Asymptotic Exactness of the Toroidal Prime Wave Function: Insensitivity to Error at Large Scale, Perfect Reconstruction of the Prime Distribution, and a Geometric Approach to the Riemann Hypothesis
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901798342623232 |
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| author | Lainé, Jean-Pierre |
| author_facet | Lainé, Jean-Pierre |
| contents | <p>We demonstrate that the toroidal prime wave function — constructed from the imaginary parts of the non-trivial zeros of the Riemann zeta function as a logarithmic chirp correction on the median axis of the Prime Vase — achieves asymptotically exact reconstruction of the prime distribution. The residual decreases monotonically with prime magnitude: the arithmetic mass principle. The larger the prime, the more precise the reconstruction. Interactive visualizations available at genesis1.net. Third in the Genesis-1 prime geometry series.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19074917 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Asymptotic Exactness of the Toroidal Prime Wave Function: Insensitivity to Error at Large Scale, Perfect Reconstruction of the Prime Distribution, and a Geometric Approach to the Riemann Hypothesis Lainé, Jean-Pierre prime numbers, Riemann hypothesis, wave function, logarithmic chirp, arithmetic mass, toroidal geometry, Genesis-1, asymptotic exactness, prime gaps, Nelder-Mead optimization <p>We demonstrate that the toroidal prime wave function — constructed from the imaginary parts of the non-trivial zeros of the Riemann zeta function as a logarithmic chirp correction on the median axis of the Prime Vase — achieves asymptotically exact reconstruction of the prime distribution. The residual decreases monotonically with prime magnitude: the arithmetic mass principle. The larger the prime, the more precise the reconstruction. Interactive visualizations available at genesis1.net. Third in the Genesis-1 prime geometry series.</p> |
| title | Asymptotic Exactness of the Toroidal Prime Wave Function: Insensitivity to Error at Large Scale, Perfect Reconstruction of the Prime Distribution, and a Geometric Approach to the Riemann Hypothesis |
| topic | prime numbers, Riemann hypothesis, wave function, logarithmic chirp, arithmetic mass, toroidal geometry, Genesis-1, asymptotic exactness, prime gaps, Nelder-Mead optimization |
| url | https://doi.org/10.5281/zenodo.19074917 |