← NS-X72 / X72-07 · Continuous-Hierarchy Analytic Re-Integration

NS-X72 · X72-07 Proof 2026-08

X72-07: Continuous-Hierarchy Analytic Re-Integration

Continuing from Round 06's STOP-C10, this round proposes the Gevrey generating carrier G_{τ,s} = ‖e^{τΛ}Λ^sS‖² and proves a continuous-hierarchy re-integration theorem: as long as the analytic radius τ > 0 stays positive, it simultaneously controls every higher real Sobolev level, so the infinite derivative hierarchy is, by itself, not an essential obstruction for Pure-C. Further establishes an adaptive radius tax ρ_{τ,s} and a compensation law τ' = −ρ under which the Gevrey norm is non-increasing along this path, and proves that a finite-time singularity, if one exists, must exhaust the analytic-radius budget (inf τ(t) = 0). Finally stops at STOP-C11 (the analytic-radius-budget-exhaustion gap): it has not yet been proven that this budget cannot be exhausted, handing off to the next round's test of whether the spectral variance automatically forms a negative feedback on the radius tax.

This round's status: Proof — Taken from the file's own objective/executive-result section, meaning preserved, not a full verbatim translation.

Connections

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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