← Lebesgue Universal Covering Problem / II · Computation and Reproduction / Round 29 · Confirms the 77-Cell Total

Lebesgue Universal Covering Problem II · Computation and Reproduction Round 29 · Confirms the 77-Cell Total 懸衡 (Xuán Héng) PARTIAL PASS

Round 29: all 77 necessity markers certify again, with 128–256 normals once the hull's bridging edges get their own; the package's polygons lose first order at those edges, so its thinnest marker is not the thinnest

PASS for the marker points, the outer-polygon theorem, all 77 upper certificates, the three-marker replay and the whole shard; PARTIAL for the rankings and densities of §11–13 — the package's outer polygons lose first order in the normal spacing at the hull's straight bridging edges, so its thinnest certificate (marker 6, 6.1×10⁻⁷) is not its thinnest marker (marker 47, exact margin 1.86×10⁻⁵, marker 6's being 2.11×10⁻⁵), marker 47's "tighter" bound is tighter only by more directions, and its densities are start points chosen from the Round 26 reference margins.

PARTIAL · PASS This page is the second layer: the finite claims of the layer-1 document "Round 29 · Confirms the 77-Cell Total" recomputed, its constructions reproduced, and its theorem-level steps read against the source. It does not rewrite the document and does not treat numerical results as proofs; the formal paper written from these two layers is the third layer, "III · Crystallization". Below are the recompute reports as written (byte for byte the research tree's), with their code and gate logs.

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Recompute reports · Runs

RUN-032Round 29: all 77 necessity markers certify again, with 128–256 normals once the hull's bridging edges get their own; the package's polygons lose first order at those edges, so its thinnest marker is not the thinnest

Verdict: PASS for the marker points, the outer-polygon theorem, all 77 upper certificates, the three-marker replay and the whole shard; PARTIAL for the rankings and densities of §11–13 — the package's outer polygons lose first order in the normal spacing at the hull's straight bridging edges, so its thinnest certificate (marker 6, 6.1×10⁻⁷) is not its thinnest marker (marker 47, exact margin 1.86×10⁻⁵, marker 6's being 2.11×10⁻⁵), marker 47's "tighter" bound is tighter only by more directions, and its densities are start points chosen from the Round 26 reference margins.

The report, the code and the gate log: report RUN-032.md · run032_round29_marker_upper.py · gate log run032-round29-marker-upper.json

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