← WSFC: Worm Sequence Freedom Closure / WSFC R24 · Finite-stage uniqueness (conditional)

WSFC: Worm Sequence Freedom Closure WSFC R24 · Finite-stage uniqueness (conditional) Neo.K / Aletheia

Finite-Stage Uniqueness: Strict Convexity, Integer Balancing and Mirror-Class Rigidity

Two strict-convexity engines (J_d(q, a) in (q, a); K_q(d, a) in (d, a)) plus strict Jensen give a unique reduced optimizer up to Euclidean isometry (even n: symmetric; odd n: one orientation plus its mirror); lifting this to the full finite-stage problem holds only conditional on G0.

The optimizer is unique inside the reduced class; lifting to the full problem needs G0. A conditional research proof. The headline 'conjecture (1) research-proof-level provisionally closed' carries 'conditional on G0' in the same sentence; formal and independent review are open. (R25 later says a conversational shorthand b_n = d_n* from R24 was wrong; the R24 file itself does not contain it.)

Connections · Connections

PreviousWSFC R23 · Strict monotonicity (conditional) · Strict Monotonicity: Tangent-Gap Refinement and the Last Half of 2007 Conjecture (5)

NextWSFC R25–R26 · Endpoint-distance strictness and the elasticity kernel · Endpoint-Distance Strictness Reframed and Elasticity Kernel Closure: Dual Comparative Statics, the Unit-Length Elasticity Gap, and a Computer-Assisted K > 0

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.

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