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| Format: | Recurso digital |
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Zenodo
2026
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| Teme: | |
| Online dostop: | https://doi.org/10.5281/zenodo.19026613 |
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- <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>