The Federico Maya Eternity Theorem: A Dual-Lock Proof of the Riemann Hypothesis v.29 with Supplementary Lean 4 Formalization

The Riemann Hypothesis asserts that every non-trivial zero of the completed Riemann zeta function ξ(s) \xi(s) ξ(s) lies on the critical line Re⁡(s)=1/2 \operatorname{Re}(s)=1/2 Re(s)=1/2. The Federico Maya Eternity Theorem provides a complete, non-circular proof of this statement by means of a dual-lock architecture constructed on the idèle class group CQ=AQ×/Q× C_{\mathbb{Q}}=\mathbb{A}_{\mathbb{Q}}^\times/\mathbb{Q}^\times CQ=AQ×/Q×. Lock 1 (Arithmetic) proceeds by exact Tate–Iwasawa identification. After algebraic annihilation of the continuous spectrum on the strict cuspidal Schwartz–Bruhat subspace, the adèlic Poisson summation formula yields an exact Mellin transform that coincides with a non-zero multiple of ξ′/ξ \xi'/\xi ξ′/ξ. Consequently the discrete spectrum of the scaling operator D \mathcal{D} D consists precisely of the non-trivial zeros of ξ(s) \xi(s) ξ(s). Lock 2 (Geometric) establishes essential self-adjointness. An explicit unitary intertwiner V V V, built solely from the group law of CQ C_{\mathbb{Q}} CQ, the Haar measure and the matrix coefficients of the residual representation, realises D \mathcal{D} D on a twelve-dimensional warped product. The kernel of V V V contains no spectral data. After the Liouville transformation the radial dynamics reduce to a Schrödinger operator whose effective potential saturates the Riccati bound. Weyl’s limit-point criterion forces both deficiency indices to vanish; unitary invariance transfers the result back to D \mathcal{D} D. The conjunction of the two locks places every non-trivial zero on the critical line. The argument relies only on the standard axioms of unbounded operator theory, classical harmonic analysis on the idèle class group, and the differential geometry of the warped product. No appeal is made, at any stage, to the numerical location of the zeros. This deposit contains: the full manuscript (v.29, 73 pages), the complete Lean 4 verification document (three modules enforcing architectural quarantine between Lock 1 and Lock 2). Implications for the eternality of spectral information are deferred to a subsequent paper. An earlier versions are available at https://doi.org/10.5281/zenodo.21500329. Intellectual Property Notice: The mathematical frameworks, equations, and topological architectures detailed in this manuscript are currently protected under United States Patent and Trademark Office (USPTO) Provisional Application No. 63/984,236, titled "System and Method for Topological-Negentropic Quantum Control via Zeta-Manifold Resonance." All commercial engineering rights are strictly reserved. FEDERICO MAYA. San José, Costa Rica 03 August 2026 [email protected]