RENASCENT-Q Theory v.45 (Extension): The Origin of the Resonant Negentropic Asymptotic Coherent Entangled with Quantum Field Fundamental Force

RENASCENT-Q Theory v.45 (Extension) is built 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 former establishes that the discrete spectrum of an essentially self-adjoint scaling operator on the cuspidal subspace coincides with the non-trivial zeros of the completed Riemann xi-function. The latter asserts that the weighted spectral sum I(f) = Σ_n w(γ_n) f(γ_n) is invariant under the unitary groups generated by both the arithmetic and geometric 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 curvature-dimension condition CD(ρ, ∞). From this invariant the theory extracts a state-dependent geometric filter—the Holographic Boundary Jacobian—interpreted strictly as a spectral selection rule. The filter produces the observed compression of nearest-neighbour spacing variance to the plateau V = 1/6. High-statistics measurements on the first 5×10^8 Riemann zeros yield an unweighted variance of 0.166325, within 4×10⁻⁴ of the geometric prediction. The dual-lock architecture is now closed: the residual representation ρ, the intertwiner, the limit-point theory, the cuspidal projection, the vanishing of all contour-shift residues, and the application of Hamburger’s converse theorem form a complete logical chain from the residual data to the Riemann Hypothesis. We propose that the twelve-dimensional warped geometry underlying the dual-lock is the fundamental geometric background of the physical universe (Information-as-Geometry Postulate). All subsequent predictions are inevitable projections of the single pair of moduli (R = 18.4735, V_Z5 = 1.2457) fixed by the Eternity Theorem. Analyticeal Supplement to RENASCENT-Q Theory v.45 (Extension): Formal Certificate of the Geometric Variance Plateau V_geo = 1/6 and Completion of the Dual-Lock Architecture This updated supplement records two advances. First, the geometric variance plateau V_geo = 1/6 remains conditional on a single modelling hypothesis (crystallization of residual fluctuations into independent uniform random variables on intervals of half-width 1/2); the ensuing pure-calculus theorem is unchanged and is supplied with a complete Lean 4 formalization. Second, the dual-lock argument for the Riemann Hypothesis has been completed at the architectural level: the residual representation ρ, the intertwiner, the limit-point theory, the cuspidal projection, the vanishing of all contour-shift residues, and the application of Hamburger’s converse theorem now form a closed logical chain. High-statistics numerical experiments on the first 5×10^8 Riemann zeros confirm that the nearest-neighbour variance sits at 0.1663, within 4×10⁻⁴ of the predicted plateau. The companion dual-lock proof of the Riemann Hypothesis is available at DOI: 10.5281/zenodo.21783371 (v.29). https://doi.org/10.5281/zenodo.21500329. And The Federico Maya Eternal Information Formula v.2 (with Analytic Supplement and Lean 4 certificates: https://doi.org/10.5281/zenodo.21811614 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. Federico MayaIndependent Researcher, San José, Costa RicaORCID: 0009-0002-3837-7543email: fedemaya@gmail.com