DCRP70/X72R53: Double-Integrability Rigidity and Straight-Tube Energy NO-GO

Continuing from the unique local phase-lock algebraic mode found in DCRP69 (strain frame and shape ratio c materially frozen, H_P uniquely specified), this round tests whether that state can simultaneously satisfy the first-order-jet versions of velocity-gradient integrability L=∇V and pressure-Hessian integrability H_P=∇²P. An exact solution shows that double integrability freezes the physical vorticity direction pointwise; incompressibility then forces any globally persistent phase-lock component to correspond to a single entire straight vortex tube, and the curl–energy duality relation gives a local energy growth of at least linear order, E(R)≳R. This directly contradicts the sub-linear tail growth E(R)=O(R^κ) (κ<1) required by DCRP30 / the strict-DSS tail, so the global phase-lock equality branch is closed — proving that it can only terminate in active X72 dynamics or material turnover — leaving DCRP71 to handle the finite cofactor-angle jump.