← WSFC: Worm Sequence Freedom Closure / WSFC R04 early draft · Finite-segment convexity and obstacle reduction (superseded)

WSFC: Worm Sequence Freedom Closure WSFC R04 early draft · Finite-segment convexity and obstacle reduction (superseded) Neo.K / Aletheia

Finite-Segment Convexity Gate, Endpoint-Disc Obstacle Reduction and the Support-Cell Allocation Calculus

Imports finite-M convexity and endpoint-strip reduction from Adhikari–Pitman 1989, recasts the problem as a convex endpoint-disc obstacle problem, proves strict convexity (diminishing returns) of the support-cell cost g(q, Δ) = 2q·tan(Δ/2q), and proves in the reduced obstacle model that even n has a centred apex and balanced allocation. Odd n is only enumerated up to n = 20, and the top plateau is numerical.

R04 proves a symmetric allocation for even n inside a reduced obstacle model; the conclusion is limited to that model and is not a global result. The paper says plainly that this is a 'reduced-model theorem'. This is an early draft of R04, superseded by the 'Support-Class Necessity I' written later in the same round (next page); the two different documents share the document code WSFC-R04-v0.1.

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PreviousWSFC R03 · Antipodal support-tangent compression · Antipodal Support-Tangent Compression: From 2n − 2 Vertex Degrees of Freedom to Low-Dimensional Sequences and the Continuum Limit of the Broadworm
NextWSFC R04 canonical · Support-Class Necessity I · Support-Class Necessity I: Convexity, Endpoint Antipodes, and Balanced Segment Allocation

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

Editor's note: this is an early draft of R04, superseded by the 'Support-Class Necessity I' written later in the same round (next page), and kept as a research record. The reasons (checked here): the two documents are not byte-identical; the BSP-A/B/C vocabulary that R05 opens with appears only in 'Support-Class Necessity I' and in R05, not in this draft; and inside the R04 package zip this draft is timestamped about 18 minutes earlier than 'Support-Class Necessity I' (17:28:14 versus 17:46:08, the packager's local clock, supporting evidence only). The recovery bundle of 2026-10-07 reached the same decision.

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