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2025
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| Online Access: | https://doi.org/10.5281/zenodo.15651382 |
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| _version_ | 1866901472182009856 |
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| author | Okolo, Hanyelichukwu Paul |
| author_facet | Okolo, Hanyelichukwu Paul |
| contents | <div> <div> <div> <p>This paper presents a novel approach to the Riemann Hypothesis (RH) by analyzing the asymptotic behavior of a prime-based vorticity function S(t) = p≤1/t p sin(pt) as t → 0+. Employing the Organized Complexity (OC) framework, we demonstrate that RH holds if and only if S(t) exhibits polynomial growth with a logarithmic correction, specifically O t−2(log(1/t))−1 . The OC framework leverages Structured Dissipation and Sixness Symmetry to enforce cancellations among oscillatory terms, ensuring controlled growth. This work not only strengthens the evidence for RH but also highlights the OC framework as a powerful tool for addressing complex problems in number theory and beyond.</p> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15651382 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Dynamical Systems Approach to the Riemann Hypothesis via the Organized Complexity Framework, Proof of S(t) behavior as it tends to 0. Okolo, Hanyelichukwu Paul <div> <div> <div> <p>This paper presents a novel approach to the Riemann Hypothesis (RH) by analyzing the asymptotic behavior of a prime-based vorticity function S(t) = p≤1/t p sin(pt) as t → 0+. Employing the Organized Complexity (OC) framework, we demonstrate that RH holds if and only if S(t) exhibits polynomial growth with a logarithmic correction, specifically O t−2(log(1/t))−1 . The OC framework leverages Structured Dissipation and Sixness Symmetry to enforce cancellations among oscillatory terms, ensuring controlled growth. This work not only strengthens the evidence for RH but also highlights the OC framework as a powerful tool for addressing complex problems in number theory and beyond.</p> </div> </div> </div> |
| title | A Dynamical Systems Approach to the Riemann Hypothesis via the Organized Complexity Framework, Proof of S(t) behavior as it tends to 0. |
| url | https://doi.org/10.5281/zenodo.15651382 |