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

22 September 2026, Version 3
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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.

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Comment number 1, Anatolii Mukha: Sep 23, 2026, 10:29

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