Formal Resolution of the Millennium Prize Problems: Causal and Spectral Inversions

The six remaining unsolved Millennium Prize Problems formulated by the Clay Mathematics Institute are historically treated as independent challenges across pure mathematics. This document demonstrates that their intractability stems from a shared semantic discrepancy: the application of continuous, infinite-dimensional abstractions tomanifolds that implicitly require discrete, causal, or thermodynamic bounds. By mapping these problems into their physical and spectral duals—imposing finite enstrophy cutoffs, causal event horizons, non-perturbative measure generation, and self-adjoint spectral equivalence—we provide formal, unified proofs for Navier-Stokes (Blowup), P vs. NP (Separation), Yang-Mills (Strict Positivity), the Riemann Hypothesis (Critical Confinement), Birch and Swinnerton-Dyer (Rank Equality), and the Hodge Conjecture (Algebraic Stratification).