← NS-INRS / DCRP52 · Null-Hessian Envelope Integrability and the X72 Lift
Building on the rank-one null-Hessian survivor cone DCRP51 obtained on the positive pseudo-eikonal sector (C>0), and drawing on X72 Round43's vorticity-stress nonlinear realizability cone (STOP-C47), this round asks whether Hessian integrability eliminates this null cone. It proves that it does not: every non-affine block is exactly a developable-envelope local normal form (its gradient curve lies on the pseudo-eikonal hyperboloid and moves along a wave-null direction), so unconditional local affine rigidity on the positive-C sector is false, and this envelope still satisfies X72 vorticity-stress realizability pointwise. But every non-affine realization necessarily produces a finite caustic/transition frontier. STOP-D52 hands the problem to DCRP53: can same-family continuation cross this finite transition set?
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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