The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant
Abstract
In the ZEBTS‑SUPER framework (Zero‑Entropy Background Topological Structure under chi‑variational optimization), the dimensionless fine‑structure constant inverse alpha^{-1} ≈ 137.035999 is not an empirical fitting parameter, but a topological‑spectral invariant. We prove that k = 137 is the unique discrete index of the eigenvalue lambda_137 of an unbounded, self‑adjoint chi‑operator D_chi(zeta) acting on the Hilbert space H_chi. This specific mode simultaneously minimizes the gauge‑information tension tensor T_inf and stabilizes Tomita–Takesaki modular dynamics sigma_t^chi at a finite characteristic scale T_chi(137). From this operator‑theoretic foundation, we present an analytical derivation of alpha, a numerical finite‑difference calculation of lambda_137 achieving 10^{-6} agreement, and a rigorous proof of electromagnetic vacuum stability. We delineate verifiable experimental signatures including hydrogen hyper‑fine shifts, QED vertex corrections, electron anomalous magnetic moment deviations (delta g_chi ~ 10^{-12}), and strong‑field Schwinger threshold corrections. Introduction and Ontological Background
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BibTeX
@misc{mukha2026number,
title = {{The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21558238},
url = {https://doi.org/10.5281/zenodo.21558238},
note = {CC BY},
}
RIS
TY - UNPB
TI - The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant
AU - Anatolii Mukha
PY - 2026
DA - 2026/07/25
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21558238
UR - https://doi.org/10.5281/zenodo.21558238
AB - In the ZEBTS‑SUPER framework (Zero‑Entropy Background Topological Structure under chi‑variational optimization), the dimensionless fine‑structure constant inverse alpha^{-1} ≈ 137.035999 is not an empirical fitting parameter, but a topological‑spectral invariant. We prove that k = 137 is the unique discrete index of the eigenvalue lambda_137 of an unbounded, self‑adjoint chi‑operator D_chi(zeta) acting on the Hilbert space H_chi. This specific mode simultaneously minimizes the gauge‑information tension tensor T_inf and stabilizes Tomita–Takesaki modular dynamics sigma_t^chi at a finite characteristic scale T_chi(137). From this operator‑theoretic foundation, we present an analytical derivation of alpha, a numerical finite‑difference calculation of lambda_137 achieving 10^{-6} agreement, and a rigorous proof of electromagnetic vacuum stability. We delineate verifiable experimental signatures including hydrogen hyper‑fine shifts, QED vertex corrections, electron anomalous magnetic moment deviations (delta g_chi ~ 10^{-12}), and strong‑field Schwinger threshold corrections. Introduction and Ontological Background
ER -