Finite-Width Curvature Layer, a Smooth Candidate's Surpassing Result, and Dual-Path Support Cross-Checks

Connections · Connections

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

“The real result is the discovery that the five-link polyline platform can be slightly surpassed by a finite-width smooth curvature layer. This result has been cross-checked through multi-resolution and dense-point-cloud support checks, but arbitrary-precision and interval-certificate confirmation are still pending.” — from Section 12, “Conclusion,” of this package's main document.

Round 8 Core Content

The original problem, the event control, four-branch contour continuation (a nine-width scan), a narrow peak scan (best tested width ε*=0.037), the four control branches, the multi-resolution audit, the independent dense-point-cloud support path, the curvature ledger, the research verdict, what cannot yet be claimed, the direction for Round 9, and the conclusion.

Round 8 Finite-Width Surpassing Review

Nine widths re-reviewed using four-branch epigraph contours; the best width is ε*=0.04, flagged as “candidate breakthrough, pending independent verification.”

Round 8 Dense Point-Cloud Cross-Check

An independent method that does not use tangent–normal stationary-point inversion, computing directly over 240017 points, supporting that the finite-width positive gain is not an artifact of a single implementation.

Round 8 Peak-Candidate Dense Point-Cloud Cross-Check

An independent point-cloud review of the peak candidate ε=0.037, incorporating the exact special phases 120° and 270° directly into the global comparison; the discrepancy between methods is only -2.997602166488e-14.

Files · Files

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