THE PRIZE LANDED. At production defaults: 6 of 40 tiles proved AllSolid, 7986
voxels brute-forced, 0 violations. 15% of tiles skip GenerateMesh entirely, one
BuildChunkCache traded against 30000+ density evaluations each, and not one
verdict is asserted -- every voxel was re-evaluated and came back on the claimed
side. The dense fixture still reports 0, exactly as the arithmetic said it must,
so this is a measurement of production rather than of a widened test.
The breakdown finally isolated the tunnels: of 34 unproved tiles, 32 were
blocked by a tunnel and 21 by a room, so >=13 were tunnel-only. That is what
justified the deferred disjunction, and why it was deferred rather than guessed.
A primitive no longer matters if it misses its cull OR its own SDF stays >= T+K
over the box. Each branch wins on a different class, by calculation: for rooms
the cull (Rmax+3K) is tighter than the threshold (Rmax+T+K), so rooms keep the
cull alone; for tunnels the cull is a capsule BOUNDING SPHERE, radius ~107 for a
200-long tube of radius 7, against a true segment distance. Order of magnitude.
The bound is exact, not cautious. TaperedCapsule was read, not assumed --
Dist(P, ClosestOnSegment) - Lerp(Ra,Rb,t) -- so SDF >= dist(P,segment) -
max(Ra,Rb); and dist(box,segment) >= dist(centre,segment) - half-diagonal by
triangle inequality. VF_DistPointSegment is written locally rather than taken
from FMath: five lines, and "I think that function does that" is not good enough
under a correctness bound.
Identity CHANGED MEANING, from "Sdf stays FLT_MAX" to "Sdf >= T" with
T = max(3*SDFBlendRadius, WormNetworkRange). Sound only because all three
consumers of the SDF channel were read one by one: FSdfConvertOp's Blend is
MakeSdfCarve(P.SDFBlendRadius, ...) => K; the twelve modifiers gate at 3K;
FWormFieldSource at WormNetworkRange. Plus the one that could have bitten --
FCaveTerraceMod re-probes the SDF at Z+-1, OUTSIDE the box, but its gate is line
13 and the probes are lines 28-29, so a gate false everywhere never emits one.
ANY NEW CONSUMER OF THE Sdf CHANNEL MUST HAVE A THRESHOLD <= T OR JOIN THAT MAX,
or it gets tiles with no geometry and no collision. Written at the site.
Why -K suffices for any N: SmoothMin's penalty is exactly zero once |A-B| >= K,
so the running minimum saturates at K below the smallest term and cannot descend
further. Sdf >= min_i(SDF_i) - K for ANY number of primitives, not - N*K/6 --
without which the slack would scale with the ~88 tunnels and be worthless.
Unbuilt.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Fr0zka
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