+DetailBand);
                        const int32 CandidateLo2=std::max(Min[2],R.Hi-DetailBand);
                        const int32 CandidateHi2=std::min(Max[2],R.Hi+DetailBand);
                        FillBits(CandidateAxisWords[2],CandidateBase,
                            CandidateLo-Min[2],CandidateHi-Min[2],true);
                        FillBits(CandidateAxisWords[2],CandidateBase,
                            CandidateLo2-Min[2],CandidateHi2-Min[2],true);
                    }
                    R.Lo=std::max(R.Lo,Min[2])-Min[2];R.Hi=std::min(R.Hi,Max[2])-Min[2];
                    if(R.Lo<=R.Hi)
                    {
                        if(!P.bCarve)Solid.push_back(R);
                        else if(P.bCritical)ProtectedAir.push_back(R);
                        else Carve.push_back(R);
                    }
                }
            }
            MergeIntervals(Carve);MergeIntervals(Solid);MergeIntervals(ProtectedAir);
            const size_t Base=Line*WordsPerZ;
            const int32 ZLo=LayerRanges[0].Lo, ZHi=LayerRanges[0].Hi;
            const int32 BaseLo=std::max(ZLo,Min[2])-Min[2],BaseHi=std::min(ZHi,Max[2])-Min[2];
            if(BaseLo<=BaseHi)FillBits(RockWords,Base,BaseLo,BaseHi,true);
            for(const FInterval& R:Carve)FillBits(RockWords,Base,R.Lo,R.Hi,false);
            for(const FInterval& R:Solid)FillBits(RockWords,Base,R.Lo,R.Hi,true);
            // Critical passage air is the final authored override, including at landing floors.
            for(const FInterval& R:ProtectedAir)FillBits(RockWords,Base,R.Lo,R.Hi,false);
        },&Timing,nullptr,16);
    }

    void BuildCandidateBands(FParallelTiming& AxisTiming,FParallelTiming& MergeTiming,
                             double& MergeSeconds)
    {
        const int32 N[3]={Size[0],Size[1],Size[2]};
        for(int32 Axis=0;Axis<3;++Axis)
        {
            if(Axis==2)continue;
            const int32 A=(Axis+1)%3,B=(Axis+2)%3;
            const size_t Lines=static_cast<size_t>(Size[A])*Size[B];
            const size_t Words=(static_cast<size_t>(N[Axis])+63u)/64u;
            CandidateAxisWords[Axis].assign(Lines*Words,0);
            ParallelLines(Lines,[&,Axis,A,B,Words](size_t Line)
            {
                const int32 CA=Min[A]+static_cast<int32>(Line%Size[A]);
                const int32 CB=Min[B]+static_cast<int32>(Line/Size[A]);
                int32 Fixed[3]{};Fixed[A]=CA;Fixed[B]=CB;
                for(uint32 Id:GetLineCandidates(Axis,CA,CB))
                {
                    const FPrimitive& P=Primitives[Id];if(P.bCritical)continue;
                    FInterval R;if(!SolveLine(P,Axis,Fixed,R))continue;
                    const int32 Lo=std::max(Min[Axis],R.Lo-DetailBand);
                    const int32 Hi=std::min(Max[Axis],R.Lo+DetailBand);
                    const int32 Lo2=std::max(Min[Axis],R.Hi-DetailBand);
                    const int32 Hi2=std::min(Max[Axis],R.Hi+DetailBand);
                    const size_t Base=Line*Words;
                    FillBits(CandidateAxisWords[Axis],Base,Lo-Min[Axis],Hi-Min[Axis],true);
                    FillBits(CandidateAxisWords[Axis],Base,Lo2-Min[Axis],Hi2-Min[Axis],true);
                }
            },&AxisTiming,nullptr,16);
        }
        const auto MergeStart=std::chrono::steady_clock::now();
        CandidateWords=std::move(CandidateAxisWords[2]);
        for(int32 Axis=0;Axis<2;++Axis)
        {
            const int32 A=(Axis+1)%3,B=(Axis+2)%3;
            const size_t Words=(static_cast<size_t>(Size[Axis])+63u)/64u;
            ParallelLines(static_cast<size_t>(Size[A])*Size[B],[&,Axis,A,B,Words](size_t Line)
            {
                const int32 CA=Min[A]+static_cast<int32>(Line%Size[A]);
                const int32 CB=Min[B]+static_cast<int32>(Line/Size[A]);
                for(size_t W=0;W<Words;++W)
                {
                    uint64 Bits=CandidateAxisWords[Axis][Line*Words+W];
                    while(Bits)
                    {
                        const uint32 Bit=std::countr_zero(Bits);Bits&=Bits-1;
                        const int32 T=Min[Axis]+static_cast<int32>(W*64+Bit);
                        if(T>Max[Axis])continue;
                        int32 Coord[3]{};Coord[Axis]=T;Coord[A]=CA;Coord[B]=CB;
                        const size_t Column=static_cast<size_t>(Coord[1]-Min[1])*Size[0]
                            +static_cast<size_t>(Coord[0]-Min[0]);
                        const size_t Zi=static_cast<size_t>(Coord[2]-Min[2]);
                        std::atomic_ref<uint64>(CandidateWords[Column*WordsPerZ+(Zi>>6)])
                            .fetch_or(uint64{1}<<(Zi&63u),std::memory_order_relaxed);
                    }
                }
            },&MergeTiming,nullptr,16);
        }
        const int32 LayerLo=LayerRanges.empty()?1:LayerRanges[0].Lo;
        const int32 LayerHi=LayerRanges.empty()?0:LayerRanges[0].Hi;
        if(LayerLo<=LayerHi)
        {
            for(size_t Line=0;Line<static_cast<size_t>(Size[0])*Size[1];++Line)
            {
                const size_t Base=Line*WordsPerZ;
                const int32 Lo0=std::max(Min[2],LayerLo-DetailBand)-Min[2];
                const int32 Hi0=std::min(Max[2],LayerLo+DetailBand)-Min[2];
                const int32 Lo1=std::max(Min[2],LayerHi-DetailBand)-Min[2];
                const int32 Hi1=std::min(Max[2],LayerHi+DetailBand)-Min[2];
                FillBits(CandidateWords,Base,Lo0,Hi0,true);
                FillBits(CandidateWords,Base,Lo1,Hi1,true);
            }
        }
        const double MergeElapsed=std::chrono::duration<double>(
            std::chrono::steady_clock::now()-MergeStart).count();
        MergeSeconds=std::max(0.0,MergeElapsed-MergeTiming.WallSeconds);
    }

    bool BuildGpuVisualDetailNodeSets(
        const std::vector<VoxelForgeCore::DetailBandTileRegion>& GpuTiles,
        const std::vector<VoxelForgeCore::DetailBandTileRegion>& CpuTiles,
        std::string& Error)
    {
        if(GpuTiles.empty()&&CpuTiles.empty())
        {
            GpuVisualDetailWords.clear();CpuVisualDetailWords.clear();
            if(bProfileDetailBand)
            {
                GpuVisualDetailWords.assign(CandidateWords.size(),0u);
                CpuVisualDetailWords.assign(CandidateWords.size(),0u);
            }
            GpuVisualDetailTileCount=CpuVisualDetailTileCount=0;
            GpuVisualDetailGridSamples=CpuVisualDetailGridSamples=0;
            GpuVisualDetailNodeCount=CpuVisualDetailNodeCount=0;
            return true;
        }
        const auto BuildSet=[&](const std::vector<VoxelForgeCore::DetailBandTileRegion>& Tiles,
            std::vector<uint64>& Nodes,uint64& GridSamples)->bool
        {
            Nodes.clear();GridSamples=0;
            uint64 ReserveSamples=0;
            for(const auto& Tile:Tiles)
            {
                if(Tile.cells<=0||Tile.cells>256||Tile.step<=0)
                {Error="GPU visual detail-band tile region has invalid cells or step";return false;}
                const uint64 Dim=static_cast<uint64>(Tile.cells)+3u;
                const uint64 TileSamples=Dim*Dim*Dim;
                if(TileSamples>std::numeric_limits<uint64>::max()-ReserveSamples)
                {Error="GPU visual detail-band tile sample count overflowed 64 bits";return false;}
                ReserveSamples+=TileSamples;
            }
            GridSamples=ReserveSamples;
            const auto IsCandidate=[&](int32 X,int32 Y,int32 Z)
            {
                if(X<Min[0]||X>Max[0]||Y<Min[1]||Y>Max[1]||Z<Min[2]||Z>Max[2])
                    return false;
                const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]
                    +static_cast<size_t>(X-Min[0]);
                const size_t Zi=static_cast<size_t>(Z-Min[2]);
                return (CandidateWords[Column*WordsPerZ+(Zi>>6)]
                    &(uint64{1}<<(Zi&63u)))!=0;
            };
            Nodes.assign(CandidateWords.size(),0u);
            for(const auto& Tile:Tiles)
            for(int32 Z=-1;Z<=Tile.cells+1;++Z)
            for(int32 Y=-1;Y<=Tile.cells+1;++Y)
            for(int32 X=-1;X<=Tile.cells+1;++X)
            {
                const int32 WX=Tile.originVoxel.x+X*Tile.step;
                const int32 WY=Tile.originVoxel.y+Y*Tile.step;
                const int32 WZ=Tile.originVoxel.z+Z*Tile.step;
                if(!IsCandidate(WX,WY,WZ))continue;
                const size_t Column=static_cast<size_t>(WY-Min[1])*Size[0]
                    +static_cast<size_t>(WX-Min[0]);
                const size_t Zi=static_cast<size_t>(WZ-Min[2]);
                Nodes[Column*WordsPerZ+(Zi>>6)]|=uint64{1}<<(Zi&63u);
            }
            return true;
        };
        if(!BuildSet(GpuTiles,GpuVisualDetailWords,GpuVisualDetailGridSamples)
            ||!BuildSet(CpuTiles,CpuVisualDetailWords,CpuVisualDetailGridSamples))return false;
        GpuVisualDetailNodeCount=0;CpuVisualDetailNodeCount=0;
        for(const uint64 Bits:GpuVisualDetailWords)GpuVisualDetailNodeCount+=std::popcount(Bits);
        for(const uint64 Bits:CpuVisualDetailWords)CpuVisualDetailNodeCount+=std::popcount(Bits);
        GpuVisualDetailTileCount=GpuTiles.size();CpuVisualDetailTileCount=CpuTiles.size();
        if(!GpuTiles.empty()||!CpuTiles.empty())
        {
            std::printf("[GpuVisualDetailBandPlan] gpu_tiles=%llu gpu_sample_nodes=%llu gpu_unique_candidate_nodes=%llu cpu_near_tiles=%llu cpu_sample_nodes=%llu cpu_unique_candidate_nodes=%llu\n",
                static_cast<unsigned long long>(GpuVisualDetailTileCount),
                static_cast<unsigned long long>(GpuVisualDetailGridSamples),
                static_cast<unsigned long long>(GpuVisualDetailNodeCount),
                static_cast<unsigned long long>(CpuVisualDetailTileCount),
                static_cast<unsigned long long>(CpuVisualDetailGridSamples),
                static_cast<unsigned long long>(CpuVisualDetailNodeCount));
        }
        return true;
    }

    bool IsGpuVisualDetailNode(int32 X,int32 Y,int32 Z) const
    {
        if(!Contains(X,Y,Z)||GpuVisualDetailWords.empty())return false;
        const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]
            +static_cast<size_t>(X-Min[0]);
        const size_t Zi=static_cast<size_t>(Z-Min[2]);
        return (GpuVisualDetailWords[Column*WordsPerZ+(Zi>>6)]
            &(uint64{1}<<(Zi&63u)))!=0;
    }

    bool IsCpuVisualDetailNode(int32 X,int32 Y,int32 Z) const
    {
        if(!Contains(X,Y,Z)||CpuVisualDetailWords.empty())return false;
        const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]
            +static_cast<size_t>(X-Min[0]);
        const size_t Zi=static_cast<size_t>(Z-Min[2]);
        return (CpuVisualDetailWords[Column*WordsPerZ+(Zi>>6)]
            &(uint64{1}<<(Zi&63u)))!=0;
    }

    void ApplyDetailBand(FParallelTiming& Timing)
    {
        using Clock=std::chrono::steady_clock;
        const bool bProfile=bProfileDetailBand;
        std::array<FDetailWorkerProfile,16> WorkerProfile{};
        std::array<double,16> WorkerActiveSeconds{};
        std::atomic<uint64> CandidateCount{0},ProxyCount{0},FlipCount{0};
        ParallelLines(static_cast<size_t>(Size[0])*Size[1],[&](size_t Line,int32 Worker)
        {
            const int32 X=Min[0]+static_cast<int32>(Line%Size[0]);
            const int32 Y=Min[1]+static_cast<int32>(Line/Size[0]);
            FDetailNoiseLineContext NoiseLine(static_cast<float>(X),static_cast<float>(Y),
                static_cast<uint32>(Owner->Seed));
            const FLayerField* LineField=nullptr;
            bool bLineFieldKnown=false;
            int32 LineFieldLo=0,LineFieldHi=-1;
            const auto FindLineLayerField=[&](double Z)->const FLayerField*
            {
                if(bLineFieldKnown&&LineField&&Z>=LineFieldLo&&Z<=LineFieldHi)
                    return LineField;
                LineField=FindLayerField(Z);
                bLineFieldKnown=LineField!=nullptr;
                if(LineField){LineFieldLo=LineField->Lo;LineFieldHi=LineField->Hi;}
                return LineField;
            };
            const int32 QueryBinX=FloorDiv(X,ActiveSpatialBinSize);
            const int32 QueryBinY=FloorDiv(Y,ActiveSpatialBinSize);
            int32 CachedQueryBinZ=std::numeric_limits<int32>::min();
            const FBinItems* CachedQueryBinItems=nullptr;
            FDetailWorkerProfile& Profile=WorkerProfile[static_cast<size_t>(Worker)];
            if(bProfile)++Profile.Lines;
            uint64 LocalCandidates=0,LocalProxies=0,LocalFlips=0;
            const size_t WordBase=Line*WordsPerZ;
            for(size_t W=0;W<WordsPerZ;++W)
            {
                uint64 Bits=CandidateWords[WordBase+W];
                const uint64 OriginalBits=Bits;
                uint64 ValidBits=0;
                int32 BatchZ[8]{};
                int32 BatchCount=0,BatchQueryBinZ=std::numeric_limits<int32>::min();
                const FBinItems* BatchBinItems=nullptr;
                const auto ProcessBatch=[&]()
                {
                    if(BatchCount==0)return;
                    FEffectiveRockSample Samples[8];
                    int32 ProfileDistanceSamples=0;
                    if(bProfile)
                    {
                        for(int32 Lane=0;Lane<BatchCount;++Lane)
                            if((Profile.Candidates++&255u)==0)++ProfileDistanceSamples;
                    }
                    const auto DistanceStart=ProfileDistanceSamples>0
                        ?Clock::now():Clock::time_point{};
                    EffectiveRockDistanceZ8(X,Y,BatchZ,BatchCount,BatchBinItems,Samples);
                    if(ProfileDistanceSamples>0)
                    {
                        Profile.DistanceSampleNanoseconds+=static_cast<uint64>(
                            std::chrono::duration_cast<std::chrono::nanoseconds>(
                                Clock::now()-DistanceStart).count());
                        Profile.DistanceSamples+=static_cast<uint64>(BatchCount);
                    }
                    for(int32 Lane=0;Lane<BatchCount;++Lane)
                    {
                        const int32 Z=BatchZ[Lane];
                        const size_t Zi=static_cast<size_t>(Z-Min[2]);
                        ++LocalCandidates;
                        const FEffectiveRockSample& Sample=Samples[Lane];
                        const float SDF=Sample.Distance;
                        if(std::abs(SDF)>DetailSupremum+0.125f)continue;
                        const size_t VisualWordIndex=WordBase+(Zi>>6);
                        const uint64 VisualMask=uint64{1}<<(Zi&63u);
                        const bool bGpuVisualNode=bProfile
                            &&(GpuVisualDetailWords[VisualWordIndex]&VisualMask)!=0;
                        const bool bCpuVisualNode=bProfile
                            &&(CpuVisualDetailWords[VisualWordIndex]&VisualMask)!=0;
                        if(bProfile)
                        {
                            if(bGpuVisualNode)++Profile.GpuVisualCandidates;
                            if(bCpuVisualNode)++Profile.CpuVisualCandidates;
                            if(bGpuVisualNode&&!bCpuVisualNode)++Profile.GpuOnlyCandidates;
                        }
                        const float SurfaceSDF=Sample.SurfaceSDF;
                        const float CaveInfluence=Sample.CaveInfluence;
                        const float FloorInfluence=Sample.FloorInfluence;
                        const float PassageInfluence=Sample.PassageInfluence;
                        const bool bCriticalAir=Sample.bCriticalAir;
                        float DetailFade=DetailBandFade(SDF);
                        float MacroValue=0.0f;
                        bool bMacroKnown=false;
                        const FLayerField* DetailField=nullptr;
                        bool bDetailFieldKnown=false;
                        if(DetailVariant==EDetailVariant::Coherent
                            &&std::abs(SDF)>DetailBandInnerRadius)
                        {
                            MacroValue=NoiseLine.Macro.Sample(static_cast<float>(Z));
                            bMacroKnown=true;
                            DetailField=FindLineLayerField(Z);
                            bDetailFieldKnown=true;
                            DetailFade=DetailBandFade(SDF,LocalDetailBandEdge(MacroValue,
                                SurfaceSDF,CaveInfluence,FloorInfluence,DetailField));
                        }
                        if(DetailFade<=0.0f&&bProfile)++Profile.LocalBandSkips;
                        const bool bTimeDetail=DetailFade>0.0f&&bProfile
                            &&((Profile.DetailEvaluations&63u)==0);
                        const auto DetailStart=bTimeDetail?Clock::now():Clock::time_point{};
                        float Displaced=SDF;
                        if(DetailFade>0.0f)
                        {
                            if(bProfile)++Profile.DetailEvaluations;
                            if(bProfile&&bGpuVisualNode)++Profile.GpuVisualDetailEvaluations;
                            if(bProfile&&bGpuVisualNode&&!bCpuVisualNode)
                                ++Profile.GpuOnlyDetailEvaluations;
                            Displaced+=DetailNoiseOnLine(X,Y,Z,Sample.SurfaceSDF,
                                CaveInfluence,FloorInfluence,PassageInfluence,NoiseLine,bTimeDetail?&Profile:nullptr,
                                DetailField,bDetailFieldKnown,bMacroKnown,MacroValue)*DetailFade;
                        }
                        if(bTimeDetail)
                        {
                            Profile.DetailSampleNanoseconds+=static_cast<uint64>(
                                std::chrono::duration_cast<std::chrono::nanoseconds>(
                                    Clock::now()-DetailStart).count());
                            ++Profile.DetailSamples;
                        }
                        if(bCriticalAir)Displaced=std::min(Displaced,-1.0f/16.0f);
                        const bool bNewRock=Displaced>=0.0f;
                        const bool bOldRock=((RockWords[WordBase+(Zi>>6)]>>(Zi&63u))&1u)!=0;
                        if(bNewRock!=bOldRock)
                        {
                            RockWords[WordBase+(Zi>>6)]^=uint64{1}<<(Zi&63u);
                            ++LocalFlips;
                            if(bProfile)++Profile.Flips;
                        }
                        const size_t Node=(Zi*static_cast<size_t>(Size[1])
                            +static_cast<size_t>(Y-Min[1]))*Size[0]
                            +static_cast<size_t>(X-Min[0]);
                        StoreSurfaceDistance(Node,-Displaced);
                        ValidBits|=uint64{1}<<(Zi&63u);
                        ++LocalProxies;
                    }
                    BatchCount=0;
                };
                while(Bits)
                {
                    const uint32 Bit=std::countr_zero(Bits);Bits&=Bits-1;
                    const size_t Zi=W*64+Bit;if(Zi>=static_cast<size_t>(Size[2]))continue;
                    const int32 Z=Min[2]+static_cast<int32>(Zi);
                    const int32 QueryBinZ=FloorDiv(Z,ActiveSpatialBinSize);
                    if(BatchCount>0&&QueryBinZ!=BatchQueryBinZ)ProcessBatch();
                    if(QueryBinZ!=CachedQueryBinZ)
                    {
                        const auto Bin=SpatialBins.find({QueryBinX,QueryBinY,QueryBinZ});
                        CachedQueryBinItems=Bin==SpatialBins.end()?nullptr:&Bin->second;
                        CachedQueryBinZ=QueryBinZ;
                    }
                    if(BatchCount==0)BatchQueryBinZ=QueryBinZ,BatchBinItems=CachedQueryBinItems;
                    BatchZ[BatchCount++]=Z;
                    if(BatchCount==8)ProcessBatch();
                }
                ProcessBatch();
                if(OriginalBits!=ValidBits)CandidateWords[WordBase+W]=ValidBits;
            }
            CandidateCount.fetch_add(LocalCandidates,std::memory_order_relaxed);
            ProxyCount.fetch_add(LocalProxies,std::memory_order_relaxed);
            FlipCount.fetch_add(LocalFlips,std::memory_order_relaxed);
        // Each X/Y column is independent. Claim eight adjacent columns at a time to
        // reduce scheduler atomics while preserving per-column scalar evaluation order.
        },&Timing,&WorkerActiveSeconds,8);
        Stats.SurfaceCandidates=CandidateCount.load(std::memory_order_relaxed);
        Stats.SurfaceProxyNodes=ProxyCount.load(std::memory_order_relaxed);
        Stats.DetailFlips=FlipCount.load(std::memory_order_relaxed);
        if(bProfile)
        {
            uint64 DistanceCalls=0,DetailCalls=0,DistanceSamples=0,DistanceSampleNs=0;
            uint64 DetailSamples=0,DetailSampleNs=0,ReliefSampleNs=0,LocalBandSkips=0;
            uint64 LayerLookupSampleNs=0,OwnerSampleNs=0,OwnerFieldCalls=0,OwnerActiveCalls=0;
            uint64 OwnerCacheHits=0,OwnerCacheMisses=0;
            uint64 GpuVisualCandidates=0,CpuVisualCandidates=0,GpuOnlyCandidates=0;
            uint64 GpuVisualDetailCalls=0,GpuOnlyDetailCalls=0;
            for(int32 Worker=0;Worker<WorkerCount;++Worker)
            {
                const FDetailWorkerProfile& P=WorkerProfile[static_cast<size_t>(Worker)];
                DistanceCalls+=P.Candidates;DetailCalls+=P.DetailEvaluations;
                DistanceSamples+=P.DistanceSamples;DistanceSampleNs+=P.DistanceSampleNanoseconds;
                DetailSamples+=P.DetailSamples;DetailSampleNs+=P.DetailSampleNanoseconds;
                LocalBandSkips+=P.LocalBandSkips;
                ReliefSampleNs+=P.ReliefSampleNanoseconds;
                LayerLookupSampleNs+=P.LayerLookupSampleNanoseconds;
                OwnerSampleNs+=P.OwnerRoughnessSampleNanoseconds;
                OwnerFieldCalls+=P.OwnerRoughnessFieldCalls;
                OwnerActiveCalls+=P.OwnerRoughnessActiveCalls;
                OwnerCacheHits+=P.OwnerNoiseCacheHits;
                OwnerCacheMisses+=P.OwnerNoiseCacheMisses;
                GpuVisualCandidates+=P.GpuVisualCandidates;
                CpuVisualCandidates+=P.CpuVisualCandidates;
                GpuOnlyCandidates+=P.GpuOnlyCandidates;
                GpuVisualDetailCalls+=P.GpuVisualDetailEvaluations;
                GpuOnlyDetailCalls+=P.GpuOnlyDetailEvaluations;
            }
            const double DistanceAverageNs=DistanceSamples?static_cast<double>(DistanceSampleNs)/DistanceSamples:0.0;
            const double DetailAverageNs=DetailSamples?static_cast<double>(DetailSampleNs)/DetailSamples:0.0;
            const double CandidateWorkerNs=Stats.SurfaceCandidates
                ?Timing.WorkerSeconds*1.0e9/static_cast<double>(Stats.SurfaceCandidates):0.0;
            std::printf("[DetailBandProfile] candidates=%llu distance_evaluations=%llu detail_noise_evaluations=%llu proxies=%llu flips=%llu candidate_worker_ns=%.1f distance_sample_ns=%.1f distance_estimated_worker_ms=%.1f detail_sample_ns=%.1f detail_estimated_worker_ms=%.1f worker_sum_ms=%.3f wall_ms=%.3f sampling=(distance_1_of_256,detail_1_of_64)\n",
                static_cast<unsigned long long>(Stats.SurfaceCandidates),
                static_cast<unsigned long long>(DistanceCalls),static_cast<unsigned long long>(DetailCalls),
                static_cast<unsigned long long>(Stats.SurfaceProxyNodes),static_cast<unsigned long long>(Stats.DetailFlips),
                CandidateWorkerNs,DistanceAverageNs,DistanceAverageNs*static_cast<double>(DistanceCalls)/1.0e6,
                DetailAverageNs,DetailAverageNs*static_cast<double>(DetailCalls)/1.0e6,
                Timing.WorkerSeconds*1000.0,Timing.WallSeconds*1000.0);
            std::printf("[DetailBandSubprofile] relief_sample_ns=%.1f relief_estimated_worker_ms=%.1f layer_lookup_sample_ns=%.1f layer_lookup_estimated_worker_ms=%.1f owner_sample_ns=%.1f owner_estimated_worker_ms=%.1f owner_sampled_field_calls=%llu owner_sampled_noise_calls=%llu owner_sampled_core_cache_hits=%llu owner_sampled_core_cache_misses=%llu local_band_skipped=%llu\n",
                DetailSamples?static_cast<double>(ReliefSampleNs)/DetailSamples:0.0,
                DetailSamples?static_cast<double>(ReliefSampleNs)/DetailSamples*DetailCalls/1.0e6:0.0,
                DetailSamples?static_cast<double>(LayerLookupSampleNs)/DetailSamples:0.0,
                DetailSamples?static_cast<double>(LayerLookupSampleNs)/DetailSamples*DetailCalls/1.0e6:0.0,
                DetailSamples?static_cast<double>(OwnerSampleNs)/DetailSamples:0.0,
                DetailSamples?static_cast<double>(OwnerSampleNs)/DetailSamples*DetailCalls/1.0e6:0.0,
                static_cast<unsigned long long>(OwnerFieldCalls),
                static_cast<unsigned long long>(OwnerActiveCalls),
                static_cast<unsigned long long>(OwnerCacheHits),
                static_cast<unsigned long long>(OwnerCacheMisses),
                static_cast<unsigned long long>(LocalBandSkips));
            std::printf("[GpuDetailConsumerProfile] gpu_near_proxy_nodes=%llu cpu_near_mesh_nodes=%llu gpu_only_nodes=%llu gpu_near_detail_noise_evaluations=%llu gpu_only_detail_noise_evaluations=%llu\n",
                static_cast<unsigned long long>(GpuVisualCandidates),
                static_cast<unsigned long long>(CpuVisualCandidates),
                static_cast<unsigned long long>(GpuOnlyCandidates),
                static_cast<unsigned long long>(GpuVisualDetailCalls),
                static_cast<unsigned long long>(GpuOnlyDetailCalls));
            for(int32 Worker=0;Worker<WorkerCount;++Worker)
            {
                const FDetailWorkerProfile& P=WorkerProfile[static_cast<size_t>(Worker)];
                std::printf("[DetailBandWorker] id=%d active_ms=%.3f lines=%llu candidates=%llu detail_evaluations=%llu flips=%llu\n",
                    Worker,WorkerActiveSeconds[static_cast<size_t>(Worker)]*1000.0,
                    static_cast<unsigned long long>(P.Lines),static_cast<unsigned long long>(P.Candidates),
                    static_cast<unsigned long long>(P.DetailEvaluations),static_cast<unsigned long long>(P.Flips));
            }
        }
    }

    uint64 CompleteSignEdgeDistances()
    {
        uint64 AddedTotal=0,SignCorrections=0;
        const size_t Columns=static_cast<size_t>(Size[0])*Size[1];
        for(int32 Pass=0;Pass<4;++Pass)
        {
            uint64 AddedThisPass=0;
            bool bSignChanged=false;
            const auto EnsureDistance=[&](int32 X,int32 Y,int32 Z)
            {
                const size_t Column=static_cast<size_t>(Y-Min[1])*Size[0]
                    +static_cast<size_t>(X-Min[0]);
                const size_t Zi=static_cast<size_t>(Z-Min[2]);
                const size_t Word=Column*WordsPerZ+(Zi>>6);
                const uint64 Mask=uint64{1}<<(Zi&63u);
                if(CandidateWords[Word]&Mask)return;

                const float Density=AnalyticDensityAt(static_cast<float>(X),
                    static_cast<float>(Y),static_cast<float>(Z));
                const size_t Node=(Zi*static_cast<size_t>(Size[1])
                    +static_cast<size_t>(Y-Min[1]))*Size[0]
                    +static_cast<size_t>(X-Min[0]);
                StoreSurfaceDistance(Node,Density);
                CandidateWords[Word]|=Mask;
                ++AddedThisPass;

                const bool bExactRock=Density<0.0f;
                const bool bPackedRock=(RockWords[Word]&Mask)!=0;
                if(bExactRock!=bPackedRock)
                {
                    if(bExactRock)RockWords[Word]|=Mask;
                    else RockWords[Word]&=~Mask;
                    ++SignCorrections;
                    bSignChanged=true;
                }
            };

            for(size_t Line=0;Line<Columns;++Line)
            {
                const int32 X=Min[0]+static_cast<int32>(Line%Size[0]);
                const int32 Y=Min[1]+static_cast<int32>(Line/Size[0]);
                const size_t Base=Line*WordsPerZ;
                for(size_t W=0;W<WordsPerZ;++W)
                {
                    const size_t Word=Base+W;
                    const uint64 Rock=RockWords[Word],Candidates=CandidateWords[Word];
                    const uint64 PreviousRock=W?RockWords[Word-1]>>63:0;
                    const uint64 PreviousCandidates=W?CandidateWords[Word-1]>>63:0;
                    uint64 Valid=(Size[2]-W*64)>=64?~uint64{0}
                        :((uint64{1}<<(Size[2]-W*64))-1);
                    if(W==0)Valid&=~uint64{1};

                    const uint64 ShiftedRock=(Rock<<1)|PreviousRock;
                    const uint64 ShiftedCandidates=(Candidates<<1)|PreviousCandidates;
                    uint64 Missing=((Rock^ShiftedRock)&Valid)
                        &~(Candidates&ShiftedCandidates);
                    while(Missing)
                    {
                        const uint32 Bit=std::countr_zero(Missing);Missing&=Missing-1;
                        const int32 Z=Min[2]+static_cast<int32>(W*64+Bit);
                        EnsureDistance(X,Y,Z);
                        EnsureDistance(X,Y,Z-1);
                    }

                    if(X<Max[0])
                    {
                        const size_t Other=Word+WordsPerZ;
                        Missing=(Rock^RockWords[Other])&Valid
                            &~(Candidates&CandidateWords[Other]);
                        while(Missing)
                        {
                            const uint32 Bit=std::countr_zero(Missing);Missing&=Missing-1;
                            const int32 Z=Min[2]+static_cast<int32>(W*64+Bit);
                            EnsureDistance(X,Y,Z);
                            EnsureDistance(X+1,Y,Z);
                        }
                    }
                    if(Y<Max[1])
                    {
                        const size_t Other=Word+static_cast<size_t>(Size[0])*WordsPerZ;
                        Missing=(Rock^RockWords[Other])&Valid
                            &~(Candidates&CandidateWords[Other]);
                        while(Missing)
                        {
                            const uint32 Bit=std::countr_zero(Missing);Missing&=Missing-1;
                            const int32 Z=Min[2]+static_cast<int32>(W*64+Bit);
                            EnsureDistance(X,Y,Z);
                            EnsureDistance(X,Y+1,Z);
                        }
                    }
                }
            }
            AddedTotal+=AddedThisPass;
            if(!bSignChanged)break;
        }
        std::printf("[GridStairDistanceRepair] exact_endpoint_proxies=%llu occupancy_corrections=%llu\n",
            static_cast<unsigned long long>(AddedTotal),
            static_cast<unsigned long long>(SignCorrections));
        return AddedTotal;
    }

    void StoreSurfaceDistance(size_t Node,float Density)
    {
        int32 Q=static_cast<int32>(std::lround(Density*256.0f));
        Q=std::clamp(Q,-32767,32767);
        if(Q==0)Q=Density<0.0f?-1:1;
        SurfaceDistanceQ[Node]=static_cast<int16>(Q);
    }

    bool IsInsideSolidOverlay(int32 X,int32 Y,int32 Z) const
    {
        const FBinKey K=PointBin(X,Y,Z);const auto It=SpatialBins.find(K);
        if(It==SpatialBins.end())return false;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(P.bCarve)continue;
            if(X<P.Min[0]||X>P.Max[0]||Y<P.Min[1]||Y>P.Max[1]||Z<P.Min[2]||Z>P.Max[2])continue;
            if(ShapeContains(P,X,Y,Z))return true;
        }
        return false;
    }

    bool IsInsideCriticalAir(int32 X,int32 Y,int32 Z) const
    {
        const auto It=CriticalAirBins.find(PointBin(X,Y,Z));
        if(It==CriticalAirBins.end())return false;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(!P.bCarve||!P.bCritical)continue;
            if(X<P.Min[0]||X>P.Max[0]||Y<P.Min[1]||Y>P.Max[1]||Z<P.Min[2]||Z>P.Max[2])continue;
            if(ShapeContains(P,X,Y,Z))return true;
        }
        return false;
    }

    bool IsNearCriticalAirBoundary(int32 X,int32 Y,int32 Z,double Margin) const
    {
        const auto It=CriticalAirBins.find(PointBin(X,Y,Z));
        if(It==CriticalAirBins.end())return false;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(!P.bCarve||!P.bCritical)continue;
            if(X<P.Min[0]-Margin||X>P.Max[0]+Margin
                ||Y<P.Min[1]-Margin||Y>P.Max[1]+Margin
                ||Z<P.Min[2]-Margin||Z>P.Max[2]+Margin)continue;
            float Distance=ShapeDistance(P,X,Y,Z);
            if(P.bHasFloorClip)
            {
                const float FloorDistance=static_cast<float>(FloorAt(P,X,Y)-Z);
                Distance=SmoothMaxDistance(Distance,FloorDistance,static_cast<float>(P.FloorBlendRadius));
            }
            if(std::abs(Distance)<=Margin)return true;
        }
        return false;
    }

    bool IsInsideSolidOverlay(double X,double Y,double Z) const
    {
        const auto It=SpatialBins.find(PointBin(X,Y,Z));
        if(It==SpatialBins.end())return false;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(P.bCarve)continue;
            if(X<P.Min[0]||X>P.Max[0]||Y<P.Min[1]||Y>P.Max[1]||Z<P.Min[2]||Z>P.Max[2])continue;
            if(ShapeDistance(P,X,Y,Z)<=0.0f)return true;
        }
        return false;
    }

    float SolidOverlayDistance(double X,double Y,double Z) const
    {
        const auto It=SpatialBins.find(PointBin(X,Y,Z));
        if(It==SpatialBins.end())return -100000.0f;
        float Best=-100000.0f;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(P.bCarve)continue;
            if(X<P.Min[0]||X>P.Max[0]||Y<P.Min[1]||Y>P.Max[1]||Z<P.Min[2]||Z>P.Max[2])continue;
            Best=std::max(Best,-ShapeDistance(P,X,Y,Z));
        }
        return Best;
    }

    bool IsInsideCriticalAir(double X,double Y,double Z) const
    {
        const auto It=CriticalAirBins.find(PointBin(X,Y,Z));
        if(It==CriticalAirBins.end())return false;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(!P.bCarve||!P.bCritical)continue;
            if(X<P.Min[0]||X>P.Max[0]||Y<P.Min[1]||Y>P.Max[1]||Z<P.Min[2]||Z>P.Max[2])continue;
            if(ShapeContains(P,X,Y,Z))return true;
        }
        return false;
    }

    float CaveDistance(double X,double Y,double Z,bool* OutFloorSurface=nullptr,
                       float* OutFloorInfluence=nullptr) const
    {
        const auto It=SpatialBins.find(PointBin(X,Y,Z));
        if(It==SpatialBins.end())
        {
            if(OutFloorSurface)*OutFloorSurface=false;
            if(OutFloorInfluence)*OutFloorInfluence=0.0f;
            return 100000.0f;
        }
        float Best=100000.0f;
        float BestFloorInfluence=0.0f;
        for(uint32 Id:It->second)
        {
            const FPrimitive& P=Primitives[Id];if(!P.bCarve)continue;
            if(X<P.Min[0]-DetailBand||X>P.Max[0]+DetailBand||Y<P.Min[1]-DetailBand||Y>P.Max[1]+DetailBand
                ||Z<P.Min[2]-DetailBand||Z>P.Max[2]+DetailBand)continue;
            float Distance=ShapeDistance(P,X,Y,Z);
            float PrimitiveFloorInfluence=0.0f;
            if(P.bHasFloorClip)
            {
                const double Floor=FloorAt(P,X,Y);
                const float FloorT=(static_cast<float>(std::abs(Z-Floor))-static_cast<float>(P.FloorBlendRadius))
                    /static_cast<float>(std::max(DetailBand*2,1));
                PrimitiveFloorInfluence=1.0f-SmoothUnit(FloorT);
                Distance=SmoothMaxDistance(Distance,static_cast<float>(Floor-Z),
                    static_cast<float>(P.FloorBlendRadius));
            }
            const float MetadataWidth=static_cast<float>(std::max(P.BlendRadius,6.0));
            const float PrimitiveWeight=SmoothUnit(0.5f+(Best-Distance)/(2.0f*MetadataWidth));
            const float Combined=SmoothMinDistance(Best,Distance,static_cast<float>(P.BlendRadius));
            BestFloorInfluence=std::lerp(BestFloorInfluence,PrimitiveFloorInfluence,PrimitiveWeight);
            Best=Combined;
        }
        if(OutFloorInfluence)*OutFloorInfluence=BestFloorInfluence;
        if(OutFloorSurface)*OutFloorSurface=BestFloorInfluence>=0.5f;
        return Best;
    }

    float StrataDistance(double Z) const
    {
        if(LayerRanges.empty())return -100000.0f;
        return static_cast<float>(std::min(Z-LayerRanges[0].Lo,LayerRanges[0].Hi-Z));
    }

    const FLayerField* FindLayerField(double Z) const
    {
        for(const FLayerField& Field:LayerFields)
            if(Z>=Field.Lo&&Z<=Field.Hi)return &Field;
        return nullptr;
    }

    float EffectiveRockDistance(double X,double Y,double Z,
                                ESurfaceFamily* OutFamily=nullptr,
                                float* OutSurfaceSDF=nullptr,
                                bool* OutFloorSurface=nullptr,
                                float* OutCaveInfluence=nullptr,
                                float* OutFloorInfluence=nullptr,
                                bool* OutCriticalAir=nullptr,
                                const FBinItems* KnownBinItems=nullptr,
                                bool bKnownBin=false,
                                float* OutPassageInfluence=nullptr) const
    {
        const float Base=StrataDistance(Z);
        float Cave=100000.0f;
        float Overlay=-100000.0f;
        float CaveFloorInfluence=0.0f;
        float CavePassageInfluence=0.0f;
        bool bCriticalAir=false;
        const FBinItems* BinItems=KnownBinItems;
        if(!bKnownBin)
        {
            const auto Bin=SpatialBins.find(PointBin(X,Y,Z));
            if(Bin!=SpatialBins.end())BinItems=&Bin->second;
        }
        if(BinItems)
        {
            for(uint32 Id:*BinItems)
            {
                const FPrimitive& P=Primitives[Id];
                if(P.bCarve)
                {
                    if(P.bCritical&&X>=P.Min[0]&&X<=P.Max[0]&&Y>=P.Min[1]&&Y<=P.Max[1]
                        &&Z>=P.Min[2]&&Z<=P.Max[2]&&ShapeContains(P,
                            static_cast<int32>(X),static_cast<int32>(Y),static_cast<int32>(Z)))
                        bCriticalAir=true;
                    if(X<P.Min[0]-DetailBand||X>P.Max[0]+DetailBand
                        ||Y<P.Min[1]-DetailBand||Y>P.Max[1]+DetailBand
                        ||Z<P.Min[2]-DetailBand||Z>P.Max[2]+DetailBand)continue;
                    float Distance=ShapeDistance(P,X,Y,Z);
                    float PrimitiveFloorInfluence=0.0f;
                    if(P.bHasFloorClip)
                    {
                        const double Floor=FloorAt(P,X,Y);
                        const float FloorT=(static_cast<float>(std::abs(Z-Floor))
                            -static_cast<float>(P.FloorBlendRadius))
                            /static_cast<float>(std::max(DetailBand*2,1));
                        PrimitiveFloorInfluence=1.0f-SmoothUnit(FloorT);
                        Distance=SmoothMaxDistance(Distance,static_cast<float>(Floor-Z),
                            static_cast<float>(P.FloorBlendRadius));
                    }
                    const float MetadataWidth=static_cast<float>(std::max(P.BlendRadius,6.0));
                    const float PrimitiveWeight=SmoothUnit(0.5f+(Cave-Distance)/(2.0f*MetadataWidth));
                    const float Combined=SmoothMinDistance(Cave,Distance,static_cast<float>(P.BlendRadius));
                    CaveFloorInfluence=std::lerp(CaveFloorInfluence,PrimitiveFloorInfluence,PrimitiveWeight);
                    if(OutPassageInfluence&&(CavePassageInfluence>0.0f||P.bPassageSurface))
                        CavePassageInfluence=std::lerp(CavePassageInfluence,
                            P.bPassageSurface?1.0f:0.0f,PrimitiveWeight);
                    Cave=Combined;
                }
                else if(X>=P.Min[0]&&X<=P.Max[0]&&Y>=P.Min[1]&&Y<=P.Max[1]
                    &&Z>=P.Min[2]&&Z<=P.Max[2])
                    Overlay=std::max(Overlay,-ShapeDistance(P,X,Y,Z));
            }
        }
        if(OutCriticalAir)*OutCriticalAir=bCriticalAir;
        const float CarveOrOverlay=std::max(Cave,Overlay);
        const ESurfaceFamily Family=Base<=CarveOrOverlay?ESurfaceFamily::Strata:
            (Cave>=Overlay?ESurfaceFamily::Cave:ESurfaceFamily::SolidOverlay);
        constexpr float FamilyBlendWidth=6.0f;
        const float CaveVsOverlay=SmoothUnit(0.5f+(Cave-Overlay)/(2.0f*FamilyBlendWidth));
        const float CarveInfluence=SmoothUnit(0.5f+(Base-CarveOrOverlay)/(2.0f*FamilyBlendWidth));
        const float CaveInfluence=CarveInfluence*CaveVsOverlay;
        const float FloorInfluence=CaveInfluence*CaveFloorInfluence;
        const float PassageInfluence=CaveInfluence*CavePassageInfluence;
        const float RockDistance=SmoothMinDistance(Base,CarveOrOverlay,StrataCaveBlendRadius);
        if(OutFamily)
            *OutFamily=Family;
        if(OutSurfaceSDF)
            *OutSurfaceSDF=Family==ESurfaceFamily::Strata?Base:
                (Family==ESurfaceFamily::Cave?Cave:Overlay);
        if(OutCaveInfluence)*OutCaveInfluence=CaveInfluence;
        if(OutFloorInfluence)*OutFloorInfluence=FloorInfluence;
        if(OutPassageInfluence)*OutPassageInfluence=PassageInfluence;
        if(OutFloorSurface)*OutFloorSurface=FloorInfluence>=0.5f;
        return RockDistance;
    }

    struct FEffectiveRockSample
    {
        float Distance=0.0f;
        float SurfaceSDF=0.0f;
        float CaveInfluence=0.0f;
        float FloorInfluence=0.0f;
        float PassageInfluence=0.0f;
        ESurfaceFamily Family=ESurfaceFamily::Strata;
        bool bFloorSurface=false;
        bool bCriticalAir=false;
    };

    void ShapeDistanceZ8(const FPrimitive& P,int32 X,int32 Y,const int32 Z[8],int32 Count,
                         float OutDistance[8]) const
    {
        const __m256d Zero=_mm256_setzero_pd();
        const __m256d One=_mm256_set1_pd(1.0);
        const __m256d SignMask=_mm256_set1_pd(-0.0);
        for(int32 Base=0;Base<Count;Base+=4)
        {
            double ZLane[4];
            const int32 Lanes=std::min(4,Count-Base);
            for(int32 Lane=0;Lane<4;++Lane)
                ZLane[Lane]=static_cast<double>(Z[Base+std::min(Lane,Lanes-1)]);
            const __m256d VZ=_mm256_setr_pd(ZLane[0],ZLane[1],ZLane[2],ZLane[3]);
            __m256d Distance;
            if(P.bCapsule)
            {
                const double VX=static_cast<double>(X)-P.CapsuleStartWorld[0];
                const double VY=static_cast<double>(Y)-P.CapsuleStartWorld[1];
                const __m256d VXv=_mm256_set1_pd(VX);
                const __m256d VYv=_mm256_set1_pd(VY);
                const __m256d VZv=_mm256_sub_pd(VZ,_mm256_set1_pd(P.CapsuleStartWorld[2]));
                __m256d VD=_mm256_mul_pd(VXv,_mm256_set1_pd(P.CapsuleAxisDelta[0]));
                VD=_mm256_add_pd(VD,_mm256_mul_pd(VYv,_mm256_set1_pd(P.CapsuleAxisDelta[1])));
                VD=_mm256_add_pd(VD,_mm256_mul_pd(VZv,_mm256_set1_pd(P.CapsuleAxisDelta[2])));
                const __m256d T=P.CapsuleAxisLengthSquared>1.0e-12
                    ?_mm256_max_pd(Zero,_mm256_min_pd(One,
                        _mm256_div_pd(VD,_mm256_set1_pd(P.CapsuleAxisLengthSquared))))
                    :Zero;
                const __m256d EX=_mm256_sub_pd(VXv,
                    _mm256_mul_pd(T,_mm256_set1_pd(P.CapsuleAxisDelta[0])));
                const __m256d EY=_mm256_sub_pd(VYv,
                    _mm256_mul_pd(T,_mm256_set1_pd(P.CapsuleAxisDelta[1])));
                const __m256d EZ=_mm256_sub_pd(VZv,
                    _mm256_mul_pd(T,_mm256_set1_pd(P.CapsuleAxisDelta[2])));
                __m256d DistanceSquared=_mm256_mul_pd(EX,EX);
                DistanceSquared=_mm256_add_pd(DistanceSquared,_mm256_mul_pd(EY,EY));
                DistanceSquared=_mm256_add_pd(DistanceSquared,_mm256_mul_pd(EZ,EZ));
                const __m256d Root=_mm256_sqrt_pd(DistanceSquared);
                double TValues[4],RootValues[4];
                _mm256_storeu_pd(TValues,T);
                _mm256_storeu_pd(RootValues,Root);
                for(int32 Lane=0;Lane<Lanes;++Lane)
                    OutDistance[Base+Lane]=static_cast<float>(RootValues[Lane]
                        -CapsuleRadiusAtT(P,TValues[Lane],P.CapsuleAxisLength));
                continue;
            }
            if(P.bRoundedBox)
            {
                const double DX=std::abs(static_cast<double>(X)-P.CenterSub[0]/16.0)
                    -P.RoundedHalfExtent[0];
                const double DY=std::abs(static_cast<double>(Y)-P.CenterSub[1]/16.0)
                    -P.RoundedHalfExtent[1];
                const double DZCenter=P.CenterSub[2]/16.0;
                const __m256d DZv=_mm256_sub_pd(_mm256_andnot_pd(SignMask,
                    _mm256_sub_pd(VZ,_mm256_set1_pd(DZCenter))),
                    _mm256_set1_pd(P.RoundedHalfExtent[2]));
                const __m256d DXv=_mm256_set1_pd(DX),DYv=_mm256_set1_pd(DY);
                const __m256d Ox=_mm256_max_pd(DXv,Zero),Oy=_mm256_max_pd(DYv,Zero);
                const __m256d Oz=_mm256_max_pd(DZv,Zero);
                __m256d OutsideSquared=_mm256_mul_pd(Ox,Ox);
                OutsideSquared=_mm256_add_pd(OutsideSquared,_mm256_mul_pd(Oy,Oy));
                OutsideSquared=_mm256_add_pd(OutsideSquared,_mm256_mul_pd(Oz,Oz));
                const __m256d MaxXY=_mm256_max_pd(DXv,DYv);
                const __m256d MaxQ=_mm256_max_pd(MaxXY,DZv);
                const __m256d Inside=_mm256_min_pd(MaxQ,Zero);
                Distance=_mm256_sub_pd(_mm256_add_pd(_mm256_sqrt_pd(OutsideSquared),Inside),
                    _mm256_set1_pd(P.Rounding));
            }
            else
            {
                const __m256d D[3]={
                    _mm256_set1_pd(static_cast<double>(X)-P.CenterSub[0]/16.0),
                    _mm256_set1_pd(static_cast<double>(Y)-P.CenterSub[1]/16.0),
                    _mm256_sub_pd(VZ,_mm256_set1_pd(P.CenterSub[2]/16.0))};
                __m256d Q=_mm256_setzero_pd();
                for(int32 I=0;I<3;++I)for(int32 J=0;J<3;++J)
                {
                    const double Coefficient=static_cast<double>(P.Q[I][J])/QScale;
                    __m256d Term=_mm256_mul_pd(_mm256_set1_pd(Coefficient),D[I]);
                    Term=_mm256_mul_pd(Term,D[J]);
                    Term=_mm256_mul_pd(Term,_mm256_set1_pd(256.0));
                    Q=_mm256_add_pd(Q,Term);
                }
                Distance=_mm256_mul_pd(_mm256_sub_pd(
                    _mm256_sqrt_pd(_mm256_max_pd(Q,Zero)),_mm256_set1_pd(1.0)),
                    _mm256_set1_pd(P.MinRadius));
            }
            double Values[4];
            _mm256_storeu_pd(Values,Distance);
            for(int32 Lane=0;Lane<Lanes;++Lane)
                OutDistance[Base+Lane]=static_cast<float>(Values[Lane]);
        }
    }

    void EffectiveRockDistanceZ8(int32 X,int32 Y,const int32 Z[8],int32 Count,
                                 const FBinItems* BinItems,FEffectiveRockSample Out[8]) const
    {
        float Base[8],Cave[8],Overlay[8],CaveFloorInfluence[8],CavePassageInfluence[8];
        bool CriticalAir[8]{};
        for(int32 Lane=0;Lane<Count;++Lane)
        {
            Base[Lane]=StrataDistance(Z[Lane]);
            Cave[Lane]=100000.0f;
            Overlay[Lane]=-100000.0f;
            CaveFloorInfluence[Lane]=0.0f;
            CavePassageInfluence[Lane]=0.0f;
        }
        if(BinItems)
        {
            for(uint32 Id:*BinItems)
            {
                const FPrimitive& P=Primitives[Id];
                bool Eligible[8]{};
                bool AnyEligible=false;
                if(P.bCarve)
                {
                    for(int32 Lane=0;Lane<Count;++Lane)
                    {
                        const int32 ZValue=Z[Lane];
                        if(P.bCritical&&X>=P.Min[0]&&X<=P.Max[0]
                            &&Y>=P.Min[1]&&Y<=P.Max[1]
                            &&ZValue>=P.Min[2]&&ZValue<=P.Max[2]
                            &&ShapeContains(P,X,Y,ZValue))
                            CriticalAir[Lane]=true;
                        if(X<P.Min[0]-DetailBand||X>P.Max[0]+DetailBand
                            ||Y<P.Min[1]-DetailBand||Y>P.Max[1]+DetailBand
                            ||ZValue<P.Min[2]-DetailBand||ZValue>P.Max[2]+DetailBand)
                            continue;
                        Eligible[Lane]=true;
                        AnyEligible=true;
                    }
                }
                else
                {
                    for(int32 Lane=0;Lane<Count;++Lane)
                    {
                        const int32 ZValue=Z[Lane];
                        Eligible[Lane]=X>=P.Min[0]&&X<=P.Max[0]
                            &&Y>=P.Min[1]&&Y<=P.Max[1]
                            &&ZValue>=P.Min[2]&&ZValue<=P.Max[2];
                        AnyEligible=AnyEligible||Eligible[Lane];
                    }
                }
                if(!AnyEligible)continue;

                float Distances[8];
                ShapeDistanceZ8(P,X,Y,Z,Count,Distances);
                if(P.bCarve)
                {
                    const double Floor=P.bHasFloorClip?FloorAt(P,X,Y):0.0;
                    const float MetadataWidth=static_cast<float>(std::max(P.BlendRadius,6.0));
                    for(int32 Lane=0;Lane<Count;++Lane)
                    {
                        if(!Eligible[Lane])continue;
                        float Distance=Distances[Lane];
                        float PrimitiveFloorInfluence=0.0f;
                        if(P.bHasFloorClip)
                        {
                            const float FloorT=(static_cast<float>(std::abs(Z[Lane]-Floor))
                                -static_cast<float>(P.FloorBlendRadius))
                                /static_cast<float>(std::max(DetailBand*2,1));
                            PrimitiveFloorInfluence=1.0f-SmoothUnit(FloorT);
                            Distance=SmoothMaxDistance(Distance,static_cast<float>(Floor-Z[Lane]),
                                static_cast<float>(P.FloorBlendRadius));
                        }
                        const float PrimitiveWeight=SmoothUnit(0.5f
                            +(Cave[Lane]-Distance)/(2.0f*MetadataWidth));
                        const float Combined=SmoothMinDistance(Cave[Lane],Distance,
                            static_cast<float>(P.BlendRadius));
                        CaveFloorInfluence[Lane]=std::lerp(CaveFloorInfluence[Lane],
                            PrimitiveFloorInfluence,PrimitiveWeight);
                        if(CavePassageInfluence[Lane]>0.0f||P.bPassageSurface)
                            CavePassageInfluence[Lane]=std::lerp(CavePassageInfluence[Lane],
                                P.bPassageSurface?1.0f:0.0f,PrimitiveWeight);
                        Cave[Lane]=Combined;
                    }
                }
                else
                {
                    for(int32 Lane=0;Lane<Count;++Lane)
                        if(Eligible[Lane])Overlay[Lane]=std::max(Overlay[Lane],-Distances[Lane]);
                }
            }
        }
        for(int32 Lane=0;Lane<Count;++Lane)
        {
            const float CarveOrOverlay=std::max(Cave[Lane],Overlay[Lane]);
            const ESurfaceFamily Family=Base[Lane]<=CarveOrOverlay?ESurfaceFamily::Strata:
                (Cave[Lane]>=Overlay[Lane]?ESurfaceFamily::Cave:ESurfaceFamily::SolidOverlay);
            constexpr float FamilyBlendWidth=6.0f;
            const float CaveVsOverlay=SmoothUnit(0.5f
                +(Cave[Lane]-Overlay[Lane])/(2.0f*FamilyBlendWidth));
            const float CarveInfluence=SmoothUnit(0.5f
                +(Base[Lane]-CarveOrOverlay)/(2.0f*FamilyBlendWidth));
            const float CaveInfluence=CarveInfluence*CaveVsOverlay;
            const float FloorInfluence=CaveInfluence*CaveFloorInfluence[Lane];
            const float PassageInfluence=CaveInfluence*CavePassageInfluence[Lane];
            Out[Lane].Distance=SmoothMinDistance(Base[Lane],CarveOrOverlay,StrataCaveBlendRadius);
            Out[Lane].Family=Family;
            Out[Lane].SurfaceSDF=Family==ESurfaceFamily::Strata?Base[Lane]:
                (Family==ESurfaceFamily::Cave?Cave[Lane]:Overlay[Lane]);
            Out[Lane].CaveInfluence=CaveInfluence;
            Out[Lane].FloorInfluence=FloorInfluence;
            Out[Lane].PassageInfluence=PassageInfluence;
            Out[Lane].bFloorSurface=FloorInfluence>=0.5f;
            Out[Lane].bCriticalAir=CriticalAir[Lane];
        }
    }

public:
    void DensityAtLatticeZRun(int32 X,int32 Y,int32 ZStart,int32 ZStep,
                              int32 Count,float* OutDensity) const
    {
        if(SharedDensitySource)
        {
            SharedDensitySource->DensityAtLatticeZRun(X,Y,ZStart,ZStep,Count,OutDensity);
            return;
        }
        if(Count<=0||OutDensity==nullptr)return;
        if(bNativeOnly)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(X,Y,ZStart+Lane*ZStep);
            return;
        }
        bool bHasResolvedBoundaryBand=false;
        for(int32 Lane=0;Lane<Count&&!bHasResolvedBoundaryBand;++Lane)
            bHasResolvedBoundaryBand=IsInsideResolvedStrateBoundaryBand(
                static_cast<float>(ZStart+Lane*ZStep));
        if(bHasResolvedBoundaryBand)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(X,Y,ZStart+Lane*ZStep);
            return;
        }
        bool bHasLegacySurfaceSample=false;
        for(int32 Lane=0;Lane<Count;++Lane)
            bHasLegacySurfaceSample|=UsesLegacySurfaceField(static_cast<float>(X),
                static_cast<float>(Y),static_cast<float>(ZStart+Lane*ZStep));
        if(bHasLegacySurfaceSample)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(X,Y,ZStart+Lane*ZStep);
            return;
        }
        if(!bAnalyticOnly)
        {
            for(int32 Lane=0;Lane<Count;++Lane)
                OutDensity[Lane]=DensityAtLattice(X,Y,ZStart+Lane*ZStep);
            return;
        }

        FDetailNoiseLineContext DetailNoiseLine(
            static_cast<float>(X),static_cast<float>(Y),static_cast<uint32>(Owner->Seed));
        for(int32 Offset=0;Offset<Count;)
        {
            int32 Z[8];
            const int32 Remaining=std::min(8,Count-Offset);
            for(int32 Lane=0;Lane<Remaining;++Lane)
                Z[Lane]=ZStart+(Offset+Lane)*ZStep;
            const int32 BinZ=FloorDiv(Z[0],ActiveSpatialBinSize);
            const auto Found=SpatialBins.find({FloorDiv(X,ActiveSpatialBinSize),
                FloorDiv(Y,ActiveSpatialBinSize),BinZ});
            const FBinItems* BinItems=Found==SpatialBins.end()?nullptr:&Found->second;
            int32 BatchCount=1;
            while(BatchCount<Remaining
                &&FloorDiv(Z[BatchCount],ActiveSpatialBinSize)==BinZ)++BatchCount;

            FEffectiveRockSample Samples[8]{};
            EffectiveRockDistanceZ8(X,Y,Z,BatchCount,BinItems,Samples);
            for(int32 Lane=0;Lane<BatchCount;++Lane)
            {
                const int32 SampleZ=Z[Lane];
                const bool bInsideFine=X>=Min[0]&&X<=Max[0]
                    &&Y>=Min[1]&&Y<=Max[1]&&SampleZ>=Min[2]&&SampleZ<=Max[2];
                float RockDistance=Samples[Lane].Distance;
                if(bInsideFine&&DetailVariant!=EDetailVariant::Smooth
                    &&std::abs(RockDistance)<=DetailSupremum+0.125f)
                {
                    const float Fade=DetailBandFadeAt(static_cast<float>(X),
                        static_cast<float>(Y),static_cast<float>(SampleZ),RockDistance,
                        Samples[Lane].SurfaceSDF,Samples[Lane].CaveInfluence,
                        Samples[Lane].FloorInfluence);
                    if(Fade>0.0f)RockDistance+=DetailNoiseOnLine(static_cast<float>(X),
                        static_cast<float>(Y),static_cast<float>(SampleZ),
                        Samples[Lane].SurfaceSDF,Samples[Lane].CaveInfluence,
                        Samples[Lane].FloorInfluence,Samples[Lane].PassageInfluence,
                        DetailNoiseLine)*Fade;
                }
                if(Samples[Lane].bCriticalAir)
                    RockDistance=std::min(RockDistance,-1.0f/16.0f);
                const bool bRock=RockDistance>=0.0f;
                float Density=-RockDistance;
                if((Density<0.0f)!=bRock||std::abs(Density)<0.05f)
                    Density=(bRock?-1.0f:1.0f)*std::max(std::abs(Density),0.05f);
                OutDensity[Offset+Lane]=ApplyEditBrushes(Density,X,Y,SampleZ);
            }
            Offset+=BatchCount;
        }
    }

    void DensityAtLatticeZ8(int32 X,int32 Y,int32 ZStart,int32 ZStep,
                            int32 Count,float OutDensity[8]) const
    {
        DensityAtLatticeZRun(X,Y,ZStart,ZStep,std::clamp(Count,0,8),OutDensity);
    }

private:

    float CoarseRockDistance(double X,double Y,double Z,bool* OutCriticalAir) const
    {
        const float Base=StrataDistance(Z);
        float Cave=100000.0f,Overlay=-100000.0f;
        bool bCriticalAir=false;
        const FBinKey QueryKey=PointBin(X,Y,Z);
        const auto QueryBin=SpatialBins.find(QueryKey);
        const FBinItems* QueryItems=QueryBin==SpatialBins.end()?nullptr:&QueryBin->second;
        if(QueryItems)
        {
            for(uint32 Id:*QueryItems)
            {
                const FPrimitive& P=Primitives[Id];
                const VF_FieldPrimitive& Shared=SharedFieldPrimitives[Id];
                if(P.bCarve)
                {
                    if(P.bCritical&&X>=P.Min[0]&&X<=P.Max[0]&&Y>=P.Min[1]&&Y<=P.Max[1]
                        &&Z>=P.Min[2]&&Z<=P.Max[2]&&ShapeContains(P,
                            static_cast<int32>(X),static_cast<int32>(Y),static_cast<int32>(Z)))
                        bCriticalAir=true;
                    if(X<P.Min[0]-DetailBand||X>P.Max[0]+DetailBand
                        ||Y<P.Min[1]-DetailBand||Y>P.Max[1]+DetailBand
                        ||Z<P.Min[2]-DetailBand||Z>P.Max[2]+DetailBand)continue;
                    float Distance=VF_FieldPrimitiveDistance(Shared,X,Y,Z);
                    if(P.bHasFloorClip)
                    {
                        const double Floor=VF_FieldPrimitiveFloorAt(Shared,X,Y);
                        Distance=VF_FieldSmoothMax(Distance,static_cast<float>(Floor-Z),
                            static_cast<float>(P.FloorBlendRadius));
                    }
                    Cave=VF_FieldSmoothMin(Cave,Distance,static_cast<float>(P.BlendRadius));
                }
                else if(X>=P.Min[0]&&X<=P.Max[0]&&Y>=P.Min[1]&&Y<=P.Max[1]
                    &&Z>=P.Min[2]&&Z<=P.Max[2])
                    Overlay=std::max(Overlay,-VF_FieldPrimitiveDistance(Shared,X,Y,Z));
            }
        }
        if(OutCriticalAir)*OutCriticalAir=bCriticalAir;
        return VF_FieldSmoothMin(Base,std::max(Cave,Overlay),StrataCaveBlendRadius);
    }

    struct FOwnerNoiseLineContext
    {
        struct FAnchorCache
        {
            const FLayerField* Field=nullptr;
            int32 GridZ0=MIN_int32;
            int32 SampleZ0=MIN_int32,SampleZ1=MIN_int32;
            float LowerCore=0.0f,UpperCore=0.0f;
        } Step8,Step2;
    };

    float OwnerCaveRoughnessCore(double X,double Y,double Z,
                                 const FStrateGenerationParams& Params) const
    {
        // Keep CPU prediction and the near-field HLSL on one scalar source. The helper
        // preserves the legacy seed offsets, octave order, and roughness families.
        return VF_FieldOwnerRoughnessCore(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z),static_cast<uint32>(Owner->Seed),Params.SurfaceRoughness,
            Params.RoughnessFrequency,Params.VerticalScale,Params.DomainWarpStrength,
            Params.DomainWarpFrequency,static_cast<uint32>(Params.RoughnessNoiseType));
    }

    float OwnerCaveRoughness(double X,double Y,double Z,float SurfaceSDF,
                             const FLayerField& Field,float CaveInfluence,
                             FOwnerNoiseLineContext& LineContext,
                             FDetailWorkerProfile* Profile=nullptr,
                             int32 AnchorStep=8) const
    {
        const FStrateGenerationParams& Params=Field.Params;
        const float Depth=Params.SurfaceRoughness*2.0f;
        if(!(Depth>0.0f)||std::abs(SurfaceSDF)>=Depth||!(Params.RoughnessFrequency>0.0f))return 0.0f;
        if(Profile)++Profile->OwnerRoughnessActiveCalls;
        const int32 ZStep=std::max(1,AnchorStep);
        const int32 GridZ0=static_cast<int32>(std::floor(Z/static_cast<double>(ZStep)))*ZStep;
        const int32 SampleZ0=std::max(GridZ0,Field.Lo);
        const int32 SampleZ1=std::min(GridZ0+ZStep,Field.Hi);
        float Total=0.0f;
        if(ZStep==1)
            Total=OwnerCaveRoughnessCore(X,Y,Z,Params);
        else if(SampleZ1>SampleZ0)
        {
            FOwnerNoiseLineContext::FAnchorCache& Cache=ZStep==2
                ?LineContext.Step2:LineContext.Step8;
            const bool bCacheHit=Cache.Field==&Field&&Cache.GridZ0==GridZ0
                &&Cache.SampleZ0==SampleZ0&&Cache.SampleZ1==SampleZ1;
            if(Profile)
            {
                if(bCacheHit)++Profile->OwnerNoiseCacheHits;
                else ++Profile->OwnerNoiseCacheMisses;
            }
            if(!bCacheHit)
            {
                const bool bReusesPreviousUpper=Cache.Field==&Field
                    &&Cache.SampleZ1==SampleZ0;
                Cache.Field=&Field;
                Cache.GridZ0=GridZ0;
                Cache.SampleZ0=SampleZ0;
                Cache.SampleZ1=SampleZ1;
                Cache.LowerCore=bReusesPreviousUpper?Cache.UpperCore
                    :OwnerCaveRoughnessCore(X,Y,SampleZ0,Params);
                Cache.UpperCore=OwnerCaveRoughnessCore(X,Y,SampleZ1,Params);
            }
            const float Alpha=static_cast<float>((Z-SampleZ0)/(SampleZ1-SampleZ0));
            Total=FMath::Lerp(Cache.LowerCore,Cache.UpperCore,Alpha);
        }
        else
            Total=OwnerCaveRoughnessCore(X,Y,Z,Params);
        if(SurfaceSDF<0.0f)
            Total=std::lerp(Total,std::min(Total,0.0f),std::clamp(CaveInfluence,0.0f,1.0f));
        const float Fade=1.0f-std::abs(SurfaceSDF)/Depth;
        return Total*Fade*Fade;
    }

    float OwnerCaveRoughnessForDetail(double X,double Y,double Z,float SurfaceSDF,
                                     const FLayerField& Field,float CaveInfluence,
                                     float PassageInfluence,
                                     FOwnerNoiseLineContext& LineContext,
                                     FDetailWorkerProfile* Profile=nullptr) const
    {
        constexpr float DirectStart=0.40f,DirectEnd=0.60f;
        constexpr int32 PassageAnchorStep=2;
        const float PassageWeight=std::clamp(PassageInfluence,0.0f,1.0f);
        if(PassageWeight>=DirectEnd)
            return OwnerCaveRoughness(X,Y,Z,SurfaceSDF,Field,CaveInfluence,
                LineContext,Profile,PassageAnchorStep);

        const float Anchored=OwnerCaveRoughness(X,Y,Z,SurfaceSDF,Field,
            CaveInfluence,LineContext,Profile);
        if(PassageWeight<=DirectStart)return Anchored;

        const float Direct=OwnerCaveRoughness(X,Y,Z,SurfaceSDF,Field,
            CaveInfluence,LineContext,Profile,PassageAnchorStep);
        const float DirectWeight=SmoothUnit((PassageWeight-DirectStart)
            /(DirectEnd-DirectStart));
        const float AnchoredWeight=1.0f-DirectWeight;
        const float Normalization=1.0f/std::sqrt(
            AnchoredWeight*AnchoredWeight+DirectWeight*DirectWeight);
        return (AnchoredWeight*Anchored+DirectWeight*Direct)*Normalization;
    }

    static float SurfaceRelief(float X,float Y,float Z,uint32 Seed,
                               float* OutPassageBandRelief=nullptr)
    {
        // Keep all active bands at four voxels or wider: the full-detail lattice can
        // resolve them without turning the surface into per-voxel steps. The broad
        // owner comparison showed that the shortest octave needed more usable relief.
        const float Macro=FStandaloneResearchTunnels::ValueNoise(X,Y,Z,32,Seed^0xB5297A4Du);
        const float Mid=FStandaloneResearchTunnels::ValueNoise(X,Y,Z,16,Seed^0x63D83595u);
        const float Fine=FStandaloneResearchTunnels::ValueNoise(X,Y,Z,4,Seed^0xA511E9B3u);
        if(OutPassageBandRelief)
            *OutPassageBandRelief=1.20f*Macro+(0.80f+0.25f*Macro)*(0.40f*Mid);
        return 1.20f*Macro+(0.80f+0.25f*Macro)*(0.40f*Mid+0.60f*Fine);
    }

    struct FValueNoiseLineContext
    {
        int32 X0=0,Y0=0,Z0=std::numeric_limits<int32>::min();
        int32 Wavelength=1;
        uint32 Seed=0;
        float Inv=1.0f,TX=0.0f,TY=0.0f;
        std::array<float,8> Corners{};

        FValueNoiseLineContext(float X,float Y,int32 InWavelength,uint32 InSeed)
            :Wavelength(InWavelength),Seed(InSeed),Inv(1.0f/static_cast<float>(InWavelength))
        {
            const float FX=X*Inv,FY=Y*Inv;
            X0=FMath::FloorToInt(FX);Y0=FMath::FloorToInt(FY);
            TX=FStandaloneResearchTunnels::Fade(FX-static_cast<float>(X0));
            TY=FStandaloneResearchTunnels::Fade(FY-static_cast<float>(Y0));
        }

        void SetPlane(int32 Z,bool bUpper)
        {
            const size_t I=bUpper?4u:0u;
            Corners[I+0]=FStandaloneResearchTunnels::NoiseValue(X0,Y0,Z,Seed);
            Corners[I+1]=FStandaloneResearchTunnels::NoiseValue(X0+1,Y0,Z,Seed);
            Corners[I+2]=FStandaloneResearchTunnels::NoiseValue(X0,Y0+1,Z,Seed);
            Corners[I+3]=FStandaloneResearchTunnels::NoiseValue(X0+1,Y0+1,Z,Seed);
        }

        float Sample(float Z)
        {
            const float FZ=Z*Inv;
            const int32 NewZ0=FMath::FloorToInt(FZ);
            const float TZ=FStandaloneResearchTunnels::Fade(FZ-static_cast<float>(NewZ0));
            if(NewZ0!=Z0)
            {
                if(NewZ0==Z0+1)
                {
                    Corners[0]=Corners[4];Corners[2]=Corners[6];
                    Corners[1]=Corners[5];Corners[3]=Corners[7];
                    SetPlane(NewZ0+1,true);
                }
                else
                {
                    SetPlane(NewZ0,false);SetPlane(NewZ0+1,true);
                }
                Z0=NewZ0;
            }
            const float Z00=FMath::Lerp(Corners[0],Corners[1],TX);
            const float Z10=FMath::Lerp(Corners[2],Corners[3],TX);
            const float Z01=FMath::Lerp(Corners[4],Corners[5],TX);
            const float Z11=FMath::Lerp(Corners[6],Corners[7],TX);
            return FMath::Lerp(FMath::Lerp(Z00,Z10,TY),FMath::Lerp(Z01,Z11,TY),TZ);
        }
    };

    struct FDetailNoiseLineContext
    {
        FValueNoiseLineContext Macro,Mid,Fine;
        FOwnerNoiseLineContext OwnerNoise;
        FDetailNoiseLineContext(float X,float Y,uint32 Seed)
            :Macro(X,Y,32,Seed^0xB5297A4Du),Mid(X,Y,16,Seed^0x63D83595u),
            Fine(X,Y,4,Seed^0xA511E9B3u)
        {}

        float SurfaceReliefAt(float Z,bool bMacroKnown=false,float KnownMacro=0.0f,
                              float* OutPassageBandRelief=nullptr)
        {
            const float MacroValue=bMacroKnown?KnownMacro:Macro.Sample(Z);
            const float MidValue=Mid.Sample(Z);
            const float FineValue=Fine.Sample(Z);
            if(OutPassageBandRelief)
                *OutPassageBandRelief=1.20f*MacroValue
                    +(0.80f+0.25f*MacroValue)*(0.40f*MidValue);
            return 1.20f*MacroValue+(0.80f+0.25f*MacroValue)
                *(0.40f*MidValue+0.60f*FineValue);
        }

    };

    float DetailNoise(double X,double Y,double Z,float SurfaceSDF,
                      float CaveInfluence,float FloorInfluence,float PassageInfluence) const
    {
        if(DetailVariant==EDetailVariant::Smooth)return 0.0f;
        if(DetailVariant==EDetailVariant::PerVoxel)
        {
            const int32 IX=static_cast<int32>(std::floor(X)),IY=static_cast<int32>(std::floor(Y)),IZ=static_cast<int32>(std::floor(Z));
            return FStandaloneResearchTunnels::NoiseValue(IX,IY,IZ,static_cast<uint32>(Owner->Seed))
                *DetailSupremum;
        }
        float PassageBandRelief=0.0f;
        const float Relief=SurfaceRelief(static_cast<float>(X),static_cast<float>(Y),
            static_cast<float>(Z),static_cast<uint32>(Owner->Seed),&PassageBandRelief);
        const float PassageWeight=std::clamp(PassageInfluence,0.0f,1.0f);
        const FLayerField* Field=FindLayerField(Z);
        FOwnerNoiseLineContext OwnerNoise;
        float OwnerRelief=0.0f;
        if(Field)
            OwnerRelief=OwnerCaveRoughnessForDetail(X,Y,Z,SurfaceSDF,*Field,
                CaveInfluence,PassageWeight,OwnerNoise);
        const float Detail=std::clamp(BlendDetailFamilies(Relief,PassageBandRelief,
            OwnerRelief,CaveInfluence,FloorInfluence,PassageWeight),-3.9f,3.9f);
        return Detail;
    }

    float DetailNoiseOnLine(double X,double Y,double Z,float SurfaceSDF,
                            float CaveInfluence,float FloorInfluence,float PassageInfluence,
                            FDetailNoiseLineContext& NoiseLine,
                            FDetailWorkerProfile* Profile=nullptr,
                            const FLayerField* KnownField=nullptr,
                            bool bFieldKnown=false,bool bMacroKnown=false,
                            float KnownMacro=0.0f) const
    {
        if(DetailVariant!=EDetailVariant::Coherent)
            return DetailNoise(X,Y,Z,SurfaceSDF,CaveInfluence,FloorInfluence,PassageInfluence);
        using Clock=std::chrono::steady_clock;
        const auto ReliefStart=Profile?Clock::now():Clock::time_point{};
        float PassageBandRelief=0.0f;
        const float Relief=NoiseLine.SurfaceReliefAt(static_cast<float>(Z),
            bMacroKnown,KnownMacro,&PassageBandRelief);
        if(Profile)
            Profile->ReliefSampleNanoseconds+=static_cast<uint64>(
                std::chrono::duration_cast<std::chrono::nanoseconds>(Clock::now()-ReliefStart).count());
        const auto LookupStart=Profile?Clock::now():Clock::time_point{};
        const FLayerField* Field=bFieldKnown?KnownField:FindLayerField(Z);
        if(Profile)
            Profile->LayerLookupSampleNanoseconds+=static_cast<uint64>(
                std::chrono::duration_cast<std::chrono::nanoseconds>(Clock::now()-LookupStart).count());
        const auto OwnerStart=Profile?Clock::now():Clock::time_point{};
        if(Profile&&Field)++Profile->OwnerRoughnessFieldCalls;
        const float PassageWeight=std::clamp(PassageInfluence,0.0f,1.0f);
        float OwnerRelief=0.0f;
        if(Field)
            OwnerRelief=OwnerCaveRoughnessForDetail(X,Y,Z,SurfaceSDF,*Field,
                CaveInfluence,PassageWeight,NoiseLine.OwnerNoise,Profile);
        if(Profile)
            Profile->OwnerRoughnessSampleNanoseconds+=static_cast<uint64>(
                std::chrono::duration_cast<std::chrono::nanoseconds>(Clock::now()-OwnerStart).count());
        const float Detail=std::clamp(BlendDetailFamilies(Relief,PassageBandRelief,
            OwnerRelief,CaveInfluence,FloorInfluence,PassageWeight),-3.9f,3.9f);
        return Detail;
    }

    bool EvaluateFast(double X,double Y,double Z) const
    {
        ESurfaceFamily SurfaceFamily=ESurfaceFamily::Strata;float SurfaceSDF=100000.0f;
        bool bFloorSurface=false,bCriticalAir=false;float CaveInfluence=0.0f,FloorInfluence=0.0f;
        float PassageInfluence=0.0f;
        float RockDistance=EffectiveRockDistance(X,Y,Z,&SurfaceFamily,&SurfaceSDF,
            &bFloorSurface,&CaveInfluence,&FloorInfluence,&bCriticalAir,nullptr,false,
            &PassageInfluence);
        const bool bInsideFine=X>=Min[0]&&X<=Max[0]&&Y>=Min[1]&&Y<=Max[1]&&Z>=Min[2]&&Z<=Max[2];
        if(bInsideFine&&DetailVariant!=EDetailVariant::Smooth
            &&std::abs(RockDistance)<=DetailSupremum+0.125f)
        {
            const float Fade=DetailBandFadeAt(X,Y,Z,RockDistance,SurfaceSDF,
                CaveInfluence,FloorInfluence);
            if(Fade>0.0f)RockDistance+=DetailNoise(X,Y,Z,SurfaceSDF,CaveInfluence,
                FloorInfluence,PassageInfluence)*Fade;
        }
        if(bCriticalAir)RockDistance=std::min(RockDistance,-1.0f/16.0f);
        return RockDistance>=0.0f;
    }

    bool ValidatePassageRoutes()
    {
        constexpr double SampleStep=0.5;
        uint32 PassageIndex=0;
        for(const FVoxelPassage& P:Owner->Manager->GetPassages())
        {
            const auto& Points=P.ControlPoints;
            if(Points.Num()<2){++PassageIndex;continue;}
            uint64 RouteSamples=0,RouteFailures=0,RouteCritical=0;
            int32 FirstFailure[3]={0,0,0};bool bFirstFailureCritical=false;
            for(int32 I=0;I+1<Points.Num();++I)
            {
                const FVector A=Points[I],B=Points[I+1];
                const double L=std::sqrt((B.X-A.X)*(B.X-A.X)+(B.Y-A.Y)*(B.Y-A.Y)+(B.Z-A.Z)*(B.Z-A.Z));
                const int32 Count=std::max(1,static_cast<int32>(std::ceil(L/SampleStep)));
                uint64 SegmentSamples=0,SegmentFailures=0,SegmentCritical=0;
                for(int32 J=0;J<=Count;++J)
                {
                    const double T=static_cast<double>(J)/Count;
                    const double X=A.X+(B.X-A.X)*T,Y=A.Y+(B.Y-A.Y)*T,Z=A.Z+(B.Z-A.Z)*T;
                    ++Stats.WalkSamples;
                    ++RouteSamples;++SegmentSamples;
                    const int32 VX=static_cast<int32>(std::lround(X));
                    const int32 VY=static_cast<int32>(std::lround(Y));
                    const int32 VZ=static_cast<int32>(std::lround(Z));
                    const bool bCritical=IsInsideCriticalAir(VX,VY,VZ);
                    if(bCritical){++RouteCritical;++SegmentCritical;}
                    if(IsRock(VX,VY,VZ))
                    {
                        ++Stats.WalkFailures;++RouteFailures;++SegmentFailures;
                        if(RouteFailures==1)
                        {FirstFailure[0]=VX;FirstFailure[1]=VY;FirstFailure[2]=VZ;bFirstFailureCritical=bCritical;}
                    }
                }
                if(SegmentFailures)
                    std::fprintf(stderr,"[WalkabilitySegment] passage=%u segment=%d failures=%llu/%llu critical=%llu length=%.2f start=(%.2f,%.2f,%.2f) end=(%.2f,%.2f,%.2f)\n",
                        PassageIndex,I,static_cast<unsigned long long>(SegmentFailures),
                        static_cast<unsigned long long>(SegmentSamples),
                        static_cast<unsigned long long>(SegmentCritical),L,
                        A.X,A.Y,A.Z,B.X,B.Y,B.Z);
            }
            if(RouteFailures)
                std::fprintf(stderr,"[WalkabilityRoute] passage=%u type=%u points=%d failures=%llu/%llu critical_centerline=%llu first_solid=(%d,%d,%d) critical=%u\n",
                    PassageIndex,static_cast<uint32>(P.PassageType),Points.Num(),
                    static_cast<unsigned long long>(RouteFailures),
                    static_cast<unsigned long long>(RouteSamples),
                    static_cast<unsigned long long>(RouteCritical),FirstFailure[0],
                    FirstFailure[1],FirstFailure[2],bFirstFailureCritical?1u:0u);
            ++PassageIndex;
        }
        if(Stats.WalkFailures)
            std::fprintf(stderr,"[Walkability] FAIL %llu/%llu passage centerline samples are solid\n",
                static_cast<unsigned long long>(Stats.WalkFailures),static_cast<unsigned long long>(Stats.WalkSamples));
        else
            std::printf("[Walkability] PASS %llu/%llu passage centerline samples remain open; native landing floors retained\n",
                static_cast<unsigned long long>(Stats.WalkSamples),static_cast<unsigned long long>(Stats.WalkSamples));
        return Stats.WalkFailures==0;
    }

    static double DetailAutocorrelation(EDetailVariant Variant)
    {
        constexpr int32 N=24;double Sum=0.0,SumSq=0.0,PairA=0.0,PairB=0.0,PairAA=0.0,PairBB=0.0,PairAB=0.0;uint64 Count=0;
        auto Value=[&](int32 X,int32 Y,int32 Z)->double
        {
            if(Variant==EDetailVariant::PerVoxel)return FStandaloneResearchTunnels::NoiseValue(X,Y,Z,11);
            if(Variant==EDetailVariant::Smooth)return 0.0;
            return SurfaceRelief(static_cast<float>(X),static_cast<float>(Y),static_cast<float>(Z),11);
        };
        for(int32 Z=0;Z<N;++Z)for(int32 Y=0;Y<N;++Y)for(int32 X=0;X<N;++X)
        {const double V=Value(X,Y,Z);Sum+=V;SumSq+=V*V;}
        const double Mean=Sum/(N*N*N),Variance=SumSq/(N*N*N)-Mean*Mean;
        if(Variance<1.0e-9)return 1.0;
        for(int32 Z=0;Z<N;++Z)for(int32 Y=0;Y<N;++Y)for(int32 X=0;X+1<N;++X)
        {
            const double A=Value(X,Y,Z)-Mean,B=Value(X+1,Y,Z)-Mean;
            PairAA+=A*A;PairBB+=B*B;PairAB+=A*B;++Count;
        }
        return Count?PairAB/std::sqrt(std::max(1.0e-12,PairAA*PairBB)):0.0;
    }

    template<class Fn> void ParallelLines(size_t Count,Fn&& Work,FParallelTiming* Timing=nullptr,
        std::array<double,16>* WorkerActiveSeconds=nullptr,size_t WorkBatch=1) const
    {
        const auto WallStart=std::chrono::steady_clock::now();
        if(WorkerCount<=1||Count<512||!Scheduler)
        {
            const auto WorkerStart=std::chrono::steady_clock::now();
            for(size_t I=0;I<Count;++I)
            {
                if constexpr(std::is_invocable_v<Fn&,size_t,int32>)Work(I,0);
                else Work(I);
            }
            if(WorkerActiveSeconds)
                (*WorkerActiveSeconds)[0]=std::chrono::duration<double>(
                    std::chrono::steady_clock::now()-WorkerStart).count();
            if(Timing)
            {
                const double WorkerSeconds=std::chrono::duration<double>(std::chrono::steady_clock::now()-WorkerStart).count();
                Timing->WallSeconds+=std::chrono::duration<double>(std::chrono::steady_clock::now()-WallStart).count();
                Timing->WorkerSeconds+=WorkerSeconds;
            }
            return;
        }
        WorkBatch=std::max<size_t>(WorkBatch,1);
        using WorkType=std::remove_reference_t<Fn>;
        struct FDispatchContext { WorkType* Work; } Dispatch{&Work};
        const auto Invoke=[](void* Opaque,size_t Index,size_t Worker)
        {
            auto& Context=*static_cast<FDispatchContext*>(Opaque);
            if constexpr(std::is_invocable_v<WorkType&,size_t,int32>)
                (*Context.Work)(Index,static_cast<int32>(Worker));
            else
                (*Context.Work)(Index);
        };
        std::array<double,16> ActiveSeconds{};
        const double WorkerSeconds=Scheduler->parallel_for(Count,WorkBatch,
            static_cast<size_t>(WorkerCount),&Dispatch,Invoke,ActiveSeconds.data(),ActiveSeconds.size());
        if(WorkerActiveSeconds)*WorkerActiveSeconds=ActiveSeconds;
        if(Timing)
        {
            Timing->WallSeconds+=std::chrono::duration<double>(std::chrono::steady_clock::now()-WallStart).count();
            Timing->WorkerSeconds+=WorkerSeconds;
        }
    }

    void InvalidateFarFieldGpuInput()
    {
        std::lock_guard<std::mutex> Lock(FarFieldGpuInputMutex);
        CachedFarFieldGpuInput.reset();
    }

    FStandaloneOwnerWorld* Owner=nullptr;
    const VoxelForgeCore::WorldAssemblyManifest* WorldAssembly=nullptr;
    const FStandaloneShapeWorld* SharedDensitySource=nullptr;
    int32 WorkerCount=6;
    const VoxelForgeCore::JobScheduler* Scheduler=nullptr;
    bool RoundTunnelsEnabled=false;
    bool bProfileDetailBand=false;
    int32 Min[3]{},Max[3]{},ClipMin[3]{},ClipMax[3]{},Size[3]{};
    FIntVector EditBoundsMin=FIntVector(MAX_int32,MAX_int32,MAX_int32);
    FIntVector EditBoundsMax=FIntVector(MIN_int32,MIN_int32,MIN_int32);
    int32 ActiveSpatialBinSize=LineBinSize;
    double ActiveBlendRadius=0.0;
    double ActiveFloorBlendRadius=0.0;
    size_t WordsPerZ=0;
    EDetailVariant DetailVariant=EDetailVariant::Coherent;
    bool Built=false;
    bool bNativeOnly=false;
    bool bUseNativeManifestFields=false;
    float BoundManagerLayoutChunkWidthVoxels=0.0f;
    FIntVector NativeOnlyMinimum=FIntVector::ZeroValue;
    FIntVector NativeOnlyMaximum=FIntVector::ZeroValue;
    mutable std::atomic<uint32> NativeOnlyViolations{0};
    bool FarBuilt=false;
    std::vector<std::array<double,2>> ResolvedBoundaryZIntervalsMicrometres;
    std::vector<FBoundStratumField> BoundStratumFields;
    std::vector<FInterval> LayerRanges;
    std::vector<FLayerField> LayerFields;
    std::vector<FPrimitive> Primitives;
    std::vector<VF_FieldPrimitive> SharedFieldPrimitives;
    std::vector<FFarConnectorSegment> FarConnectorSegments;
    std::unordered_map<FBinKey,std::vector<uint32>,FBinHash> FarConnectorSpatialBins;
    std::vector<FEditBrush> EditBrushes;
    std::vector<FStandalonePassageVoidCrossing> PassageVoidCrossings;
    std::array<FAxisBins,3> AxisBins;
    std::unordered_map<FBinKey,FBinItems,FBinHash> SpatialBins;
    std::unordered_map<FBinKey,FBinItems,FBinHash> CriticalAirBins;
    mutable std::mutex FarFieldGpuInputMutex;
    mutable std::shared_ptr<const VoxelForgeCore::FarFieldWorldInput> CachedFarFieldGpuInput;
    std::vector<uint64> RockWords;
    std::unique_ptr<int16[]> SurfaceDistanceQ;
    std::array<std::vector<uint64>,3> CandidateAxisWords;
    std::vector<uint64> CandidateWords;
    std::vector<uint64> GpuVisualDetailWords,CpuVisualDetailWords;
    uint64 GpuVisualDetailTileCount=0,CpuVisualDetailTileCount=0;
    uint64 GpuVisualDetailGridSamples=0,CpuVisualDetailGridSamples=0;
    uint64 GpuVisualDetailNodeCount=0,CpuVisualDetailNodeCount=0;
    FBuildStats Stats;
    bool bAnalyticOnly=false;
    inline static thread_local const FScopedPassageTileQueries* ActivePassageTileQueries=nullptr;
    std::vector<FStampSpatialBound> StampSpatialBounds;
    std::vector<FStampSpatialNode> StampSpatialNodes;
    std::vector<std::uint32_t> StampSpatialOrder;
    std::vector<FStampRuntime> StampRuntime;
    std::vector<FCavernRuntimeFeature> CavernRuntime;
    std::vector<VoxelForgeCore::WorldAssemblyFeatureBoundsV1> PassageFeatureBounds;
    std::vector<FPassageTileFeature> PassageTileFeatures;
    std::vector<std::uint32_t> PassageFeatureOrder;
    std::vector<FPassageFeatureNode> PassageFeatureNodes;
    bool PassageFeatureBoundsFailOpen=false;
    std::vector<std::vector<FPassageNearestNode>> PassageNearestNodes;
    std::vector<FPassageProofBound> PassageProofBounds;
    std::vector<FPassageProofNode> PassageProofNodes;
    std::vector<std::vector<std::uint8_t>> PassageColumnSegmentFlags,PassageShortSpanSegmentFlags;
    std::vector<std::uint8_t> PassageHasShortSpanFlags;
};