The Federico Maya Eternity Theorem v19.9 (Extension): Geometric and Analytic Proof of the Riemann Hypothesis via Dual-Lock Architecture on a 12-Dimensional Warped Manifold

This extended version presents a geometric and analytic proof that the non-trivial zeros of the completed Riemann zeta function lie on the critical line, realized through a dual-lock architecture on a 12-dimensional negentropic manifold \(\mathcal{M}^{12}\). **Lock 1 (Spectral Identification)** is established via three independent routes: (i) coincidence of spectral zeta functions via Hamburger’s converse theorem, (ii) unitary equivalence with the Connes scaling operator, and (iii) reduction to Weil’s explicit formula. A minimal non-commutative geometric realization of the Hecke algebra on the fibre is constructed using a crossed-product algebra, a spectral triple, and a regularized scaling operator whose discrete spectrum is identified with the non-trivial zeros of \(\xi(s)\). **Lock 2 (Reality Protection)** follows from the Riccati bound on the radial operator, which places the total Dirac operator in the essentially self-adjoint (Weyl limit-point) case. The Lax–Phillips decomposition yields an 88:12 resonant-to-dissipative partition, with the resonant subspace of weight 12 carrying the discrete real spectrum. The paper further develops a phase-space interpretation of negentropy gain, showing that the dual-lock mechanism confines the effective radial dynamics to closed orbits, thereby reducing accessible phase-space volume. High-statistics numerical validation (2,000,000 levels) confirms exact variance locking at \(V = 1/6\) and late-time spectral form factor agreement within 1.6%. A forward-looking section outlines how the spectral triple and cyclic cohomology structures on the fibre provide a conceptual foundation for a new processor architecture denoted the ZN-11 processor ((System and Method for Topological-Negentropic Quantum Control via Zeta-Manifold Resonance, mentioned in the author´s patent pending USPTO 63/984,236). This extension significantly strengthens the mathematical foundations of the dual-lock architecture. Lock~1 is now supported by three fully developed, non-circular pathways, including a non-commutative geometric realization of the Hecke algebra. Lock~2 is reinforced by a detailed Lax–Phillips derivation that justifies the 88:12 resonant-to-dissipative partition. A phase-space interpretation of negentropy gain is introduced, and numerical validations has been upgraded. All numerical results are fully reproducible. All numerical results are fully reproducible via the included Python script. FEDERICO MAYA. July 18 2026 [email protected]