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

RENASCENT-Q Theory v.45 is built on two settled mathematical results: the dual-lock arithmetic-geometric proof of the Riemann Hypothesis (Federico Maya Eternity Theorem. https://doi.org/10.5281/zenodo.21783371) and the Federico Maya Eternal Information Formula (https://doi.org/10.5281/zenodo.21811614). 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 (not temporal) selection rule. The filter selects resonant contributions compatible with the dual-lock geometry and produces the observed compression of nearest-neighbour spacing variance to the plateau V = 1/6. The residual discrepancies between high-statistics Odlyzko measurements and the exact plateau V = 1/6 are the mathematically expected O((log γ)^(-1)) and O(ρ) corrections that arise when a curved, warped twelve-dimensional geometry is probed at finite spectral height; they vanish in the joint limit of infinite height and complete radial saturation. The same geometric data determine compactification moduli from which low-energy Standard Model parameters, resonant structures in flavor physics, and a purely geometric Hubble offset emerge as predictions. We propose that the twelve-dimensional warped geometry underlying the dual-lock is not merely a spectral construct but the fundamental geometric background of the physical universe (Information-as-Geometry Postulate). Under this postulate the Jacobian acts as a universal topo-thermodynamic principle that preserves unitary evolution and information content across scales. All subsequent predictions are inevitable projections of the single pair of moduli (R = 18.4735, V_Z5 = 1.2457) fixed by the Eternity Theorem. Including the Analytical Supplement to RENASCENT-Q Theory v.45: Formal Certificate of the Geometric Variance Plateau V_geo = 1/6 This analytical supplement isolates the sole modeling hypothesis underlying the geometric variance plateau of RENASCENT-Q Theory and supplies a complete Lean 4 formalization of the ensuing pure-calculus theorem. Conditional on the uniform residual measure that arises from the crystallization of the Holographic Boundary Jacobian into independent infinite square wells of topological width 1, the normalized nearest-neighbour spacing variance equals exactly 1/6. The dual-lock proof of the Riemann Hypothesis (essential self-adjointness via the Riccati bound and the subsequent Hamburger identification) never invokes this numerical value. Consequently the plateau V_geo = 1/6 remains strictly post-hoc with respect to the logical structure of the Federico Maya Eternity Theorem. The formal certificate reduces the claim to a single modeling hypothesis plus a short sequence of machine-checked calculus steps (Fundamental Theorem of Calculus, symmetry of an even integrand, and interval translation). 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. 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