Fourier Curvature Function Spaces, Adjoint Sensitivity, and Non-Convex Container Reduction

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.

“The support function records only the convex hull; a non-convex container must also record: concavities, narrow channels, local gaps, and the complementary interlocking between tubular boundaries. Hence: convex support redundancy is not the same as non-convex container redundancy. Round 1's finite-width family is already redundant in the convex problem, but still makes a nonzero contribution in the non-convex container's leave-one-out analysis.” — from Section 9, “Structural Assessment,” of this package's main document.

Round 4 Core Content

The definition of the Fourier curvature function space, dimension progression (6→8→10 modes), the curvature box and chirality audit for the Fourier-10 candidate, spectrum and sensitivity (amplitude does not imply tension sensitivity), derivation of the adjoint gradient, the convex finite-family container, the non-convex finite-family container (a 37.31% reduction), structural assessment, honest bounds, and the next milestone (the alternating adversarial system).

Method · Method

Parametrization of the curvature function space, the three-tier search layering, convex/non-convex container formulas, and the list of verification layers.

Curvature Function—Support Function Adjoint Sensitivity

The complete derivation of the adjoint gradient (curvature normalization, centerline variation, support function variation), and numerical cross-checking (finite differences vs. the adjoint gradient).

Non-Convex Container Reduction

The non-convex union area of the seven test families, hole-filling, the 37.31% reduction relative to the convex container, and a family-by-family leave-one-out analysis.

Files · Files

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