MORP-05: Escape Reprofiling, Ancient Spatial-Tail Rigidity, Diffuse Minimal Carriers, and Cycle-VII Final Audit

Escape Reprofiling, Ancient Spatial-Tail Rigidity, Diffuse Minimal Carriers, and Cycle-VII Final Audit

MORP Cycle VII's route runs: native obstruction geometry → defect-completed compactness → minimal return dynamics → equality-manifold rigidity. MORP-04 reduced the surviving kernel classes to three (A-KERNEL, E-KERNEL, S-KERNEL). This paper asks: can escape-type carriers be reprofiled into state-visible objects? Can general ancient kernels be eliminated? Can zero-tax splitting remain diffuse after every known rigidity cut? The answer is mixed. It proves an atomic-escape reprofiling theorem: if a normalized trace/spatial-scale escape sequence retains a fixed positive-proportion carrier in some spatial-scale cell, re-centering and rescaling produces a nonzero state-visible subleading profile — so an escape that truly cannot be reprofiled must be diffuse (the largest cell proportion tends to zero, effective carrier multiplicity diverges). It proves an ancient compact-tail Liouville reduction (a backward-sequence ancient solution bounded globally in L³ is, by Albritton–Barker, trivial), and proves a diffuse minimal splitting theorem. Cycle VII's final survivor is a minimal, zero-tax, kernel-saturated diffuse carrier, arising through spatial/scale/trace escape or a non-L³-compact ancient state — this does not prove global regularity, and explicitly hands off the next step to "NS-DCRP: Navier–Stokes Diffuse Carrier Rigidity Program."