wip(assembler): round S13 -- tile cost counted per LOD (diagnostics only, no output change)

Exclusive per-stage tile timers and probes. Findings: LOD0 is MC-exclusive
(10.4 of 14 ms p95, 243 ns/sample); LOD4's 3x cost is column-cache misses
(8,224 vs ~1,600-1,900 at LOD3/5), cap refine secondary; per-tile feature lists
cost ~0.001 ms; cross-worker column repeats common (277k at LOD0). Global octave
drop and stride-2 interpolation probes fail the 2 cm gate. Worker cap 1 kept
(cap 0 worse 40 m/s tick tail). Report: Standalone/Research/WorldAssemblerM3/Round17.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MmSoF64BbRFmk9C3p1VsBJ

ARCHITECTURE.md

@@ -1756,6 +1756,28 @@ near and `BackgroundNormal` for horizon tasks. The task-pickup changes do not al
 triangulation, collision, or Core output, so no recipe version changes.
 See [`Standalone/Research/WorldAssemblerM3/Round16/REPORT.md`](Standalone/Research/WorldAssemblerM3/Round16/REPORT.md).
 
+### 8.34 Tile cost and column reuse audit — World Assembler S13 / M3 Round 17
+
+The owner SurfaceWorld uses 32 marching-cubes cells only at LOD0–1; LOD2 and farther use 16
+coarse cells. Including the normal halo, those are 35³ and 19³ density samples, respectively.
+Round 17 added exclusive timing for classification, column evaluations during MC/ground/cap,
+non-column MC/refinement work, and mesh assembly. Percentiles are independent. The measured
+owner route is a planar `Heightfield2D` surface: its recipe noise is evaluated while computing XY
+columns, with no volumetric cave, tunnel, room, or route density term. The two-tile interpolation
+probe reduced measured column-compute time by about 71–74% at stride two, but exceeded the 2 cm error gate at
+LOD1 and every tested coarse LOD; stride four also exceeded it on LOD0. It had no near-zero fallback
+and was not enabled in generation.
+
+LOD4 is the first far-cap refinement level: its cap grid is 16 voxels (4 m), while LOD5–7 use the
+128-voxel boundary grid (32 m); ground refinement begins at LOD5. LOD4's cap pass costs about
+4.87 ms of column evaluation plus 1.26 ms exclusive at the eight-tile p95, but its largest measured
+cost is 29.36 ms of column evaluation during MC. LOD4 also has 8,224 column-cache misses per sampled
+tile p95 versus 1,634 at LOD3 and 1,916 at LOD5. The cache remains thread-local. The all-LOD overlap
+probe found substantial cross-worker duplicate XY evaluations, which is evidence for a future
+shared-page A/B test, not proof that a shared cache will pay after synchronization and lifetime
+costs. Round 17 changed no density, mesh, collision, or recipe output; recipe versions remain
+unchanged. See [`Standalone/Research/WorldAssemblerM3/Round17/REPORT.md`](Standalone/Research/WorldAssemblerM3/Round17/REPORT.md).
+
 ## 9. Multiplayer model (listen-server first, dedicated-friendly)
 
 > **Status: transport is DESIGN ONLY — nothing is networked in-tree yet** (no `Replicated`/`HasAuthority`/RPCs; a