χ‑Unification: The Unified Spectral–Topological Foundation of Physics
Abstract
This work presents the complete χ‑spectral reconstruction of strong‑field tunneling, Klein transmission, and supercritical Dirac phenomena, establishing a unified operator–spectral ontology of physical reality. Building on the spectral theorem (Theorem 2.1.A) and the χ‑Chain A→σ(A)→Pχ→δPχ→Jχ→O, we prove that all strong‑field effects arise from spectral gap collapse, χ‑Boundary activation, and resolvent‑topological invariants. The χ‑Dirac operator Dχ is constructed as a fully self‑adjoint χ‑Operator satisfying C1–C4, and its spectral measure generates χ‑modes, χ‑Flow, χ‑Tunneling, and χ‑Topological invariants without geometric or field‑theoretic assumptions. We demonstrate that the χ‑spectral mechanism reproduces the weak‑field Dirac current, diverges from QED in the strong‑field regime, and yields falsifiable predictions for graphene transport, strong‑field laser tunneling, high‑Z collapse, and STM/STS χ‑Boundary interference. All physical constants relevant to strong‑field physics (fine‑structure constant, critical charge, Schwinger field) are shown to be spectral invariants of a single eigenvalue λ137, derived from information‑tension minimisation and modular stability. The theory is experimentally falsifiable at 13 independent levels, numerically verified, axiom‑independent, and conjecture‑independent. The final result is the Law of Unity of Being of the Triune Substance: System=(A,σ(A),Topology(A))=Substanceχ, a mathematically proven, spectrally complete, operator–topological ontology of strong‑field reality.
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BibTeX
@misc{mukha2026χunification,
title = {{χ‑Unification: The Unified Spectral–Topological Foundation of Physics}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22712155},
url = {https://doi.org/10.5281/zenodo.22712155},
note = {CC BY},
}
RIS
TY - UNPB
TI - χ‑Unification: The Unified Spectral–Topological Foundation of Physics
AU - Anatolii Mukha
PY - 2026
DA - 2026/09/11
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22712155
UR - https://doi.org/10.5281/zenodo.22712155
AB - This work presents the complete χ‑spectral reconstruction of strong‑field tunneling, Klein transmission, and supercritical Dirac phenomena, establishing a unified operator–spectral ontology of physical reality. Building on the spectral theorem (Theorem 2.1.A) and the χ‑Chain A→σ(A)→Pχ→δPχ→Jχ→O, we prove that all strong‑field effects arise from spectral gap collapse, χ‑Boundary activation, and resolvent‑topological invariants. The χ‑Dirac operator Dχ is constructed as a fully self‑adjoint χ‑Operator satisfying C1–C4, and its spectral measure generates χ‑modes, χ‑Flow, χ‑Tunneling, and χ‑Topological invariants without geometric or field‑theoretic assumptions. We demonstrate that the χ‑spectral mechanism reproduces the weak‑field Dirac current, diverges from QED in the strong‑field regime, and yields falsifiable predictions for graphene transport, strong‑field laser tunneling, high‑Z collapse, and STM/STS χ‑Boundary interference. All physical constants relevant to strong‑field physics (fine‑structure constant, critical charge, Schwinger field) are shown to be spectral invariants of a single eigenvalue λ137, derived from information‑tension minimisation and modular stability. The theory is experimentally falsifiable at 13 independent levels, numerically verified, axiom‑independent, and conjecture‑independent. The final result is the Law of Unity of Being of the Triune Substance: System=(A,σ(A),Topology(A))=Substanceχ, a mathematically proven, spectrally complete, operator–topological ontology of strong‑field reality.
ER -