The Federico Maya Eternal Information Formula v.2 (with Analytic Supplement and Lean 4 Certificates)

Abstract

The Federico Maya Eternity Theorem established a dual-lock arithmetic-geometric proof of the Riemann Hypothesis. The present work isolates the deeper mathematical consequence of that architecture: the information content of the spectrum is eternal. We formulate the Federico Maya Eternal Information Formula with complete precision. The formula asserts that the weighted spectral sum I(f) = Σ_n w(γ_n) f(γ_n) remains invariant under the unitary groups generated by both the arithmetic scaling operator and its geometric counterpart. The invariance is derived from the spectral theorem once essential self-adjointness has been secured; it does not rely on the numerical location of the zeros. Quantitative signatures of the same weight (most notably the compression of nearest-neighbour spacing variance to the geometric value 1/6) are recorded as post-hoc consistency checks. A brief, non-enabling outlook on the existence of a spectral processor capable of hosting the invariant is included; concrete architectural and industrial details are deliberately withheld. This deposit contains: 1. The main paper (v.2).2. An analytic supplement that supplies the classical derivations of the scalar spectral measure, the polarization identity, the conjugation rule, and the first-order invariance of the geometric spectral weight, together with the corresponding Lean 4 formalization under a minimal axiomatic interface. 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