← NS-X72 / X72-32 · Source-Participation Dynamics Renormalization

NS-X72 · X72-32 Gap Closure 2026-08

X72-32: Source-Participation Dynamics Renormalization

Picks up the participation ratio 𝔍_W to which Round 31 compressed the persistent-lock occupancy problem (STOP-C35), and builds an exact tilt dynamics for the relative critical mass of general smooth positive sources. Proves that (log𝔍_W)' is given exactly by three terms — viscous Fisher information, tilt selection, and relative-source bias — so smooth positive sources possess a universal viscous anti-concentration structure, and Round 31's occupancy gap can be closed conditionally on this class of sources. At the same time, it shows that three classes of genuinely dangerous sources — determinant sources, positive-Q-growth sources, and pair singular kernels — all carry a sign interface or a near-diagonal singular kernel whose positive part cannot be controlled by the same mechanism; the pair kernel's positive-part measure may even diverge near the diagonal. STOP-C36 (Source-Participation Trapping/Singular-Source Renormalization Gap) hands the problem of signed sources to the next round.

This round's status: Gap Closure — 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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