← NS-INRS / DCRP73/X72R56 · Cylinder Mosaic Absorbed into the Turnover Branch

NS-INRS · DCRP73/X72R56 Gap Closure 2026-08

DCRP73/X72R56: Cylinder Mosaic Absorbed into the Turnover Branch

Continuing from DCRP72's reduction of the critical transparent tail to a multi-axis mosaic of straight cylinders, this round proves that the mosaic is not an independent third branch: from the axial local velocity-invariance already proved in D72, the stretching term within every active sector of the mosaic is identically zero, and the similarity vorticity equation reduces to D_sΩ=-Ω, so vorticity decays exponentially as e^{-s} along material paths with fixed direction; the corresponding enstrophy density satisfies D_s e_ω+2e_ω=0 and, after the similarity-volume correction, decays as e^{-(2-3γ)s}. Consequently, a finite material-sector cycle cannot recur periodically without replenishment — a periodic cylindrical state must carry a strictly positive inward enstrophy/material-replacement budget, which is exactly the defining feature of the existing T turnover branch. The conclusion is that the critical-cylinder-mosaic endpoint is fully absorbed into T, restoring the native global frontier to the 'active X vs. material turnover' dichotomy, and leaving DCRP74 to jointly analyze enstrophy turnover and PFET on the same finite annulus.

This round's status: Gap Closure — Taken from the file's own Executive result / STOP node, meaning preserved, not a full verbatim translation. The original paper itself was authored directly in English; only this page's own commentary (title, status, and summary) is translated here.

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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