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NS-INRS · DCRP71/X72R54 Correction 2026-08

DCRP71/X72R54: Endpoint Energy Audit and Critical Twisting Residue

This round conducts a scope audit of the 'endpoint' of DCRP61-70, distinguishing the project-native, unconditionally valid time-sliced Morrey bound ∫_{B_R}|V|²≤CM₀R from the Xue-type DSS sub-linear tail R^{3-2α}, which requires an additional global-integrability hypothesis (conditionally valid only for 1<α<3/2). It points out that earlier exclusion results relying only on R^{3-2α}=o(R) must all be flagged as conditional, unless they can be repaired using the native Morrey bound instead. This round repairs and strengthens several existing results on that basis: it proves that the phase-lock tube actually forces cubic energy growth E(R)≳R³, which the native Morrey bound alone excludes without needing the Xue exponent (a stronger result than DCRP70), and likewise natively excludes both a flat pressure source and a globally straight cylindrical tail. After the audit, the only residue that cannot be natively excluded is the 'critical twisting transparent cylinder', which can exactly saturate the linear Morrey bound; the native frontier is reset to a three-way case — 'active X72, material turnover, or critical-twisting cylindrical tail' — leaving DCRP72 to handle that cylinder endpoint.

This round's status: Correction — 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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