DCRP53: Global Cylindricity and the X72 One-Quarter Visibility Slice

Building on DCRP52's local developable-envelope and finite-caustic conclusions, this round brings in the Hartman–Nirenberg cylinder theorem as an external tool and asks whether an entire self-similar time-slice can globally sustain a rank-one central perfect response. It proves that if the whole slice is C³ with rank ≤1, its image is a complete flat hypersurface and, by the cylinder theorem, must be a generalized cylinder; but the wave equation requires the cylinder-axis direction to be G-isotropic, while the pseudo-eikonal identity requires that same direction to be M-isotropic, and the two are compatible only for the zero vector. Hence no nonzero global central perfect-response solution exists, lifting DCRP52's local caustic conclusion to a coordinate-independent global statement. It is also shown that null-Hessian blocks satisfy an exact X72 differential identity with visibility fixed at 1/4. STOP-D53 hands to DCRP54 the question of whether the visibility defect on the transition shell can be localized into transparency.