Normal Injectivity Theorem, Curvature Bounding Boxes, Clarke Boundary Ledger, and the New Dual-Frequency Log-Curvature Skeleton

Connections · Connections

Relationship to other packages, stated as far as possible in the document's own words, not my interpretation. This case's theoretical foundation is in From the Original Kakeya Needle to Moser's Worm.

“If the radius of curvature R(v)≥R₀, the signed distance where two normal lines meet satisfies t+u≥2R₀. So it is impossible to have both |t|<R₀ and |u|<R₀ at once. What this theorem proves is the global injectivity of the direct bidirectional normal band; it does not automatically complete a proof of global reach for the circular end caps.” — from the full text of this package's Normal Injectivity Theorem.

Round 3 Core Content

A summary of the Normal Injectivity Theorem, curvature bounding boxes, the Clarke Boundary Ledger, the definition and coefficients of the new dual-frequency log-curvature family, Round 3's final dual-skeleton, verification that all the old families are redundant, area advancement, honest boundaries, and the milestone for Round 4 (moving to B-spline/Fourier curvature function spaces).

Half-Turn Positive Curvature Normal Injectivity Theorem

A standalone theorem statement and proof in full — to date, the only document in this case that is an analytic proof rather than a numerical candidate.

Method · Method

Parametrization of the curvature function, the search-and-verification pipeline, and the five-layer certificate architecture (analytic normal injectivity, outward floating-point curvature boxes, discrete normal-intersection replay, end-cap buffer audit, and projected Clarke secant boxes).

Files · Files

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