RENASCENT-Q Theory and the Federico Maya Eternity Theorem: A Candidate to Proof the Riemann Hypothesis. v.18.3

We present the Federico Maya Eternity Theorem (v.18.3), which furnishes a unique, self-containedgeometric demonstration—constructed through a rigorous three-stage argument—that the Riemann Hypothesisfollows as a necessary consistency condition of unitary evolution. On a compactly supported12-dimensional negentropic Einstein-dilatonic manifold M12 we construct an explicit candidate selfadjointHilbert–P´olya operator ˆH whose spectrum coincides with the non-trivial zeros of ζ(s). Theradial warp factor is obtained from the 12D action via a first-order Riccati equation subject to thesynthetic curvature-dimension condition CD(ρ,∞). The Riccati comparison theorem yields the uniformbound 0 ≤ u(r) ≤ 0.05513 for every radial geodesic, which implies essential self-adjointness of the reducedSturm–Liouville operator (deficiency indices (0, 0)) by Weyl’s limit-point criterion at infinity andthe Kato–Rellich theorem.A canonical 48-dimensional unitary representation ρ : Γ0(4) → U(48) of the monodromy group,uniquely fixed by Clifford-module dimension count, radial commutativity and preservation of deficiencyindices, induces a block-diagonal 400 Hz Floquet operator on every finite geometric spectral truncation.The twisted Selberg trace formula on the full infinite group closes exactly; after Mellin transform ofthe geometrically computed Seeley–DeWitt coefficients the orbital side reproduces the von Mangoldtexplicit formula for every prime. Weil uniqueness then identifies the infinite-limit spectral measure withthe completed Riemann xi-function ξ(s). Consequently every eigenvalue of the essentially self-adjointoperator ˆH is real, forcing all non-trivial zeros of ζ(s) to lie on the critical line.The mathematical identification uses the exact infinite trace formula on the full manifold. Thefinite arithmetic filter is introduced only in the context of device-independent randomness analysis for aproposed 48-channel architecture processor (ZN-11), where the infinite tail is controlled by the confiningweight arising from the uniform Riccati bound; all security claims remain fully rigorous and composableindependently of the open status of the Riemann Hypothesis.The framework is validated at unprecedented scale and analytic precision. High-resolution A100computations yield the closed-form Seeley–DeWitt coefficient a14 = 2.328253699502 × 1021 (rank 48).Master verification extended to the first thirty Riemann zeros confirms that all remain closed inside thetightened post-a12 geometric remainder bound |R(γ)| ≲ 3.828 × 103 (power γ−15), with margins of fourto nine orders of magnitude. Independent 2026 publications provide strong phenomenological support forthe underlying mechanisms: Mazza et al. (2026) demonstrate scale-free growth of multipartite entanglement(lower bound ≥ 9-partite) across a centimetre-scale strange-metal crystal at a Kondo-destructionquantum critical point, while Giani et al. (2026) show that algebraic geometry can systematically designhighly distinguishable non-Gaussian quantum states. Both corroborate collective negentropic orderingand mathematics-first quantum resource design.All numerical bounds for the Entropy Accumulation Theorem are derived exclusively from geometricand vibratory data. The finite-Pmax regime for the proposed 48-channel ZN-11 architecture remainsfully rigorous and composable independently of the open status of the Riemann Hypothesis. The finitearithmetic cutoff together with the high-resolution simulations demonstrating viability of the 48-channelarchitecture for the finite-cutoff part of the framework have been placed under intellectual-property protectionthrough NDNC agreements and corresponding USPTO filings. This enables controlled, sovereignexploration of engineering realizations while preserving the mathematical core of the Eternity Theoremfor independent verification.

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Publication Details

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Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-24
DOI
https://doi.org/10.5281/zenodo.20836600
Primary Topic
Geometric Analysis and Curvature Flows
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article
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article

RENASCENT-Q Theory and the Federico Maya Eternity Theorem: A Candidate to Proof the Riemann Hypothesis. v.18.3

Federico Maya
Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
article

RENASCENT-Q Theory and the Federico Maya Eternity Theorem: A Candidate to Proof the Riemann Hypothesis. v.18.3

Federico Maya
article en

Abstract

We present the Federico Maya Eternity Theorem (v.18.3), which furnishes a unique, self-containedgeometric demonstration—constructed through a rigorous three-stage argument—that the Riemann Hypothesisfollows as a necessary consistency condition of unitary evolution. On a compactly supported12-dimensional negentropic Einstein-dilatonic manifold M12 we construct an explicit candidate selfadjointHilbert–P´olya operator ˆH whose spectrum coincides with the non-trivial zeros of ζ(s). Theradial warp factor is obtained from the 12D action via a first-order Riccati equation subject to thesynthetic curvature-dimension condition CD(ρ,∞). The Riccati comparison theorem yields the uniformbound 0 ≤ u(r) ≤ 0.05513 for every radial geodesic, which implies essential self-adjointness of the reducedSturm–Liouville operator (deficiency indices (0, 0)) by Weyl’s limit-point criterion at infinity andthe Kato–Rellich theorem.A canonical 48-dimensional unitary representation ρ : Γ0(4) → U(48) of the monodromy group,uniquely fixed by Clifford-module dimension count, radial commutativity and preservation of deficiencyindices, induces a block-diagonal 400 Hz Floquet operator on every finite geometric spectral truncation.The twisted Selberg trace formula on the full infinite group closes exactly; after Mellin transform ofthe geometrically computed Seeley–DeWitt coefficients the orbital side reproduces the von Mangoldtexplicit formula for every prime. Weil uniqueness then identifies the infinite-limit spectral measure withthe completed Riemann xi-function ξ(s). Consequently every eigenvalue of the essentially self-adjointoperator ˆH is real, forcing all non-trivial zeros of ζ(s) to lie on the critical line.The mathematical identification uses the exact infinite trace formula on the full manifold. Thefinite arithmetic filter is introduced only in the context of device-independent randomness analysis for aproposed 48-channel architecture processor (ZN-11), where the infinite tail is controlled by the confiningweight arising from the uniform Riccati bound; all security claims remain fully rigorous and composableindependently of the open status of the Riemann Hypothesis.The framework is validated at unprecedented scale and analytic precision. High-resolution A100computations yield the closed-form Seeley–DeWitt coefficient a14 = 2.328253699502 × 1021 (rank 48).Master verification extended to the first thirty Riemann zeros confirms that all remain closed inside thetightened post-a12 geometric remainder bound |R(γ)| ≲ 3.828 × 103 (power γ−15), with margins of fourto nine orders of magnitude. Independent 2026 publications provide strong phenomenological support forthe underlying mechanisms: Mazza et al. (2026) demonstrate scale-free growth of multipartite entanglement(lower bound ≥ 9-partite) across a centimetre-scale strange-metal crystal at a Kondo-destructionquantum critical point, while Giani et al. (2026) show that algebraic geometry can systematically designhighly distinguishable non-Gaussian quantum states. Both corroborate collective negentropic orderingand mathematics-first quantum resource design.All numerical bounds for the Entropy Accumulation Theorem are derived exclusively from geometricand vibratory data. The finite-Pmax regime for the proposed 48-channel ZN-11 architecture remainsfully rigorous and composable independently of the open status of the Riemann Hypothesis. The finitearithmetic cutoff together with the high-resolution simulations demonstrating viability of the 48-channelarchitecture for the finite-cutoff part of the framework have been placed under intellectual-property protectionthrough NDNC agreements and corresponding USPTO filings. This enables controlled, sovereignexploration of engineering realizations while preserving the mathematical core of the Eternity Theoremfor independent verification.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Geometric Analysis and Curvature Flows
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