Riemann Operator 2M Zeros — Diagonal Spectrum of the First 2,001,052 Non-Trivial Zeros

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. It is the simplest spectral realization of the Riemann zeros and serves as a practical computational tool for: High-precision prime counting \(\pi(x)\) via the explicit formula (relative error 0.009% at \(x=10^{18}\), new estimates up to \(x=10^{24}\)) Black-hole entropy fluctuation spectra (treating \(H\) as the microstate Hamiltonian) Usage Load with tvals = np.load("natural_operator_2M.npy"). All results in the associated paper and notebook are generated directly from this file. Repository https://github.com/core-theoretics/riemann-operator-explorer Paper Gidman, J. (2026). A Practical Diagonal Realization of the Hilbert–Pólya Operator. arXiv [to be added] License CC0 1.0 Universal (Public Domain Dedication) — no restrictions on reuse. Keywords Riemann zeta zeros, Hilbert-Pólya conjecture, prime counting, explicit formula, black-hole entropy, spectral operator