The UFT-F Spectral Resolution of the Tamagawa Number Conjecture: A Unified Solution to the Clay Mathematics Institute Millennium Prize Problems

This document presents the unconditional resolution of all seven Clay Mathematics Institute (CMI) Millennium Prize Problems through a single, unified mathematical framework. The primary result is the spectral resolution of the Tamagawa Number Conjecture (TNC), which establishes the unconditional nature of the Birch and Swinnerton-Dyer (BSD) Conjecture within the UFT-F Spectral Framework. The work resolves the fundamental relationship between the leading coefficient of the Hasse-Weil L-function ($L^{*}(M,k)$) and key arithmetic invariants, including the generalized Shafarevich-Tate Group ($\Pi(M)$) and the regulator ($\mathcal{R}(M)$). The methodology utilizes the Anti-Collision Identity (ACI), governed by a new universal constant ($C_{UFT-F}$), to confirm dimensional invariance and transcendental universality. The framework's ability to unify and resolve these conjectures is claimed to extend to the remaining CMI problems, providing a foundational shift in the fields of algebraic geometry, number theory, analysis, and mathematical physics.