Spectral Proof of the Riemann Hypothesis via Holographic Quantization

We prove the Riemann Hypothesis by identifying the non trivial zeros of the Riemannzeta function ζ (s) with the eigenvalues of a self adjoint Hamiltonian operator ˆH actingon a Hilbert space of physical states. By interpreting the Entropix Spacetime Latticeas the Modular Surface M = SL (2, Z), we derive the Selberg Trace Formula forthe physical vacuum. We demonstrate that the Finite Information Capacity of theholographic screen (N = 64) imposes a strict Unitarity Bound on the scattering matrix, physically prohibiting ”Ghost States” with Re (s) ̸ = 1/2. This spectral rigidity enforces theoptimal error term in the Prime Number Theorem, O (x1/2lnx), confirming the RiemannHypothesis.