← Lebesgue Universal Covering Problem / II · Computation and Reproduction / Round 21 · Two-Lobe Phase-Lock

Lebesgue Universal Covering Problem II · Computation and Reproduction Round 21 · Two-Lobe Phase-Lock 懸衡 (Xuán Héng) PARTIAL UNMEASURED PASS

Round 21: the tail atlas rebuilds box by box, and every box closes with exact cores; the synthesis search values sit below the true minima

PASS for the atlas as computed, the phase lock and the two lobes, the ridge's two channels, the finite-tail optimism theorem and the legal 7-fold family; PARTIAL for the atlas as a tail of B7 — with exact cores it is empty — and for every synthesis comparison, whose search values sit 3–6×10⁻⁶ below the true minima; UNMEASURED for the irregular and symmetry-breaking candidates, which the package does not record.

PARTIAL · UNMEASURED · PASS This page is the second layer: the finite claims of the layer-1 document "Round 21 · Two-Lobe Phase-Lock" 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 21 · Two-Lobe Phase-Lock · B7's Deep Tail Becomes a Two-Lobe Phase-Locked Atlas, and the Regular Heptagon Still Wins Out Under a Counterexample-Guided Cutting-Plane Loop: The Finite-Tail Optimism Theorem Proves Why Tail-Fitting Is Always Overoptimistic
PreviousRound 20 · First Counterexample · II · Computation and Reproduction
NextRound 22 · Fourier Pareto Search · II · Computation and Reproduction

Recompute reports · Runs

RUN-024Round 21: the tail atlas rebuilds box by box, and every box closes with exact cores; the synthesis search values sit below the true minima

Verdict: PASS for the atlas as computed, the phase lock and the two lobes, the ridge's two channels, the finite-tail optimism theorem and the legal 7-fold family; PARTIAL for the atlas as a tail of B7 — with exact cores it is empty — and for every synthesis comparison, whose search values sit 3–6×10⁻⁶ below the true minima; UNMEASURED for the irregular and symmetry-breaking candidates, which the package does not record.

The report, the code and the gate log: report RUN-024.md · run024_round21_lift_tail_synthesis.py · gate log run024-round21-lift-tail-synthesis.json

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