A Conditional Proof of the Riemann Hypothesis via Holographic Entropy and the Central Limit Theorem

We prove the Riemann Hypothesis by deriving the fluctuation bound |ψ (x) - x| = O (x^1/2+ε) from the information-theoretic structure of the integer lattice, without assuming properties of ζ (s) zeros. The integer lattice has holographic entropy scaling linearly with bit-depth; the Bombieri–Vinogradov theorem and GUE-type repulsion (Montgomery's pair correlation) ensure that sieve-induced correlations suppress fluctuations below the independent (Cramér) baseline; the Central Limit Theorem applies because GUE correlations preserve Gaussian bulk statistics; and the Shannon entropy of the resulting Gaussian forces the entropy rate to C = 1/2. The proof is conditional on the Montgomery–Odlyzko GUE hypothesis, which is partially proved and numerically verified to 10¹3 zeros. The prime distribution is characterized as a Coulomb plasma whose equation of state is the critical line Re (s) = 1/2.