← NS-INRS / 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.
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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