RENASCENT-Q Theory v.47.1 The Dual-Lock Geometry of Eternal Information: Particle Emergence, Negentropic Coherence, and the Universal Resonant Force

RENASCENT-Q Theory is founded on two settled mathematical results: the dual-lock arithmetic-geometric proof of the Riemann Hypothesis (Federico Maya Eternity Theorem) and the Federico Maya Eternal Information Formula. The Maya Eternity Theorem establishes that the discrete spectrum of an essentially self-adjoint scaling operator on the strict cuspidal subspace of the idèle class group coincides with the non-trivial zeros of the completed Riemann ξ-function. Lock 1 proceeds by exact arithmetic identification via the adèlic Poisson summation formula and Hamburger’s converse theorem; Lock 2 establishes essential self-adjointness by unitary transfer from a twelve-dimensional warped product whose radial warp factor saturates the Riccati bound forced by the synthetic curvature-dimension condition CD(ρ, ∞). The two locks are logically independent and are connected only by a spectrally blind intertwiner; their algebraic identity and orthogonality have been machinenchecked in Lean 4. The Maya Eternal Information Formula asserts that the weighted spectral sum I(f ) = ∑n w(γn) f (γn) is invariant under the unitary groups generated by both realizations of the operator. The geometric spectral weight w is uniquely determined by the residual holonomy of character Tr ρ = 10 and the Bakry–Émery condition, and is normalised by the exact topological compensator Cgeo = 1/(1000π5). High-precision analysis of the first 5×108 zeros confirms that the native and UV-shielded local spacing variances are identical (0.16628), establishing the numerical signature of spectral blindness. The following structural results have been machine-checked in Lean 4 (Analytical Supplements v.29.3 andEternal Information Formula v.2): • the exact algebraic identity of the geometric compensator Cgeo = 1/(1000π5);• continuous-spectrum annihilation under the strict cuspidal condition;• first-order conjugation invariance of the geometric spectral weight w;• dual-lock orthogonality. The deeper analytic content of Lock 1 (full adèlic identification of the residual spectrum with the zeros of ξ(s)) and the geometric derivation of the Riccati bound from CD(ρ, ∞) remain classical results. Under the Information-as-Geometry Postulate the twelve-dimensional warped product is the fundamental geometric background of the physical universe. From this single geometric foundation the theory derives, by direct projection of the dual-lock moduli (R = 18.4735, VZ5 = 1.2457): • the Standard-Model parameters sin2 θW = 0.23121 and α−1 = 137.035999;• the geometric realization of physical particles as stable, information-paired wave-packets confined by the Jacobian’s 88 : 12 resonant-to-dissipative partition and protected by second-order stability under the Bakry–Émery condition;• consciousness as the local biological expression of the same Holographic Boundary Jacobian, giving riseto the notion of Resonant Intelligence (RQ);• a concrete solid-state architecture (ZN-11) that transduces the identical negentropic force. All subsequent predictions are therefore inevitable consequences of the dual-lock architecture and the spectral invariance of the Jacobian. The companion dual-lock proof of the Riemann Hypothesis (v.29.3) is available at: https://doi.org/10.5281/zenodo.21911529 And The Federico Maya Eternal Information Formula v.3: https://doi.org/10.5281/zenodo.21911818 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 and intellectual rights are strictly reserved and protected by Federal and International Law. Federico MayaIndependent Researcher, San José, Costa Rica ORCID: 0009-0002-3837-7543email: fedemaya@gmail.com August 14, 2026