Universal Support Tension Comparison among Constant Curvature, Archimedean, Contact-Saturated, and Finite-Width Curvature Stratum

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 contact-saturated spiral reaches max κ≈25, but accounts for only about 1.46% of the active directions. The finite-width curvature stratum has lower maximum curvature, yet dominates more than half the directions…the finite-width distribution of curvature and the global support configuration matter more than a single maximum curvature.” — from Section 6, “First Major Finding,” of this package's main document.

Method · Method

The fixed parameters (L, ρ, τ), precise definitions of the four curve families, the common convex container surrogate, and the definition of leave-one-out support tension.

Round 1 Core Content

A comparison table for the four curve families, the area of the common convex thickened container, the leave-one-out support tension table, the distribution of active support directions, three major findings, feedback to the “Measure-Conserving Skew-Line Fiber—Universal Covering Tension Theory,” honest boundaries, and the next-round node.

Files · Files

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