χ‑Unification: The Unified Spectral–Topological Foundation of Physics

16 August 2026, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

ZEBTS‑SUPER 9.0 introduces a unified operator‑spectral framework in which spacetime, matter, fields, forces, information, entropy, causality, computation, biology, and cosmology emerge as macroscopic projections of a single non‑Hermitian χ‑operator Dχ with eigenvalues λ_n = 1/2 + i t_n. The χ‑Absolute A = Ker(Dχ) defines the zero‑entropy ground state, while the χ‑Boundary B = S^3 / I* arises from spectral activation t_n ≠ 0 and functions as the universal topological engine generating χ‑modular flows, χ‑prime‑mode topology, χ‑holography, and χ‑spectral protection. The pseudo‑Riemannian metric follows from the Dixmier trace invariant Trω([Dχ, Xμ] χJ [Dχ, Xν] χJ) = diag(1, −1, −1, −1), and the invariant speed of light is shown to be a topological constant of the noncommutative χ‑boundary ∂Sχ. A universal functional Uχ(Dχ, Sχ, Rχ, Jχ, Tχ) = 0 yields all known physical laws as macroscopic projections: gravity from χ‑entropy curvature, electrodynamics from χ‑information currents, Yang–Mills theory from χ‑boundary invariants, Dirac spectra from Riemann‑zero ordinates, and cosmology from χ‑entropic expansion. The theory develops χ‑thermodynamics, χ‑computing, χ‑condensed‑matter physics, χ‑quantum information, χ‑black‑hole dynamics, χ‑cosmogenesis, χ‑biology, and χ‑mathematics as operator‑spectral disciplines. ZEBTS‑SUPER is presented as a complete, closed, minimal Theory of Everything, deriving all physical and mathematical structure from χ‑spectral dynamics and establishing χ‑ontology as the foundational architecture of reality.

Keywords

χ‑operator
χ‑algebra Aχ
spectral dynamics
arithmetic spectrum
modular flow
Tomita–Takesaki theory
deformed Dirac–Kähler operator
Dixmier trace
Connes metric
noncommutative boundary ∂Sχ
Lorentz transformations
inner automorphisms
Wigner rotation
operator‑theoretic transitivity
spectral geometry
noncommutative space‑time.

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting and Discussion Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.
Comment number 2, Anatolii Mukha: Aug 16, 2026, 19:44

Mukha, A. (2026). Why Modern Physics Still Thinks Like Newton: A χ‑Ontological Analysis of Algebraic Substantialism in 21st‑Century Theoretical Frameworks. Zenodo. https://doi.org/10.5281/zenodo.21969597

Comment number 1, Anatolii Mukha: Aug 16, 2026, 12:51

Рекомендуемая литература. Для полного и расширенного изложения теории ZEBTS читателям рекомендуется обратиться к следующим работам: Муха, А. (2026). χ‑Спектральная реальность: Основы операторно-геометрической Вселенной. Zenodo. https://doi.org/10.5281/zenodo.21937654 Муха, А. (2026). ZEBTS — Топологический фон нулевой энтропии: χ‑Реальность. Теория всего — Версия SUPER 10 plus. Zenodo. https://doi.org/10.5281/zenodo.21921468 Муха, А. (2026). ZEBTS — Топологический фон нулевой энтропии: χ‑Реальность. Теория всего — Версия SUPER 10. Zenodo. https://doi.org/10.5281/zenodo.21893842 В этих публикациях представлена ​​структура ZEBTS в полном объеме и в процессе ее развития.