Spectral Reconstruction of Lorentz Structure from the χ‑Operator An Operator‑Theoretic Resolution of Non‑Transitivity in Special Relativity
Abstract
This work establishes a complete reconstruction of Lorentz structure as a χ‑spectral phenomenon, demonstrating that spacetime geometry is not a primitive assumption but a derived spectral invariant of the χ‑operator Dχ. The metric, signature, curvature, Lorentz group, and transformation laws arise from three spectral primitives: the χ‑spectral density ρχ, the χ‑Boundary projection Pk∗, and the χ‑flow Φτ. Classical non‑transitivity of Lorentz boosts in strong fields is reinterpreted as a physical signature of χ‑defects — local perturbations of the χ‑Boundary — and is fully resolved by the χ‑flow, which restores exact transitivity at the spectral level. Thus Lorentz symmetry is not broken; it is spectrally conserved. The χ‑Spectral Lorentz Geometry is fully consistent with ZEBTS‑SUPER ∞ and the Law of Unity of Being: space is the support of the χ‑Boundary, time is the logarithmic spectral derivative of ρχ, curvature is the second spectral derivative, and Lorentz transformations are modular flows. No geometric object is postulated; every geometric structure is reconstructed from spectral data. The theory produces six independent, falsifiable predictions — χ‑peaks, χ‑shifts, χ‑topological transitions, χ‑Boundary deviations, χ‑modified tunnelling exponents, and χ‑qubit relaxation — each with explicit scaling laws and experimental thresholds. Three predictions are testable immediately with existing technology. This work forms the Lorentz‑spectral chapter of the Universal Law of Everything, completing the spectral reconstruction of relativistic structure.
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BibTeX
@misc{mukha2026spectral,
title = {{Spectral Reconstruction of Lorentz Structure from the χ‑Operator An Operator‑Theoretic Resolution of Non‑Transitivity in Special Relativity}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22734575},
url = {https://doi.org/10.5281/zenodo.22734575},
note = {CC BY},
}
RIS
TY - UNPB
TI - Spectral Reconstruction of Lorentz Structure from the χ‑Operator An Operator‑Theoretic Resolution of Non‑Transitivity in Special Relativity
AU - Anatolii Mukha
PY - 2026
DA - 2026/09/13
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22734575
UR - https://doi.org/10.5281/zenodo.22734575
AB - This work establishes a complete reconstruction of Lorentz structure as a χ‑spectral phenomenon, demonstrating that spacetime geometry is not a primitive assumption but a derived spectral invariant of the χ‑operator Dχ. The metric, signature, curvature, Lorentz group, and transformation laws arise from three spectral primitives: the χ‑spectral density ρχ, the χ‑Boundary projection Pk∗, and the χ‑flow Φτ. Classical non‑transitivity of Lorentz boosts in strong fields is reinterpreted as a physical signature of χ‑defects — local perturbations of the χ‑Boundary — and is fully resolved by the χ‑flow, which restores exact transitivity at the spectral level. Thus Lorentz symmetry is not broken; it is spectrally conserved. The χ‑Spectral Lorentz Geometry is fully consistent with ZEBTS‑SUPER ∞ and the Law of Unity of Being: space is the support of the χ‑Boundary, time is the logarithmic spectral derivative of ρχ, curvature is the second spectral derivative, and Lorentz transformations are modular flows. No geometric object is postulated; every geometric structure is reconstructed from spectral data. The theory produces six independent, falsifiable predictions — χ‑peaks, χ‑shifts, χ‑topological transitions, χ‑Boundary deviations, χ‑modified tunnelling exponents, and χ‑qubit relaxation — each with explicit scaling laws and experimental thresholds. Three predictions are testable immediately with existing technology. This work forms the Lorentz‑spectral chapter of the Universal Law of Everything, completing the spectral reconstruction of relativistic structure.
ER -