DCRP69/X72R52: Cofactor Phase-Lock Normal Form

Continuing from DCRP68's proof of 'mandatory cofactor-shape activity', this round further asks whether that activity can be algebraically cancelled by the pressure and vorticity terms and phase-locked. First, the full similarity Euler strain equation is reduced to the identity D_sS+S+E_p+¼W_Ω=0, in which all quadratic strain self-amplification terms and the isotropic pressure term cancel exactly; on the aligned branch this yields the exact material evolution equation for the cofactor C, together with the exact angular-rate equation for the normalized cofactor direction Ĉ. It classifies the unique exact phase-lock equality mode, which requires the strain frame and the non-axisymmetric shape ratio c=d/λ to be materially frozen, and uniquely determines E_p=-(1+λ'/λ)S-¼W_Ω, together with a strict pointwise defect lower bound — leaving DCRP70 to test whether this forced local pressure tensor can be globally integrated into a pressure Hessian.