feat(maze): a spanning tree -- it is a maze now, not a grid

Jahni: "mostly a cube full of straight pathway along the edges... basically
just a repeating pattern of tunnel connecting to each other, definitely
unwanted". And the measurement: the arrival mouth in a 30-cell pocket while
the network held 1,217. SAME CAUSE -- edge selection was independent hash
gating per +X/+Y/+Z edge, i.e. a random subgraph of the cubic lattice.
Every junction identical, and connectivity left to chance.

Fixed the way VerticalShafts was fixed in 7a20eee: guarantee it by
construction. Each non-origin node hashes ONE parent axis toward
(0,0,0) so Manhattan distance strictly decreases -- a proof of a global
rooted tree, not a probability. Loops are capped at 0.18 x
BranchProbability and 0.10 x Verticality and can never supply connectivity.
⛔ No edge probability was raised; percolation is a phase transition, not a
knob.

  64 seeds x 9,261 nodes:  0 disconnected cells, 0 edge-count violations
  determinism:             20,000 bit-identical checks
  seam freedom:            42 probes, 0 legacy and 0 op-stack mismatches

⭐ AND IT READS AS A MAZE, in numbers rather than adjectives:

  degree   1 (dead ends)  15.9%      mean degree 2.504
  degree   2              36.6%      run length median 1, p90 3, max 18
  degree   3              31.7%
  cubic-grid control:     100% degree-6, 0% dead ends, mean 6.000

Two abreast, derived not nudged: 3 m usable floor / 0.7 = 4.286 m clear
bore, + roughness reach 3.75 voxels => CorridorRadius 12.5 (6.25 m bore),
giving 3.06 m of usable floor. CellSize 64 still leaves a 7.875 m wall
between neighbouring bores.

BranchProbability and Verticality are now LOOP-DETAIL knobs, not
connectivity controls. Documented at their declarations so nobody tunes
them expecting the old meaning.

⚠️ The player-fit law still fails, and Codex named the likely reason in its
caveats: "global tree connectivity does not guarantee connectivity inside
an arbitrary finite cropped measurement window." The tree routes toward the
ORIGIN, and the fitted window is the AABB of the two mouths -- so the
connecting path runs A -> origin -> B and leaves the box. The coarse maze
graph now measures Connected while the fine windowed law does not. That
smells like the sixth measurement artifact of this session, and it is the
next thing to test rather than to assume.

Box audits: existing maze 104 proved / 0 violations; novel fill stack 240
proved / 319,440 voxels / 0 violations. Op-stack bit-identical over 20,000
samples. Perf 1.13 us rebuild, 0.145 us hot call.

Showcase regenerated. Build clean, 32 tests, 30 clean successes, 2 known
deliberate warnings, 0 failed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01K8V9my1PL68pmQb2gutZZV

COMPOSER-NOTES.md

@@ -392,6 +392,9 @@ covers each archetype plus the shared passage/disturbance and optional transport
 The requested maze test was run first on the same seed/index and a mouth-fitted step-1 ROI. The
 radius is the tunnel radius; the bore is twice the radius:
 
+This is the **pre-spanning-tree radius sweep**. It remains useful as historical evidence about
+mouth/fine-resolution behaviour, but it is not a connectivity result for the new topology.
+
 | Corridor radius | Bore | Player-fit fraction | Traversable share | Minimum clearance | Arrival→departure |
 |----------------:|-----:|--------------------:|------------------:|------------------:|-------------------|
 | 4 vox / 1.00 m | 2.00 m | 0.009007 | 0.078358 | 1 voxel / 0.25 m | NotConnected |
@@ -406,16 +409,20 @@ failure is not explained by the nominal tunnel diameter alone: the generated fie
 floor/cap interaction, and/or resolution still need separate diagnosis.
 
 The new defaults use separate derivations: rooms are 8-20 m diameters with a 24 m origin hub and
-32 m cells; round passages are 3-4 m bores; Maze is a 16 m cell with a 4 m bore; slabs reserve a
-22.4 m floor-to-ceiling span; shaft diameters are 4-7 m with 3 m connectors; islands are 12-24 m
-diameters on 28 m cells; ordinary passages are 3-4 m bores and reach 8-24 m. `RoomSpacing` keeps
-the largest room 6 m radially clear of the next cell, `CorridorRadius` is 8/32 = 0.25 of Maze half-cell,
-and `StrateHeightInChunks` grows from 4 to 8 because 17 m tall rooms, 20 m terrain relief,
-vertical shafts, and a high cap do not share a comfortable 32 m envelope. No global multiplier was
-used. The roughness reach is `1.875 × roughness` voxels: the new default ratios are
-**0.625** (minimum tunnel), **0.469** (Maze), **0.469/0.625** (shaft/connector), **0.234** island
-radius (**0.484** including blend), **0.625/0.938** slab column for floor/ceiling, and **0.047**
-against SurfaceWorld's 80-voxel relief scale.
+32 m cells; round passages are 3-4 m bores; Maze is a 16 m cell with a 6.25 m nominal bore;
+slabs reserve a 22.4 m floor-to-ceiling span; shaft diameters are 4-7 m with 3 m connectors;
+islands are 12-24 m diameters on 28 m cells; ordinary passages are 3-4 m bores and reach 8-24 m.
+`RoomSpacing` keeps the largest room 6 m radially clear of the next cell. For Maze, the target is
+3 m of usable two-abreast floor: `3 / 0.7 = 4.286 m` clear diameter, or an 8.571-voxel clear
+radius; adding the proven 3.75-voxel roughness reach gives 12.321 voxels, rounded to
+`CorridorRadius=12.5`. Thus the worst-case usable floor is
+`0.7 × 2 × (12.5−3.75) × 0.25 = 3.0625 m`, and the roughness ratio is `3.75/12.5 = 0.300`.
+The 64-voxel cell leaves `64−2×(12.5+3.75)=31.5` voxels (7.875 m) of worst-case wall
+between neighbouring bores. `StrateHeightInChunks` grows from 4 to 8 because 17 m tall rooms,
+20 m terrain relief, and a high cap do not share a comfortable 32 m envelope. No global multiplier
+was used. The other default ratios remain **0.625** (minimum tunnel), **0.469/0.625**
+(shaft/connector), **0.234** island radius (**0.484** including blend), **0.625/0.938** slab
+column for floor/ceiling, and **0.047** against SurfaceWorld's 80-voxel relief scale.
 
 The architecture sanity check uses [Epic's Unreal level-blockout guidance](https://dev.epicgames.com/documentation/en-us/unreal-engine/designer-01-project-setup-and-level-blockout-in-unreal-engine) (player-sized reference, 2-3 m halls and 3-4 m heights as starting guidance), the [2010 ADA Standards](https://www.ada.gov/law-and-regs/design-standards/2010-stds/) (915 mm clear walking width and larger passing/turning spaces), and [NPS Lehman Cave dimensions](https://www.nps.gov/grba/learn/nature/lehman-caves-dimensions.htm) (real chambers ranging from passages to 20 m-plus vertical volumes). These are sanity anchors, not claims that one universal ratio makes a good cave.
 
@@ -713,7 +720,7 @@ checks that question rather than assuming it.
 | Tunnel reach | Neighboring-room horizontal jitter can be `1.7S` in each axis, hence `1.7S√2`; vertical center separation can be `2*R*RoomHeightRatio`. Derive `MaxTunnelLength` as at least the Euclidean sum of those bounds. This matches the generator’s distance gate. | `VoxelCaveMorphology.cpp:1388` and `:1502` reject out-of-reach links; implemented/validated at `VoxelStrateComposer.cpp:1557-1564` and `:3114-3121`. |
 | Room vertical fit | `BoundarySealThickness + max(MaxRoomRadius,OriginRoomRadius)*RoomHeightRatio < H/2`, because room centers are restricted to the seal-free interval and the room Z radius is `Radius*RoomHeightRatio`. | `VoxelCaveMorphology.cpp:137-140` and `:248-250` establish the room/seal buffer; validated at `VoxelStrateComposer.cpp:3106-3112`. |
 | Slab floor/ceiling | Worst floor is `H*FloorRelativeHeight + 1.25*FloorRoughness`; worst ceiling is `H*CeilingRelativeHeight - 1.25*CeilingRoughness`. Derive both relative heights from seal + clearance and require a two-voxel void. | `VoxelCaveMorphology.cpp:329-362` and `VoxelGenerator.cpp:2175-2212`; implemented/validated at `VoxelStrateComposer.cpp:1602-1626` and `:3143-3185`. |
-| Maze corridor | Derive `CorridorRadius = CellSize*(0.12..0.24)` so it leaves lattice wall; cap roughness below `CorridorRadius+2` so the centerline remains carveable. | `VoxelCaveMorphology.cpp:428-458` bounds the lattice; `VoxelGenerator.cpp:2412-2432` applies roughness and subtracts `2*BaseDensity`; implemented/validated at `VoxelStrateComposer.cpp:1629-1642` and `:3188-3216`. |
+| Maze corridor | For a 25 cm voxel, derive `3/0.7 = 4.286 m` clear diameter for two-abreast floor, hence an 8.571-voxel clear radius. Add the proven `SurfaceRoughness*VOXEL_NOISE_SCALE*1.5 = 3.75` voxels and round to `CorridorRadius=12.5`; require `CellSize=64` so the worst-case bore gap remains `64−2*(12.5+3.75)=31.5` voxels. | `VoxelCaveMorphology.cpp` bounds the lattice and applies the roughness-safe landing; `VoxelGenerator.cpp` applies roughness and subtracts `2*BaseDensity`; implemented/validated at `VoxelStrateComposer.cpp:1629-1642` and `:3188-3216`. |
 | Surface ground/cap and height features | The structural height is bounded by `ElevationRange*(1+MountainStrength)+2*1.25*SurfaceRoughness`. Add conservative budgets for cliff displacement (`CliffStrength*CliffSharpness` times that spread), terrace step, layer depth, and beach width. Derive `BaseGroundRelative` above the bottom seal and `CeilingRelative` below the top seal with cap roughness, undulation, ridge, overhang height, and two-voxel headroom. Cliff is sampled as a scalar and reduced only when this derived height budget cannot contain it. | `VoxelGenerator.cpp:2470-2517` is the structural height equation; `:2537-2557` is the cliff remap; `:2607-2654` is the cap; `:2670-2686` caps overhang height. Implemented/validated at `VoxelStrateComposer.cpp:1645-1724` and `:3219-3269`. |
 | Vertical shafts and ledges | Require `ShaftMaxRadius≤ShaftSpacing/2`; require `ShaftMinRadius > 1.5*1.25*SurfaceRoughness + 0.25`; derive `ConnectorRadius > 1.5*1.25*SurfaceRoughness + 1`; derive ledge spacing greater than `2*(LedgeDepth + floor-clearance)`. | `VoxelCaveMorphology.cpp:628-654` moves landings out of roughness/ledge bands; `VoxelGenerator.cpp:3944-3954` derives tree roughness reach and `:4209-4214` applies ledges; implemented/validated at `VoxelStrateComposer.cpp:1730-1755` and `:3272-3310`. |
 | Floating islands | Require `IslandMaxRadius≤IslandSpacing/2`; derive island radius and thickness so `BoundarySealThickness + max(0.2R,ThicknessRatio*R) < H/2`; require the minimum radius to exceed roughness plus SDF blend. | `VoxelCaveMorphology.cpp:852-935` computes island radius, underside, warp, and blend pad; `VoxelGenerator.cpp:4268-4344` starts with void and fills the island; implemented/validated at `VoxelStrateComposer.cpp:1757-1780` and `:3313-3355`. |
@@ -963,7 +970,7 @@ cave design
 (https://store.steampowered.com/news/posts/?appgroupname=Deep+Rock+Galactic&appids=548430&enddate=1729500950&feed=steam_community_announcements),
 and Team Cherry map design (https://www.pcgamer.com/how-to-design-a-great-metroidvania-map/).
 
-#### Final post-scale measurement (2026-09-05)
+#### Historical post-scale measurement before the Maze spanning-tree correction (2026-09-05)
 
 The new defaults are applied in `VoxelStrateTypes.h`; the production definition, season defaults, and
 the owner-facing showcase use `StrateHeightInChunks=8` (64 m). The bounded test fixture remains at
@@ -1027,8 +1034,10 @@ The default derivations are not a global multiplier:
 * FlatPlain/CrystalChamber: floor `0.25×256=64 vox=16 m`, ceiling `0.60×256=153.6 vox=38.4 m`,
   leaving `22.4 m` before roughness. Columns are `8..16 vox` radii (4-8 m diameters) on 96-voxel
   (24 m) cells. The two names intentionally retain the same slab generator and parameter block.
-* Maze: `CellSize=64 vox=16 m`; `CorridorRadius=8 vox=2 m`, hence a 4 m bore; the corridor radius
-  is `8/32=0.25` of the half-cell, leaving a 6 m centre-to-wall radial margin before other geometry.
+* Maze: `CellSize=64 vox=16 m`; `CorridorRadius=12.5 vox=3.125 m`, hence a 6.25 m nominal bore.
+  The 3.75-voxel proven roughness reach leaves an 8.75-voxel effective radius and
+  `0.7×(2×8.75×0.25)=3.0625 m` of usable floor; the worst-case neighbouring-bore wall is
+  `64−2×16.25=31.5 vox=7.875 m`.
 * SurfaceWorld: `ElevationRange=80 vox=20 m`, base ground `0.25×256=16 m`, warp `48 vox=12 m`,
   sky cap `0.95×256=243.2 vox=60.8 m`; terrace/layer/beach/overhang values are separately
   2 m / 2 m / 3 m / 4 m reach + 6 m height optional features.
@@ -1669,6 +1678,75 @@ passed; the full `VoxelForge` namespace finished with **29 successes, 2 known wa
 0 not-run** in 2,388.35 s. The warnings remain the gated lateral-region 9/16 law and the known
 TunnelNetwork op-stack outside-gate sample count; box violations stayed zero.
 
+### 12.2 2026-09-06 Maze spanning-tree correction
+
+The Maze lattice no longer uses independent per-edge hash gating. Each non-origin cell chooses one
+parent from the non-zero coordinate axes and steps one unit toward the origin. The parent reduces
+`|x|+|y|+|z|` by exactly one, so the undirected parent edges form one infinite rooted tree: no cycle
+can exist, and following parents reaches `(0,0,0)` from every cell. A canonical lower node plus
+axis edge is emitted when either endpoint selects the other. Optional loop edges use capped hash
+rolls (`0.18 × BranchProbability` horizontally and `0.10 × Verticality` vertically); they add
+visual choice without carrying the connectivity guarantee.
+
+This is locally computable. The evaluator's exact window is the eight lower nodes in
+`{-1,0}³` (a 2×2×2 node window); the adjacent `+1` endpoint is one of the two endpoints of each
+canonical edge, so its parent decision is still inside that same bounded window. The source and
+op-stack cache use the identical predicate. No wide collect was needed, and no parent decision
+depends on the stored window or chunk origin. `WorldRadiusVoxels` remains `0`; lateral regions
+remain gated off.
+
+The focused topology audit sampled **64 seeds** over a centred radius-10 graph (**9,261 cells per
+seed**). With loops disabled, every graph had exactly `N−1` parent edges and **0 edge-count or
+disconnected-cell violations**. With default loop settings, disconnected cells were also **0**.
+The default sample added **103,297** optional loop edges in total. Repeating the same seed produced
+bit-identical edge keys across **20,000** checks.
+
+The output is measurably unlike the old cubic grid. Across **216,000 interior cells** and all
+64 seeds, the degree distribution was `d0=0, d1=34,371 (15.9%), d2=79,046, d3=68,545,
+d4=27,965, d5=5,531, d6=542`, with mean degree **2.504**. Maximal degree-2 corridor runs were
+`n=464,360`, minimum **1**, median **1**, p90 **3**, maximum **18**. The cubic-grid control was
+`d6=100%`, `d1=0%`, mean **6.000**. The tree therefore supplies real dead ends, varied runs,
+and non-uniform junctions even before the optional loops are considered.
+
+The seam test `VoxelForge.Generation.MazeSeamFreedom` passed **42/42 boundary probes** with
+**0 legacy mismatches and 0 operator mismatches**. It explicitly records the 2×2×2 local window
+and “no wide collect” contract.
+
+The player-fit law is still not connected, and was not tuned toward. The pre-tree baseline at the
+same style of fine measurement was **5,759 fit cells / 82 components / largest 1,217 / arrival 30 /
+departure 1,217 / gap 121.598 voxels**, `NotConnectedAtThisResolution`. The new spanning-tree
+showcase candidate (seed `0`, candidate `57`) measured **2,453 / 72 / 473 / arrival 100 /
+departure 415 / gap 149.730 voxels**, also `NotConnectedAtThisResolution`; its coarse lattice
+verdict was `Connected`. This separates the proven corridor-graph law from the remaining physical
+player-fit problem: the gap is at the passage mouths/fine floor-resolution interaction (and must
+not be “fixed” by raising edge probability), not evidence that the lattice graph is probabilistically
+fragmented. The other archetypes retain their own independent fit findings.
+
+The 3 m two-abreast radius derivation is explicit: `3/0.7 = 4.286 m` clear diameter, or an
+8.571-voxel clear radius at 0.25 m/voxel. Add the proven roughness reach
+`2×1.25×1.5 = 3.75 voxels`, giving 12.321 voxels; round up to `CorridorRadius=12.5`.
+The effective floor diameter is `2×(12.5−3.75)×0.25 = 4.375 m`, so usable floor is
+`0.7×4.375 = 3.0625 m`. With `CellSize=64`, worst-case neighbouring-bore wall is
+`64−2×(12.5+3.75)=31.5 voxels = 7.875 m`.
+
+Box audits stayed sound after adding guaranteed air: the existing Maze box audit proved **104
+uniform boxes**, classified **152 Mixed**, sampled **138,424 voxels**, and found **0 violations**;
+the novel fill audit covered **240 boxes** (`0 AllSolid`, `240 AllAir`) plus **16 Mixed** cases,
+**319,440 voxels**, and **0 violations**. The focused audit measured **1.436 μs** per forced cache
+rebuild and **0.150 μs/call** for 20,000 hot evaluations; the final namespace run measured
+**1.130 μs** and **0.145 μs/call**, respectively, on the validation machine. Parent/loop work stays
+in the thread-local rebuild.
+
+The regenerated owner-facing artifact is
+`E:/Projet Unreal/VoxelM/Saved/VoxelForge/Showcase/index.html`; the selected Maze card is
+`candidate_1003_plan.png` (with matching `candidate_1003_vertical.png` and fine ROI variants).
+The post-fix showcase rendered **6 fine views**, refused **2**, and produced **0 blank** cards.
+
+The final full namespace verification is `Saved/AutomationReports/VoxelForgeFullMazeTreeFinal3/index.json`:
+**32 tests, 30 clean successes, 2 warning-bearing successes, 0 failures, 0 not-run** in **2,523.978 s**.
+The two warnings are the pre-existing gated lateral-region result and the known TunnelNetwork
+outside-gate sample count; neither is a Maze or box-soundness failure.
+
 ### ⚠️ Correct the record: commit `1ab8c0c` overstated what worked
 It reported *"3 checked, 48/48 ring samples air"* and read as Tier 1 working. A million-seed sweep later
 showed the room query left the landing point **OUTSIDE the selected room 92.795% of the time**. The