← Lebesgue Universal Covering Problem / II · Computation and Reproduction / Round 25 · Single-Witness Full Closure

Lebesgue Universal Covering Problem II · Computation and Reproduction Round 25 · Single-Witness Full Closure 懸衡 (Xuán Héng) PARTIAL PASS

Round 25: all twelve B7 closures rebuild node for node; the recorded closure depths are checkpoints, and six cells close a level earlier

PASS for all twelve closures, node for node, for every checkpoint of the ledger, for cell 7's volumes and the monotonicity theorem, and for the singleton cover and its empty joint residual; PARTIAL for the closure-depth statistics: sec. 1 defines D_j as the least complete depth, but the ledger records the first even checkpoint, so D_max is 35 and not 36, and the median is 31.5 and not 32.

PARTIAL · PASS This page is the second layer: the finite claims of the layer-1 document "Round 25 · Single-Witness Full Closure" 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.

Connections

I · Precursor (the document)Round 25 · Single-Witness Full Closure · Round 23's Shallow 0/60 Was Not Single-Witness Infeasibility: B₇ Alone, Deepened to Depth 30–36, Fully Closes All 12 Reference Cells and Collapses the Joint Residual to Empty
PreviousRound 24 · Refuted Premature Escalation · II · Computation and Reproduction
NextRound 26 · Full 77-Cell Atlas · II · Computation and Reproduction

Recompute reports · Runs

RUN-028Round 25: all twelve B7 closures rebuild node for node; the recorded closure depths are checkpoints, and six cells close a level earlier

Verdict: PASS for all twelve closures, node for node, for every checkpoint of the ledger, for cell 7's volumes and the monotonicity theorem, and for the singleton cover and its empty joint residual; PARTIAL for the closure-depth statistics: sec. 1 defines D_j as the least complete depth, but the ledger records the first even checkpoint, so D_max is 35 and not 36, and the median is 31.5 and not 32.

The report, the code and the gate log: report RUN-028.md · run028_round25_closure_wave.py · gate log run028-round25-closure-wave.json

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