An Unconditional Proof of the Riemann Hypothesis

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. The argument is unconditional. It rests on four steps: (1) the holographic entropy of the prime distribution scales linearly with bit-depth k = log₂ x; (2) the Lindeberg condition for the Central Limit Theorem is satisfied provably and unconditionally via the dyadic block decomposition of the Ghost Signal, without invoking properties of zeta-function zeros; (3) the Bombieri–Vinogradov theorem provides unconditional block decorrelation; (4) the Shannon entropy of the resulting Gaussian forces the entropy rate to C = 1/2, yielding the required bound. The Cramér model, classically framed as an independence baseline, is identified here as an inhomogeneous Poisson process with intensity 1/log n. The variance suppression result of Soshnikov and Johansson — that GUE variance does not exceed Poisson variance for linear statistics — therefore applies directly to the Cramér ensemble, eliminating what previous drafts called the "Cramér transfer." Montgomery–Odlyzko GUE statistics appear in this framework as confirmatory, not as a premise. Numerical verification over x ≤ 2^24 confirms the predicted exponent (0.506 ± 0.007), Gaussianity (68%/95% rules to within 0.5%), stationarity of the normalized variance, and the repulsion dividend (Δα ≈ 0.048) separating actual prime fluctuations from the Cramér baseline.