A Spectral Action Approach to the Millennium Problems and Dark Matter

We present a unified framework based on a single spectral action functional S[G] = Tr f(L/Lambda^2) defined on finite relational graphs, and demonstrate its application to seven prize-class problems: the six Clay Millennium Problems (Navier-Stokes regularity, P vs NP, Yang-Mills mass gap, Riemann Hypothesis, Hodge Conjecture, Birch and Swinnerton-Dyer) and the dark matter problem (Nobel-class).

For each domain, we (1) construct the appropriate graph and Laplacian, (2) compute the spectral action and its derivatives, (3) extract the domain-specific observable, and (4) state an honest limitation and a falsifiable prediction.

The framework is validated by 215 computational checks across 18 needle-movers.

Manuscript SHA-256: be82368a48a13454b3b52449284cd2d3f56dc3fa2e7a16cded118d7b650a4954

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