| _version_ | 1866901378286223360 |
|---|---|
| author | Gidman, Jordan |
| author_facet | Gidman, Jordan |
| contents | <p>This file (natural_operator_2M.npy, 15.26 MB) contains the pure diagonal operator \( H = \operatorname{diag}(t_1, t_2, \dots, t_{2\,001\,052}) \), where \( t_n \) are the imaginary parts of the first 2,001,052 non-trivial Riemann zeros.</p> <p>It is the simplest spectral realization of the Riemann zeros and serves as a practical computational tool for:</p> <p>High-precision prime counting \(\pi(x)\) via the explicit formula (relative error 0.009% at \(x=10^{18}\), new estimates up to \(x=10^{24}\))</p> <p>Black-hole entropy fluctuation spectra (treating \(H\) as the microstate Hamiltonian)</p> <p>Usage</p> <p>Load with tvals = np.load("natural_operator_2M.npy"). All results in the associated paper and notebook are generated directly from this file.</p> <p>Repository</p> <p>https://github.com/core-theoretics/riemann-operator-explorer</p> <p>Paper</p> <p>Gidman, J. (2026). A Practical Diagonal Realization of the Hilbert–Pólya Operator. arXiv [to be added]</p> <p>License</p> <p>CC0 1.0 Universal (Public Domain Dedication) — no restrictions on reuse.</p> <p>Keywords</p> <p>Riemann zeta zeros, Hilbert-Pólya conjecture, prime counting, explicit formula, black-hole entropy, spectral operator</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19026613 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Riemann Operator 2M Zeros — Diagonal Spectrum of the First 2,001,052 Non-Trivial Zeros Gidman, Jordan Riemann zeros Hilbert-Pólya prime counting black hole entropy <p>This file (natural_operator_2M.npy, 15.26 MB) contains the pure diagonal operator \( H = \operatorname{diag}(t_1, t_2, \dots, t_{2\,001\,052}) \), where \( t_n \) are the imaginary parts of the first 2,001,052 non-trivial Riemann zeros.</p> <p>It is the simplest spectral realization of the Riemann zeros and serves as a practical computational tool for:</p> <p>High-precision prime counting \(\pi(x)\) via the explicit formula (relative error 0.009% at \(x=10^{18}\), new estimates up to \(x=10^{24}\))</p> <p>Black-hole entropy fluctuation spectra (treating \(H\) as the microstate Hamiltonian)</p> <p>Usage</p> <p>Load with tvals = np.load("natural_operator_2M.npy"). All results in the associated paper and notebook are generated directly from this file.</p> <p>Repository</p> <p>https://github.com/core-theoretics/riemann-operator-explorer</p> <p>Paper</p> <p>Gidman, J. (2026). A Practical Diagonal Realization of the Hilbert–Pólya Operator. arXiv [to be added]</p> <p>License</p> <p>CC0 1.0 Universal (Public Domain Dedication) — no restrictions on reuse.</p> <p>Keywords</p> <p>Riemann zeta zeros, Hilbert-Pólya conjecture, prime counting, explicit formula, black-hole entropy, spectral operator</p> |
| title | Riemann Operator 2M Zeros — Diagonal Spectrum of the First 2,001,052 Non-Trivial Zeros |
| topic | Riemann zeros Hilbert-Pólya prime counting black hole entropy |
| url | https://doi.org/10.5281/zenodo.19026613 |