← NS-INRS / DCRP58 · Cylindrical Transparent-Tail Elimination and Outer Closure

NS-INRS · DCRP58 Gap Closure 2026-08

DCRP58: Cylindrical Transparent-Tail Elimination and Outer Closure

Building on DCRP57's result, which excluded only the straight cylinder and left the twisted-cylinder and affine-hinge routes unclosed, this round closes both out using DCRP30/Xue's DSS periodic-average velocity-energy sublinear bound E(R)=O(R^κ) (κ=3−2α∈(0,1)). For the general representation of a fixed-plane transparent tail, it proves: if the transverse affine vorticity offset β≠0, a dual-curl test gives E(CR)≳R², contradicting the sublinear bound, so β≡0 must hold; in the pure cylindrical-shear case, a nonzero constant slope likewise violates the sublinear bound, so f_r≡0. Altogether, divdiv(Ω⊗Ω)=0 combined with a fixed plane and the sublinear energy bound forces Ω=0, ruling out every fixed-plane transparent tail — straight, twisted, or affine-hinged — entirely. STOP-D58 therefore declares the rank-two zero-residual visibility-compensation branch globally closed, handed to a later residual-branch confluence round (DCRP59, not included in this folder) for further treatment.

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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