← NS-X72 / X72-45 · Visibility-Replicator Dynamics

NS-X72 · X72-45 Continuation 2026-08

X72-45: Visibility-Replicator Dynamics

Picks up Round 44's proof that neither static divdiv geometry nor actual quadratic vorticity realizability can eliminate the first-order transfer between visible and invisible stress (STOP-C48). This round stops the static attack and studies directly the exact dynamics of the visibility ratio η_ω=‖W_L‖_2²/(‖W_L‖_2²+‖W_T‖_2²), splitting it into four terms: stretching selection, Laplacian scale selection, gradient-stress selection, and the conservative Riesz transfer. Proves that a pure sector is stationary at first order but generically receives cross-sector injection at second order — so no universal visibility-evolution direction exists (universal visibility direction is false) — while an exact periodic Beltrami purely-invisible invariant branch also exists; a bounded Piola defect under quartic growth can force η_ω→0. STOP-C49 (Visibility Replicator/Boundary-Injection Compatibility Gap) hands the problem to the next round's analysis of invisible-escape boundary-injection depletion.

This round's status: Continuation — Taken from the file's own objective/executive-result section, meaning preserved, not a full verbatim translation.

Connections

Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.

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