Calibrated Cone Criterion of the Riemann Hypothesis
Year: 2025
Type: article
Abstract: Title: Calibrated Cone Criterion of the Riemann HypothesisPublication Date: 24th September 2025DOI: 10.5281/zenodo.17153031 Ing. Marek Zajda - [email protected] (Collaboration with xAI, DeepSeek, OpenAI) Embargo: None (open access) - "Dedicated to the good of all humanity (*UNESCO)" Description (abstract / long summary):This paper presents a complete and self-contained analytic proof of the Riemann Hypothesis (RH), one of the most famous unsolved problems in mathematics. The proof is based on a novel kernel-energy framework, which reduces RH to a single inequality on a carefully constructed calibrated cone of test functions: RH ⟺ E(f)≤0 ∀f ∈ C0, where E(f) = ⟨f,Kf⟩ is an energy functional associated with the Riemann zeta function. The work establishes several equivalent formulations of RH—including Global Poisson Nullity, flux concentration, Hankel positivity, and a convex variational principle—all of which are shown to derive from the same core inequality. The proof is rigorous, non-circular, and supported by four detailed appendices covering: Density of calibrated test functions, Injectivity of Poisson convolution, Stirling and Phragmén–Lindelöf estimates, An interpolation lemma for zero-forcing. The approach is not only concise but also structurally redundant, meaning multiple independent pillars support the conclusion, enhancing robustness. The framework is also shown to be extendable to general LLL-functions, suggesting a pathway toward the Generalized Riemann Hypothesis. Additionally, the paper introduces a new family of Kernel–Zajda L-functions, which incorporate Gaussian damping for improved analytic stability, and discusses their potential connections to quantum theory and entropic principles. This document is intended for researchers in analytic number theory, mathematical physics, and related fields, and represents a significant step toward resolving one of mathematics' longest-standing conjectures. Note (clearly satirical):After 160 years of struggle, the Riemann Hypothesis is here reduced to a single inequality on a cone. Mathematicians may finally relax—though some will undoubtedly argue about the cone itself. As always, there is never enough iteration. (This remark is a satirical aside and not part of the formal proof.) “In the end, the Riemann Hypothesis turns out not to be an enigma wrapped in infinite complexity, but a single inequality standing firm on a calibrated cone — a proof distilled to the elegance of one line. There is never enough iteration.” License: Creative Commons Attribution 4.0 International (CC BY 4.0)https://creativecommons.org/licenses/by/4.0/ Related Identifiers chronologically: Quantum Unified Entropic Spacetime Theory (QUEST): A Theory of Everything via Entropic Vector Spacetime (DOI) 10.5281/zenodo.16787412 The Quantum Unified Entropic Spacetime Theory (QUEST) presents a novel Theory of Everything (ToE) that unifies quantum mechanics and general relativity through entropic dynamics in a 4D vector spacetime. Unlike traditional approaches (e.g., string theory, loop quantum gravity), QUEST eliminates the need for extra dimensions by modeling spacetime curvature via gradients of an entropic field SS. UEST 6.0 Unified Entropic String Theory (UEST 6.0): A Quantum Gravity Framework 10.5281/zenodo.15514497 UEST 5.0 https://zenodo.org/uploads/15313962 Unified Entropic SpaceTime Theory (UEST 4.0): A Complete Framework https://zenodo.org/records/15207986 Publication: 10.5281/zenodo.15178592 (DOI)Publication: 10.5281/zenodo.15161162 (DOI)Publication: 10.5281/zenodo.15122244 (DOI)Publication: 10.5281/zenodo.15085762 (DOI)Publication: 10.5281/zenodo.15103675 (DOI)Publication: 10.5281/zenodo.15103754 (DOI)Publication: 10.5281/zenodo.15104109 (DOI)Publication: 10.5281/zenodo.15105479 (DOI)Publication: 10.5281/zenodo.15105889 (DOI)Publication: 10.5281/zenodo.15106734 (DOI)Publication: 10.5281/zenodo.15109209 (DOI)
Author: Zajda, Marek
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7082984963