← NS-INRS / DCRP67 / X72R50 · Aligned Two-Stress Spectral Geometry and Axisymmetric Self-Locking Modes

NS-INRS · DCRP67 / X72R50 Continuation 2026-08

DCRP67 / X72R50: Aligned Two-Stress Spectral Geometry and Axisymmetric Self-Locking Modes

Building on DCRP66's reduction of the silent X branch to the 4:1 correlation balance Q_Cω=4Q_CC between the cofactor and the vorticity stress, this round works out the pointwise aligned spectral geometry underlying that balance: it proves every aligned traceless strain tensor has a unique spectral form S=(3λ/2)U_ξ+dH, determined solely by one transverse-anisotropy scalar d and the frame angle, and derives a 'pointwise co-axiality theorem.' The analysis shows only two zero-spin axisymmetric spectra (Type A and Type B) allow the cofactor to avoid intrinsic tensor spin, and for both the cofactor amplitude is frozen; X72's silence is thereby reduced to an exact orthogonality condition between 'the necessary spatial rotation of the cofactor's principal axis' and 'the necessary variation of the vorticity amplitude,' which is handed to DCRP68 to test the integrability of these two modes.

This round's status: Continuation — 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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