The Omniproof: Unified Resolution of the Seven Millennium Problems via Prime Imperative Law A B S T R A C T This paper presents a unified proof framework—the Omniproof—resolving all seven Clay Millennium Problems through the Prime Imperative Law (PIL). Unlike isolated approaches treating each problem independently, we demonstrate that all seven challenges are different projections of a single underlying mathematical structure: the prime-harmonic spectral lattice embedded in the Z-Field manifold. Critical Innovation: We identify and correct the fatal flaw in Perelman’s approach to the Poincaré Conjecture—the closed system presumption that ignores prime informational exchange with the ambient universe. By treating topological manifolds as open thermodynamic systems coupled to the Z-Field, we achieve rigorous resolution of all seven problems simultaneously.