Gravity and Temporal Coherence in the Zero‑Point Event‑Based Time‑Spectrum (ZEBTS) Paradigm: A Closed Axiomatic Proof System
Abstract
The χ‑Reality SUPER 9.0 and ZEBTS‑SUPER frameworks developed in this work establish a unified operator‑spectral foundation for physics that replaces the ontologically fragile continuum geometry with a discrete ultrametric arithmetic substrate. Classical spacetime, curvature, quantum fields, gauge interactions, and measurement processes do not exist microscopically; instead, they emerge as continuum projections of bounded operators acting across modular scale layers Λ(k) and prime‑indexed temporal progression K = π(N). This operator‑spectral substrate eliminates curvature singularities, ultraviolet divergences, infrared instabilities, and temporal inconsistencies inherent to General Relativity and Quantum Field Theory. The χ‑phase operator Φχ, boundary tension Bχ, spectral curvature Rχ, gauge operator Fχ, and temporal operator H_time form the unified algebra A_total, from which all physical structures are reconstructed. Effective geometry arises from spectral gradients ∇ΛΦχ, producing gμν, Rμν, and Gμν without assuming a smooth manifold. Time is a spectral phenomenon determined by the eigenvalues of H_time, corresponding to imaginary parts of non‑trivial zeta zeros, ensuring vacuum stability and eliminating the continuum’s temporal paradoxes. Quantum mechanics is fully compatible with ZEBTS‑SUPER gravity because all dynamical, geometric, and measurement processes are operator‑spectral. Quantum probabilities arise from the χ‑inner product; collapse is a finite modular projection; decoherence is governed by spectral gradients; and all observables remain bounded. Gravitational curvature Rχ enters the unified Hamiltonian Hχ as an operator term, allowing quantum states to propagate on χ‑spectral geometry without singularities or background inconsistencies. The theory yields strict ultraviolet stability, divergence‑free dynamics, bounded curvature, and a unified description of gravity, gauge fields, matter excitations, and measurement. GR, QFT, and the Standard Model appear as continuum shadows of A_total. The framework provides new predictions for quantum coherence, horizon formation, cosmology, and operator‑geometric quantum gravity. χ‑Reality and ZEBTS‑SUPER together establish a mathematically complete, physically finite, and globally unified operator‑spectral foundation for fundamental physics.
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BibTeX
@misc{mukha2026gravity,
title = {{Gravity and Temporal Coherence in the Zero‑Point Event‑Based Time‑Spectrum (ZEBTS) Paradigm: A Closed Axiomatic Proof System}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22673777},
url = {https://doi.org/10.5281/zenodo.22673777},
note = {CC BY},
}
RIS
TY - UNPB
TI - Gravity and Temporal Coherence in the Zero‑Point Event‑Based Time‑Spectrum (ZEBTS) Paradigm: A Closed Axiomatic Proof System
AU - Anatolii Mukha
PY - 2026
DA - 2026/09/09
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22673777
UR - https://doi.org/10.5281/zenodo.22673777
AB - The χ‑Reality SUPER 9.0 and ZEBTS‑SUPER frameworks developed in this work establish a unified operator‑spectral foundation for physics that replaces the ontologically fragile continuum geometry with a discrete ultrametric arithmetic substrate. Classical spacetime, curvature, quantum fields, gauge interactions, and measurement processes do not exist microscopically; instead, they emerge as continuum projections of bounded operators acting across modular scale layers Λ(k) and prime‑indexed temporal progression K = π(N). This operator‑spectral substrate eliminates curvature singularities, ultraviolet divergences, infrared instabilities, and temporal inconsistencies inherent to General Relativity and Quantum Field Theory. The χ‑phase operator Φχ, boundary tension Bχ, spectral curvature Rχ, gauge operator Fχ, and temporal operator H_time form the unified algebra A_total, from which all physical structures are reconstructed. Effective geometry arises from spectral gradients ∇ΛΦχ, producing gμν, Rμν, and Gμν without assuming a smooth manifold. Time is a spectral phenomenon determined by the eigenvalues of H_time, corresponding to imaginary parts of non‑trivial zeta zeros, ensuring vacuum stability and eliminating the continuum’s temporal paradoxes. Quantum mechanics is fully compatible with ZEBTS‑SUPER gravity because all dynamical, geometric, and measurement processes are operator‑spectral. Quantum probabilities arise from the χ‑inner product; collapse is a finite modular projection; decoherence is governed by spectral gradients; and all observables remain bounded. Gravitational curvature Rχ enters the unified Hamiltonian Hχ as an operator term, allowing quantum states to propagate on χ‑spectral geometry without singularities or background inconsistencies. The theory yields strict ultraviolet stability, divergence‑free dynamics, bounded curvature, and a unified description of gravity, gauge fields, matter excitations, and measurement. GR, QFT, and the Standard Model appear as continuum shadows of A_total. The framework provides new predictions for quantum coherence, horizon formation, cosmology, and operator‑geometric quantum gravity. χ‑Reality and ZEBTS‑SUPER together establish a mathematically complete, physically finite, and globally unified operator‑spectral foundation for fundamental physics.
ER -