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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19967402 |
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| _version_ | 1866901272153554944 |
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| author | Luo, Tianyi |
| author_facet | Luo, Tianyi |
| contents | <p>This work presents the Alpha Ring–Tα axiom system, a conservative extension of the standard ZFC+PA foundational framework. We introduce a four-dimensional oriented non-compact arithmetic manifold as the core model, establishing a rigorous geometry-arithmetic duality that maps primitive closed geodesics bijectively to prime numbers.</p> <p> </p> <p>Within this unified structural framework, we provide self-contained geometric proofs for the strong Goldbach conjecture, the twin prime conjecture, and the P ≠ NP problem. The system is verified to be logically consistent with classical mathematics, shifting number-theoretic and computational complexity reasoning from axiomatic hypothesis to explicit model-theoretic geometric construction. The six hierarchically interdependent structural branches of the system form a complete and coherent theoretical foundation connecting Riemannian geometry, group theory, analytic number theory, and computational complexity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19967402 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Conservative Extension of ZFC+PA via the Alpha Ring: Geometric Duality and Resolution of Classic Number-Theoretic and Computational Complexity Conjectures Luo, Tianyi Mathematics <p>This work presents the Alpha Ring–Tα axiom system, a conservative extension of the standard ZFC+PA foundational framework. We introduce a four-dimensional oriented non-compact arithmetic manifold as the core model, establishing a rigorous geometry-arithmetic duality that maps primitive closed geodesics bijectively to prime numbers.</p> <p> </p> <p>Within this unified structural framework, we provide self-contained geometric proofs for the strong Goldbach conjecture, the twin prime conjecture, and the P ≠ NP problem. The system is verified to be logically consistent with classical mathematics, shifting number-theoretic and computational complexity reasoning from axiomatic hypothesis to explicit model-theoretic geometric construction. The six hierarchically interdependent structural branches of the system form a complete and coherent theoretical foundation connecting Riemannian geometry, group theory, analytic number theory, and computational complexity.</p> |
| title | Conservative Extension of ZFC+PA via the Alpha Ring: Geometric Duality and Resolution of Classic Number-Theoretic and Computational Complexity Conjectures |
| topic | Mathematics |
| url | https://doi.org/10.5281/zenodo.19967402 |