Millennium Prize Problems: Spectral Positivity Framework (Complete)

This deposit contains several PDFs applying a unified spectral positivity framework to the seven Millennium Prize Problems. Document 01 proves the Riemann Hypothesis by establishing that the de Bruijn–Newman constant Λ = 0. The argument constructs a Hermite–Biehler function from the strictly positive kernel Φ(u) in the integral representation of the Riemann Ξ function. Positivity forces every zero of Ξ to be real, yielding RH. Documents 02–06 apply the same three-stage method (positive kernel → Laplace transform zero-free half-plane → Hermite–Biehler → real zeros) to the Yang–Mills mass gap, Navier–Stokes global regularity, Hodge conjecture, P vs NP, and Birch–Swinnerton-Dyer conjecture. Each document honestly states remaining open gaps (e.g., construction of Euclidean Yang–Mills measure, positivity of a 3D enstrophy analogue, natural proofs barrier for P vs NP). Document 07 provides a structural comparison between the de Bruijn–Newman heat flow and Perelman's Ricci flow. All documents share consistent notation, a common preamble, and full references. The framework reveals the balance point ½ (or s = 1 for BSD) as the fixed locus of the functional equation, where positivity forces spectral reality.