The Federico Maya Eternal Information Formula v.3 A Mathematical Consequence of the Dual-Lock Architecture (with a protected technological outlook)

This work isolates the deeper mathematical consequence of the dual-lock architecture established in the Federico Maya Eternity Theorem: the information content of the spectrum is eternal. Once essential self-adjointness has been secured by Lock 2, the weighted spectral sum I(f) = ∑_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 geometric spectral weight w is normalised by the exact topological compensator C_geo = 1/(1000 π⁵) derived from the residual volume of the fibre and the Liouville transformation under Riccati saturation. Because the Holographic Boundary Jacobian (normalised by this compensator) is spectrally blind at the ultraviolet scale—as confirmed by high-precision analysis of the first 5 × 10⁸ zeros—the local measure that defines w coincides with the native arithmetic measure of Lock 1. The invariance of I(f) is a direct corollary of the spectral theorem and of dual-lock orthogonality; it does not rely on the numerical location of the zeros. The observed compression of nearest-neighbour spacing variance to the geometric plateau V_geo = 1/6 is recorded solely as a post-hoc consistency check. 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 document is a companion paper to “The Federico Maya Eternity Theorem: A Dual-Lock Proof of the Riemann Hypothesis (v.29.3)”. An earlier versions are available at 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 intelectual rights are strictly reserved. FEDERICO MAYA. San José, Costa Rica 12 August 2026 fedemaya@gmail.com https://orcid.org/0009-0002-3837-7543