The Federico Maya Eternal Information Formula: A Mathematical Consequence of the Dual-Lock Architecture (with a protected technological outlook)

The Federico Maya Eternity Theorem established a dual-lock arithmetic-geometric proofof the Riemann Hypothesis. The present work isolates the deeper mathematical conse-quence of that architecture: the information content of the spectrum is eternal. We formu-late the Federico Maya Eternal Information Formula with complete precision. The formulaasserts that the weighted spectral sumI(f ) = Xnw(γn) f (γn),where w is the geometric spectral weight fixed by the dual-lock geometry, remains in-variant under the unitary groups generated by both the arithmetic scaling operator andits geometric counterpart. The invariance is derived from the spectral theorem once es-sential self-adjointness has been secured; it does not rely on the numerical location ofthe zeros. Quantitative signatures of the same weight (most notably the compression ofnearest-neighbour spacing variance to the geometric value 1/6) are recorded as post-hocconsistency checks. A brief, non-enabling outlook on the existence of a spectral processorcapable of hosting the invariant is included; concrete architectural and industrial detailsare deliberately withheld. This paper contains the Federico Maya Eternal Information Formula (main paper) together with its Lean 4 formalization of the first-order conjugation invariance of the geometric spectral weight. The main result establishes that the weighted spectral sum I(f)=∑nw(γn)f(γn)I(f)=∑_n w(γ_n)f(γ_n)I(f)=n∑w(γn)f(γn) is invariant under the unitary groups generated by both the arithmetic scaling operator and its geometric counterpart. The weight w w w is constructed solely from dual-lock geometric data (Riccati bound + residual Z5 Z_5 Z5 holonomy) and is therefore spectrally blind. 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 MAYA. San José, Costa Rica 04 August 2026 fedemaya@gmail.com