← NS-INRS / 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.
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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