# Linux 74 — legacy uniform tile proofs

## Ceiling

Full-grid signs were counted per camera observation. “Visited / sampled” separates tiles with no captured density grid; those are not counted as uniform. Block columns are the fraction of captured samples belonging to sign-uniform, disjoint cubes. Partial edge cubes are included. Repeated tile keys in different camera contexts are separate observations. Strate labels are SW=SurfaceWorld, FI=FloatingIslands, TN=TunnelNetwork, VS=VerticalShafts. Unlisted stratum/LOD pairs had no observations.

| Strate | LOD | Visited / sampled | Uniform tiles / sampled (%); % visited | Samples in uniform 8³ | Samples in uniform 4³ |
|---|---:|---:|---:|---:|---:|
| SW | 0 | 512 / 147 | 35 / 147 (23.81%); 6.84% | 79.74% | 90.77% |
| SW | 1 | 448 / 448 | 317 / 448 (70.76%); 70.76% | 94.33% | 97.36% |
| SW | 2 | 448 / 448 | 391 / 448 (87.28%); 87.28% | 92.78% | 97.01% |
| SW | 3 | 320 / 320 | 270 / 320 (84.38%); 84.38% | 93.65% | 96.76% |
| SW | 4 | 432 / 432 | 48 / 432 (11.11%); 11.11% | 70.51% | 85.37% |
| SW | 5 | 288 / 288 | 0 / 288 (0%); 0% | 75.44% | 82.46% |
| SW | 6 | 192 / 192 | 0 / 192 (0%); 0% | 42.11% | 63.16% |
| FI | 0 | 512 / 287 | 132 / 287 (45.99%); 25.78% | 89.41% | 95.24% |
| FI | 1 | 432 / 432 | 339 / 432 (78.47%); 78.47% | 96.73% | 98.55% |
| FI | 2 | 272 / 272 | 237 / 272 (87.13%); 87.13% | 95.99% | 98.35% |
| FI | 3 | 384 / 384 | 243 / 384 (63.28%); 63.28% | 90.33% | 95.70% |
| FI | 4 | 192 / 192 | 56 / 192 (29.17%); 29.17% | 82.44% | 92.62% |
| FI | 5 | 144 / 144 | 0 / 144 (0%); 0% | 61.03% | 84.63% |
| FI | 7 | 192 / 192 | 0 / 192 (0%); 0% | 0% | 53.04% |
| TN | 0 | 576 / 266 | 146 / 266 (54.89%); 25.35% | 92.07% | 96.07% |
| TN | 1 | 640 / 640 | 524 / 640 (81.88%); 81.88% | 97.49% | 98.88% |
| TN | 2 | 416 / 416 | 250 / 416 (60.10%); 60.10% | 92.03% | 97.15% |
| TN | 3 | 240 / 240 | 60 / 240 (25.00%); 25.00% | 73.52% | 88.85% |
| TN | 4 | 144 / 144 | 36 / 144 (25.00%); 25.00% | 81.70% | 88.85% |
| TN | 6 | 192 / 192 | 0 / 192 (0%); 0% | 25.98% | 57.46% |
| VS | 0 | 448 / 226 | 117 / 226 (51.77%); 26.12% | 90.25% | 95.42% |
| VS | 1 | 272 / 272 | 218 / 272 (80.15%); 80.15% | 97.05% | 98.66% |
| VS | 2 | 272 / 272 | 171 / 272 (62.87%); 62.87% | 92.39% | 97.29% |
| VS | 3 | 160 / 160 | 20 / 160 (12.50%); 12.50% | 67.72% | 84.82% |
| VS | 4 | 96 / 96 | 0 / 96 (0%); 0% | 40.22% | 88.00% |
| VS | 5 | 144 / 144 | 0 / 144 (0%); 0% | 29.12% | 56.92% |

The 8³/4³ ceiling is high, but legacy sub-tile proofs did not survive the falsifier. The safe implementation below uses whole-tile skips only for legacy fields.

## Method and falsifier

`ShapeWorldInternal.h` now marks a legacy tile skippable only when the compiled analytic stratum interval stays beyond the detail envelope (and smooth-min slack for solid), with no intersecting primitive, edit, native field, composer candidate, passage, or active boundary transition. Unbounded or mixed cases fail closed. The shared stream layer uses this proof for FI/TN/VS whole tiles. Legacy block early-outs remain off; native block early-outs remain native-only.

The full-grid `--stream-hash` reference and `--stream-hash-tiles-allow-skips` candidate matched all per-tile mesh, payload, and topology hashes for all four views on Clang and GCC: 16 matrix comparisons, no missing/extra tile keys, zero geometry mismatches. Processed density hashes also matched. Tile counts were SW 2,850, FI 2,249, TN 2,233, VS 2,329. The W1/W8/W12 matrix added 32 exact comparisons with zero mismatches.

The deliberately tight control omits the primitive/composer and detail envelope. It was caught in every view: changed mesh tiles SW 3, FI 184, TN 233, VS 238. The initial detail-only control was not caught; the control was strengthened before accepting the proof.

### 20-position sweep

Each stratum had 20 passing camera positions. `classifier ms` is aggregate tile-worker time per view (p50 / p95). Every reference/skip pair matched exact geometry hashes; violations: 0.

| Strate | Proof hits / tile visits | Hit rate | Classifier ms p50 / p95 |
|---|---:|---:|---:|
| SW | 13,594 / 57,000 | 23.85% | 566.399 / 587.473 |
| FI | 9,786 / 44,980 | 21.76% | 3.728 / 4.086 |
| TN | 11,472 / 44,660 | 25.69% | 2.004 / 2.222 |
| VS | 10,328 / 46,580 | 22.17% | 0.875 / 0.919 |

## Whole-view timing

Three interleaved clean pairs per view, eight workers. Values are median whole-view readiness seconds, before L73 / after L74.

| Strate | Before | After | Change |
|---|---:|---:|---:|
| SW | 2.613 | 2.479 | -5.13% |
| FI | 7.178 | 5.052 | -29.62% |
| TN | 5.970 | 4.633 | -22.40% |
| VS | 2.702 | 2.397 | -11.29% |

`verify.py fast` passed in 277.0 s (269 passes, five diagnostics); owner passage, transition, and worker gates stayed green. All benchmark and verification processes were wrapped with `taskset -c 0-11 prlimit --as=6442450944`. No Unreal build was needed because root `Source/` did not change.

## Identity and failed runs

- Branch / HEAD: `assembler/world` / `bd1b2a8f1d6c97dfabd90b1ee15aece9fcff0aa3`.
- Owner manifest: `bcc0d0d33ea39435`; resolved layout: `resolved-layout-v3-fnv64:0589300eb07dfe06`.
- Owner recipe evaluator: 4; resolved layout schema: 3; `WorldAssemblyEvaluatorVersion`: 213. No mesh or topology version bump: all generated geometry hashes match the full-grid reference.
- Source stamp: `93cd38dc2fb4a6a22b86d8c690ec6074d6eb070898e109f3bc2cb2490476d464`. Clang binary SHA256: `975d65c32ce26573aad3b0ede6a0985dfa2851a516d731842cd0eac25bdccc8b`; GCC: `ad2a936ad310e1e1c28b37b71d9d355f6fb30e9f1bf99ae0b80985b0cd713408`.
- The corrected legacy full-grid path changes only raw density hash rows versus the L70 FI fixture (whole view and LOD2); mesh, payload, and topology rows remain equal. The L70 fixture is preserved; fast verification now pins the L74 full-grid signature separately.
- Two exploratory legacy block proofs failed in one TN tile at sample `(-80,-20,-3218)` (exact density `+0.063384`); legacy sub-tile skips were disabled. A broad negative camera offset failed the passage gate before generation, so the final sweep stayed within passing camera positions. The first fast run detected the density-signature drift above; after adding the separate L74 full-grid fixture, fast passed.

No commit, push, or stash was made. Exploratory and final logs are in `Saved/Linux/l74/logs/`.