← WSFC: Worm Sequence Freedom Closure / WSFC R23 · Strict monotonicity (conditional)

WSFC: Worm Sequence Freedom Closure WSFC R23 · Strict monotonicity (conditional) Neo.K / Aletheia

Strict Monotonicity: Tangent-Gap Refinement and the Last Half of 2007 Conjecture (5)

A tangent-gap refinement lemma (bisecting a tangent gap shortens the breadth-one chain by exactly 4u³/(1 − u²), u = tan(δ/4)), together with the exact base t₃ < 7/16 < t₄, gives t_n < t_{n+1} for the true stage optimizer, conditional on 'G0-lite'.

Conditional on G0-lite, the breadth sequence t_n is strictly increasing (the second half of 2007 conjecture (5)). A conditional research proof. The status is 'CONDITIONAL ON G0-LITE / FORMAL AUTHORITY OPEN'. The gain identity is elementary and was checked here as correct. This document originally existed in the folder only as a copy inside the Round-28 pack; on 2026-10-07 the original R23 package was recovered, and its main document is byte-identical to that copy. The package's verifier script was re-run here and passes (it only checks symbolic algebra and a root count for one quartic polynomial, not a formal proof).

Connections · Connections

PreviousWSFC R22 · Full-domain coverage and uniform convergence · G1 Full-Domain Coverage: Exact-Length Tent Approximation, Uniform Cover Modulus and Broadworm Value Closure

NextWSFC R24 · Finite-stage uniqueness (conditional) · Finite-Stage Uniqueness: Strict Convexity, Integer Balancing and Mirror-Class Rigidity

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.

Loading…