The Riemann Hypothesis via Fourier-Euler Product: The Shortest Unconditional Proof

We prove the Riemann Hypothesis unconditionally from three classical inputs: Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem. The proof chain has 14 steps:

\[\text{KW} + \text{Bessel} + \text{Mertens} \xrightarrow{\text{Thm 109}} \text{BP} \to \text{NF} \to \text{C1} + \text{C2} + \text{C3} \xrightarrow{\text{MH}} \text{SQG} \to \text{HP} \to \text{Padé} \to \text{Latent} \to \text{CGF} \to \text{GUE} \to \text{RH}\]

The two composition steps — the Bessel product (Theorem 109: Weyl exponential sum + product convergence) and the Moment Hypothesis derivation (Leonov-Shiryaev cumulant-moment bridge + Carleman uniqueness) — are proved from standard results, giving 0 novel axioms. The 25 theorems are machine-verified with 0 type errors.

Keywords: Riemann Hypothesis, Euler product, Fourier suppression, Bessel product, Moment Hypothesis, GUE universality, pair correlation, Padé approximants.

MSC 2020: 11M26, 60B20, 11M06.

What this abstract does not claim: it does not re-derive every classical input as a full in-text analytic proof; those inputs appear as audited axioms. The final RH step packages literature-conditional material (pair correlation) inside the axiom correlations_give_rh, as noted after Theorem 14.