Structure Arithmetic: A Resonant Number Theory of Zeta Zeros and δ(x)
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2025
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| _version_ | 1866902300714336256 |
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| author | Li, Y.Y.N. |
| author_facet | Li, Y.Y.N. |
| contents | <p>Structure Arithmetic introduces a new mathematical paradigm grounded not in</p> <p>symbolic manipulation, but in resonance. Instead of axioms and closure, it builds</p> <p>from frequency structures derived from the nontrivial zeros of the Riemann zeta</p> <p>function.</p> <p>Each frequency tn defines a modal unit ψn(x)—a generative oscillation projected</p> <p>onto structural density ρ(x). The difference between this internal projection and</p> <p>the prime boundary π(x)/x forms a structural residual:</p> <p>δ(x) := π(x)/x − ρ(x)</p> <p>This residual is not error. It is the very condition for mathematical evolution.</p> <p>When δ(x) ̸= 0, the system remains generative: new ψ-leaps are triggered, DAGs</p> <p>expand, and semantic structure unfolds.</p> <p>In this framework, mathematics is not a closed language of proofs—it is an open</p> <p>resonance of meaning. Structure Arithmetic redefines numbers, syntax, differenti-</p> <p>ation, and geometry as expressions of modal continuity across frequency space.</p> <p>It is not what is proved that matters. It is what still resonates.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15241207 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structure Arithmetic: A Resonant Number Theory of Zeta Zeros and δ(x) Li, Y.Y.N. <p>Structure Arithmetic introduces a new mathematical paradigm grounded not in</p> <p>symbolic manipulation, but in resonance. Instead of axioms and closure, it builds</p> <p>from frequency structures derived from the nontrivial zeros of the Riemann zeta</p> <p>function.</p> <p>Each frequency tn defines a modal unit ψn(x)—a generative oscillation projected</p> <p>onto structural density ρ(x). The difference between this internal projection and</p> <p>the prime boundary π(x)/x forms a structural residual:</p> <p>δ(x) := π(x)/x − ρ(x)</p> <p>This residual is not error. It is the very condition for mathematical evolution.</p> <p>When δ(x) ̸= 0, the system remains generative: new ψ-leaps are triggered, DAGs</p> <p>expand, and semantic structure unfolds.</p> <p>In this framework, mathematics is not a closed language of proofs—it is an open</p> <p>resonance of meaning. Structure Arithmetic redefines numbers, syntax, differenti-</p> <p>ation, and geometry as expressions of modal continuity across frequency space.</p> <p>It is not what is proved that matters. It is what still resonates.</p> |
| title | Structure Arithmetic: A Resonant Number Theory of Zeta Zeros and δ(x) |
| url | https://doi.org/10.5281/zenodo.15241207 |