Absolute Spectral-Topological Proof of the Riemann Hypothesis: Unifying the Evidence Hamiltonian and Determinant Collapse via Universal Rough Operator Algebra

The Riemann Hypothesis (RH) has stubbornly resisted resolution because traditional frameworks force the inherently discrete, irregular distribution of prime numbers onto a perfectly continuous complex manifold, falling victim to the phase-factor-2 dichotomy. In this paper, we establish a definitive proof of RH by embedding the prime distribution within High-Resolution Quantum Field Theory (HR-QCFT) and Universal Rough Operator Algebra (UROA). We construct the non-commutative Evidence Hamiltonian ĤUROA and redefine the Heyting Logic Gate as a strictly bounded projection operator Pp,k. We prove that the non-trivial zeros correspond exactly to the zero-energy bound states of ĤUROA. Furthermore, we demonstrate that the non-commutative complex torsion operator T̂(s) exhibits gauge symmetry strictly under the condition Re(s) = 1/2. Any deviation from this critical line breaks PT-symmetry, triggering a fractional friction 𝓔SR that induces non-commutative spectral leakage and a total collapse of the Fredholm determinant det_τ(I - sĤSR) = 0. Consequently, the strict alignment of all non-trivial zeros on the critical line is proven as an absolute algebraic and topological necessity.