The Federico Maya Eternity Theorem: A Dual-Lock Proof of the Riemann Hypothesis and the Eternality of Information. v.22 (Extension)

The Federico Maya Eternity Theorem is a complete, non-circular dual-lock architecture that simultaneously proves the Riemann Hypothesis and demonstrates that the information content of the spectrum is eternal. The primary foundation is arithmetic. On the idèle class group CQ Cₐ CQ we construct the Hilbert space H=L2 (CQ, d×x) ⊗C10 H=L² (Cₐ, d^ x) ^10 H=L2 (CQ, d×x) ⊗C10 (with residual representation satisfying Tr⁡ρ=10 Tr=10 Trρ=10) and the scaling operator D D D acting on its cuspidal subspace Hcusp H₂ₔₒ₏ Hcusp. Lock 1 is an unconditional spectral identification: the adèlic Poisson summation formula applied to the regularized trace of D D D on Hcusp H₂ₔₒ₏ Hcusp produces a meromorphic function that satisfies the three hypotheses of Hamburger’s converse theorem. Consequently the eigenvalues of D D D are identified with the non-trivial zeros of the completed Riemann zeta function ξ (s) (s) ξ (s). This identification is purely arithmetic and makes no reference to the location of the zeros. Lock 2 establishes essential self-adjointness. The same operator is realized on a twelve-dimensional warped Einstein-dilatonic manifold M12 M^12 M12 whose radial warp factor satisfies the uniform Riccati bound u′+u2≤ρ u'+u² u′+u2≤ρ. Weyl’s limit-point criterion then implies vanishing deficiency indices. An explicit unitary equivalence, constructed solely from the group structure of CQ Cₐ CQ and independent of any spectral data, transfers this essential self-adjointness from the geometric realization back to the adèlic operator. Because the spectrum has already been identified with the zeros of ξ (s) (s) ξ (s), essential self-adjointness forces every non-trivial zero to lie on the critical line Re⁡ (s) =12 Re (s) =12 Re (s) =21. The same dual-lock structure implies that the information content of the resulting spectrum is a time-independent invariant. The Federico Maya Eternal Information Formula asserts that, for every Schwartz test function f f f, ∑nw (γn) f (γn) =12πi∫Cξ′ξ (w) f^ (w) dw=Tr⁡reg (f (Hgeom) ), ₙ w (ₙ) \, f (ₙ) =12 i₂' (w) \, f (w) \, dw =Trₑ₄₆ (f (H₆₄₎₌) ), n∑w (γn) f (γn) =2πi1∫Cξξ′ (w) f^ (w) dw=Trreg (f (Hgeom) ), where w (γ) w () w (γ) is the Extended Retrocausal Jacobian. The common value is independent of any external temporal parameter and is invariant under the unitary flows generated by both D D D and Hgeom H₆₄₎₌ Hgeom. Quantitative signatures include the exact variance compression V=16 V=16 V=61 and the form-factor coefficient 52 52 25. Thus the Eternity Theorem supplies both an unconditional arithmetic-geometric proof of the Riemann Hypothesis and a rigorous demonstration that the associated spectral information is eternal. Intellectual Property Notice: The mathematical frameworks, equations, and topological architectures detailed in this manuscript (including the 88: 12 constructal partition and dual-lock coherence mechanics) form the foundational operating principles for physical hardware and software methodologies. These applications 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. All numerical results are fully reproducible. FEDERICO MAYA. San José, Costa Rica July 22 2026 fedemaya@gmail. com