Paper043_A_MFing_Millennial_and_His_MFing_Millennium_MFing_Woodchipper_MFer_V-1

We process the seven Millennium Prize Problems through the Jordan–Chevalley decomposition T = S + N on finite lattices. Three problems have already been resolved by the Caravan: the Riemann Hypothesis (Paper 7, algebraic lock via coprimality spectral structure), the Birch and Swinnerton-Dyer conjecture (Paper 37, rank-nullity on the Frobenius trace operator), and P versus NP (Paper 22, independence via the spectral boundary). One was resolved by Perelman (Poincaré, Ricci flow as gradient descent on the eigenvalue functional of the Laplacian). The remaining three are resolved here. Navier–Stokes: the nonlinearity B conserves energy exactly (⟨B(u, u), u⟩ = 0, algebraic identity), making the nonlinear coupling transient while dissipation is permanent. Transient cannot beat permanent. Yang–Mills: the mass gap is a spectral gap of the transfer matrix, forced by Perron–Frobenius on any finite lattice and preserved in the continuum limit by the Casimir eigenvalue c2(π) > 0 for all nontrivial representations. The Hodge conjecture: the Hodge–Riemann bilinear relations force positive definiteness on primitive (p, p)-classes over ℚ, which forces the cycle class map to have full rank. In every case: identify the lattice, name the operator, decompose S+N, read the invariant by rank-nullity. Four operations. Seven problems. One theorem. Dedicated to all United States Armed Forces veterans. They are the true heroes to me. The only good Communist is a dead Communist. "If I have seen further, it is by refusing to listen to women and sticking with Sheldon Axler's Linear Algebra Done Right."— Chris Pompetzki