A Computational Realization of the Riemann Zeta Spectrum: High-Precision Prime Counting up to 1024

We construct a computational realization of the Riemann zeta spectrum using the imaginary parts of the first 2,001,052 non-trivial zeros. This 15.26 MB diagonal matrix H =diag(tn) (archived at Zenodo, DOI 10.5281/zenodo.19026613) serves as a high-fidelity tool for evaluating eigenvalue-dependent functions in number theory. We apply this realization to the explicit formula for the prime-counting function π(x), yielding a relative error of 0.009% at x = 1018. Additionally, we utilize the spectral density to model black-hole entropy fluctuation spectra.Zenodo Dataset: 10.5281/zenodo.19026613 Project Repository: https://github.com/core-theoretics/riemann-operator-explorer