Phase Jumps, the Dual Contact-Pressure Ledger, and Topology-Guided Curve Search

Connections · Connections

Relationship to other packages, stated as far as possible in the document's own words, not my interpretation.

“Because the curve is covered up to congruence as long as either chirality fits… s₊>1 therefore does not refute the Wetzel covering result; the mirror branch can still fit.” — excerpted from this package's chirality-correction report, explaining why an apparently record-breaking candidate is not actually a counterexample.

Core Content of Round 2

The dual contact-pressure ledger, the full phase-sweep table, structural analysis of the phase jumps, the topology-guided three-link search, the contact-pressure ledger of the best candidate, this round's assessment, and the design of the next round's contact-ledger reverse generator.

Chirality Correction

Finds that the original three-link search considered only the orientation-preserving version, missing the convention in the Wetzel paper that permits reflection; defines the congruence difficulty s_cong = min(s₊,s₋) and the chirality skew χ, re-searches to obtain a more robust candidate, and establishes the rule that “the two theoretical branches must remain permanently separated.”

Exact Three-Normal Re-Verification Appendix

The Wetzel triangle is the intersection of three half-planes, so the exact minimal scale can be computed via a closed-form vertex formula, without angular discretization approximation. Re-verification finds that the grid approximation did indeed underestimate the scale; an exact re-search yields a three-segment polyline approaching the certified scale of 1.

Files · Files

sha256 4375eba4e285a87c400383914dadf8fe3a5ef8327583674f1434e409b1a2fd40