A structural reformulation and computational verification of Bernhard Riemann's 1859 hypothesis about the zeros of the zeta function. Riemann observed that the roots of ξ(t) appear to be real, wished for a stricter proof, and closed his paper asking future mathematicians to track the influence of the individual periodic terms on the density of primes. This paper answers all three requests. The formal framework (Parts I–VII) reduces Riemann's observation to a single integrated anticorrelation bound (S1*), proven equivalent to RH in both directions. Lemma 8 (Pair Positivity) and its k-body generalization (Corollary 8.1, cost (k−1)² matching GUE Vandermonde repulsion) are proven unconditionally. The NOXA computational engine (Parts VIII–IX, XI) directly implements Riemann's closing request, tracking the periodic terms across 1,628 scans (130,240 zeros, sieve windows to x ≈ 9.5 million). S1* holds in every scan with the ratio declining from 0.000862 to 0.000216. The paper distinguishes Riemann's actual hypothesis (an empirical observation) from the Clay Millennium Prize reformulation (a theorem demand formulated by later mathematicians). Six independent AI systems have cross-validated the mathematical framework.
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Daniel Santiago
Universitas Pamulang
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Daniel Santiago (Sun,) studied this question.
www.synapsesocial.com/papers/69a67ed1f353c071a6f0a5ad — DOI: https://doi.org/10.5281/zenodo.18827898