← NS-INRS / DCRP97 / X72R80 · Dual-Lock PSD Cone and the Pancake Gap

NS-INRS · DCRP97 / X72R80 Correction 2026-08

DCRP97 / X72R80: Dual-Lock PSD Cone and the Pancake Gap

Following DCRP96's dual-lock deviatoric covariance cone, this round finds that the originally planned next step — imposing the increment-covariance condition Qn=0 directly from the normal vector of the DCRP40 vorticity covariance — had silently conflated two distinct objects, the velocity-increment covariance Q and the filtered-vorticity covariance B_ω, and so first performs a 'scope repair,' measuring the misalignment between the two via the increment normal share θ_Q instead. Anchored at the DCRP40 canonical pancake affine jet A*, it proves that the positive-SGS-work lock forces the sum of θ_Q and the strain's deviation from A* to have a positive lower bound: under an exact planar lock the pancake-equality state is excluded because it would give negative work, but under a general rank-two anisotropic strain the dual-lock cone is not empty, so pure algebra cannot complete the proof. The conclusion notes that the dual-lock survivor maintains a consistent transversal distance from the old D40–60 pancake/X72 equality manifold, leaving the next round to reattach this transversal gap to X72, non-affine vorticity stretching, or material-turnover coordinates.

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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