Riemann Hypothesis as a Physical Law: Operator‑Spectral Reconstruction of Time from Zeta Zero Dynamics
Abstract
A time‑spectral framework is proposed in which the imaginary parts of the non‑trivial zeros of the Riemann zeta function are interpreted as physical time eigenvalues of a fundamental quantum evolutionary operator. Within this paradigm, the Riemann prime‑counting function becomes an exact, non‑perturbative dynamical law governing discrete quantum time, while the Riemann Hypothesis is reinterpreted as a necessary and sufficient spectral stability condition for temporal coherence and vacuum unitarity. The work establishes a rigorous operator‑spectral bridge mapping zeta zero data to prime indexing as a discrete temporal register. Cosmological scaling is incorporated by demonstrating that the observed age of the Universe corresponds to a specific discrete selection within a 10^233‑order time domain. A minimal Hamiltonian model, a unit‑conversion mechanism, and a non‑perturbative metric on number‑space are constructed, elevating the Riemann Hypothesis from a complex‑analytic conjecture to a fundamental physical law governing the stability of time.
Related
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- Spectral Reconstruction of Lorentz Structure from the χ‑Operator An Operator‑Theoretic Resolution of Non‑Transitivity in Special Relativity
- χ‑Spectral Reconstruction of the Klein Paradox: Operator‑Topological Origin of χ‑Current in Strong Fields
- Spectral Reconstruction of Hyperbolic Geometry as a Topological Invariant of a Self‑Adjoint Operator
BibTeX
@misc{mukha2026riemann,
title = {{Riemann Hypothesis as a Physical Law: Operator‑Spectral Reconstruction of Time from Zeta Zero Dynamics}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = aug,
doi = {10.5281/zenodo.21841095},
url = {https://doi.org/10.5281/zenodo.21841095},
note = {CC BY},
}
RIS
TY - UNPB
TI - Riemann Hypothesis as a Physical Law: Operator‑Spectral Reconstruction of Time from Zeta Zero Dynamics
AU - Anatolii Mukha
PY - 2026
DA - 2026/08/07
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21841095
UR - https://doi.org/10.5281/zenodo.21841095
AB - A time‑spectral framework is proposed in which the imaginary parts of the non‑trivial zeros of the Riemann zeta function are interpreted as physical time eigenvalues of a fundamental quantum evolutionary operator. Within this paradigm, the Riemann prime‑counting function becomes an exact, non‑perturbative dynamical law governing discrete quantum time, while the Riemann Hypothesis is reinterpreted as a necessary and sufficient spectral stability condition for temporal coherence and vacuum unitarity. The work establishes a rigorous operator‑spectral bridge mapping zeta zero data to prime indexing as a discrete temporal register. Cosmological scaling is incorporated by demonstrating that the observed age of the Universe corresponds to a specific discrete selection within a 10^233‑order time domain. A minimal Hamiltonian model, a unit‑conversion mechanism, and a non‑perturbative metric on number‑space are constructed, elevating the Riemann Hypothesis from a complex‑analytic conjecture to a fundamental physical law governing the stability of time.
ER -