← Lebesgue Universal Covering Problem / II · Computation and Reproduction / Round 22 · Fourier Pareto Search

Lebesgue Universal Covering Problem II · Computation and Reproduction Round 22 · Fourier Pareto Search 懸衡 (Xuán Héng) FAIL PARTIAL PASS

Round 22: the legality rules and the lift pilot rebuild exactly; with dense cores the Pareto map's volume axis inverts, and the "cheap" harmonics cannot close their cell

PASS for the legality rules, the full-orientation rule and its example, the recorded multi-mode candidate and its verdict, and the lift pilot as computed; PARTIAL for the search minima of B7 and of the harmonics, which sit on both sides of the true ones; FAIL for the proof-cost Pareto map's volume axis — with dense cores the ranking inverts, and the two "cheap" witnesses cannot close the cell at all.

FAIL · PARTIAL · PASS This page is the second layer: the finite claims of the layer-1 document "Round 22 · Fourier Pareto Search" 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 22 · Fourier Pareto Search · Multi-Mode Fourier Legality Compiler and Full-Orientation Oracle Rule Both Close, Yet No New Witness Beats B7: This Round Pivots to a Proof-Cost Pareto Map and a Witness Portfolio
PreviousRound 21 · Two-Lobe Phase-Lock · II · Computation and Reproduction
NextRound 23 · Strict Cover Scores Zero · II · Computation and Reproduction

Recompute reports · Runs

RUN-025Round 22: the legality rules and the lift pilot rebuild exactly; with dense cores the Pareto map's volume axis inverts, and the "cheap" harmonics cannot close their cell

Verdict: PASS for the legality rules, the full-orientation rule and its example, the recorded multi-mode candidate and its verdict, and the lift pilot as computed; PARTIAL for the search minima of B7 and of the harmonics, which sit on both sides of the true ones; FAIL for the proof-cost Pareto map's volume axis — with dense cores the ranking inverts, and the two "cheap" witnesses cannot close the cell at all.

The report, the code and the gate log: report RUN-025.md · run025_round22_fourier_pareto.py · gate log run025-round22-fourier-pareto.json

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