A Prime–Resonance Hilbert–Polya Operator and the Riemann Hypothesis

We construct a self-adjoint operator on a prime-based Hilbert space whose spectral determinant matches the completed Riemann ξ-function on the critical line. This operator arises naturally within a prime-resonance framework where primes serve as fundamental eigenstates and entropy-driven stabilization enforces spectral alignment. Using a block chiral form, calibrated prime-power trace identity, and functional antiuni- tary symmetry, we prove that all non-trivial zeros of ζ(s) lie on Rs = 12. This provides a resolution of the Riemann Hypothesis via the Hilbert–Po ́lya strategy, extended with resonance and entropy considerations.