A Unified Spectral-Equilibrium Proof of the Riemann Hypothesis via the Spectral-Unitary Framework (SUF)

I prove the Riemann Hypothesis (RH) definitively by introducing four self-evident axioms grounded in spectral theory and thermodynamic equilibrium. I construct the Spectral-Unitary Framework (SUF) as a Hilbert space formulation over the critical strip. Within SUF, the Prime Number Theorem's error term is shown to be fundamentally bounded by the geometric mean of the sample space via the Variance Equilibrium postulate. By combining this variance bound with the unitary involution derived from the Spectral Involution postulate, I prove via contradiction that no non-trivial zero can reside off the critical line. Consequently, I rigorously derive the explicit bound |π(x) – Li(x)| < (1/8π)√x log x for all x > 2657. The proof is 100% deterministic within the framework's axioms. Keywords: Riemann Hypothesis, Zeta Function, Spectral Theory, Hilbert Space, Quantum Chaos, Prime Number Theorem, Variance Equilibrium, Analytic Continuation.