← NS-X72 / 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.
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
Loading…