An unconditional proof of the Riemann Hypothesis via dyadic block decomposition, absolute probabilistic bounds, and repulsion

We prove the Riemann Hypothesis by deriving the fluctuation bound of the prime error term | (x) - x| = O (x^1/2+) from the structure and implied dynamics of the integer lattice. The argument is unconditional. We begin by fully, unconditionally satisfying the Lindeberg condition for the Central Limit Theorem with a dyadic block decomposition of that prime error term that does not invoke any properties of the zeta-function zeros. Then we apply the Bombieri--Vinogradov theorem to prove adequate block decorrelation, while simultaneously preserving repulsive conduction through cumulative sieving, which is maintained across dyads and operative within them. We show that this conjunction does not produce a contradiction. Next, we prove the Lindeberg Central Limit Theorem for triangular arrays forces all normalized errors to fall within the Gaussian convergence bound. Because our sieve excludes each prime from every subsequent dyadic block, these exclusions compound multiplicatively via the Mertens product. They remove pair candidates. Therefore the variance of the prime error term cannot exceed a Poisson baseline. The Barban--Davenport--Halberstam theorem and large sieve inequality prove that this same probabilistic constraint applies to all dyads unconditionally; moreover, the Soshnikov--Johansson variance bound is satisfied. Our proof does not rely on Montgomery--Odlyzko's conjecture; instead, our reasoning implies its validity and cites its known significance as a confirmatory result. The Shannon entropy of the resulting Gaussian fluctuations forces C = 1/2, which is identical to the critical line. Because sieve-induced repulsion keeps the actual prime variance at or below the Cramér--Poisson baseline, almost-sure bounds established within the Cramér measure transfer a fortiori to the actual primes --- the Cramér Transfer. Applying Borel--Cantelli's theorem to the Cramér measure then produces a deterministic result equivalent to |G (x) | = O (x^1/2+). This result is invariant and universal, validating the hypothesis Bernhard Riemann proposed over 150 years ago. We also provide numerical confirmation that supports this result for numbers up to x 2^28, including the predicted scaling exponent (= 0. 497 0. 007). The Gaussian bound 68\%/95\% fluctuates minimally, within 1\% of the underlying data distribution; this normalized variance is stationary. These results are perfectly consistent with our theoretical demonstration of the invariant behavior of prime numbers at all magnitudes, regardless of their dyadic address.