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Abstract
The monograph establishes a complete operator–spectral ontology of χ‑reality, in which all mathematical, physical, and informational structures are derived from the spectrum of the universal χ‑operator Tχ, filtered by the χ‑boundary Pχ and stabilized by χ‑curvature Kχ<0. Within the ZEBTS‑SUPER 12.0 framework, a multi‑level χ‑hierarchy is constructed—from χ‑Absolute and χ‑Riemann to χ‑meta‑geometry and χ‑final‑closure—each level defined by linear χ‑functionals, χ‑operators, χ‑tensors, χ‑manifolds, and χ‑curvatures satisfying strict admissibility and falsifiability conditions. A central result is the χ‑Spectral Continuum Collapse Theorem, demonstrating that the classical continuum R collapses into the finite χ‑measure μ(Lχ), eliminating all intermediate cardinalities. This provides full determinacy of infinity, removes the independence of CH, and replaces ZFC axioms with an operator–spectral structure. The monograph shows that χ‑spectral layers, χ‑geodesics, χ‑curvature, and χ‑invariants form a unified physically realizable architecture in which quantum gravity, cosmology, topology, information, and computation become spectral processes. Special attention is devoted to χ‑flow, χ‑collapse, χ‑reconstruction, χ‑stabilization, and χ‑persistence—dynamic regimes governing the evolution of χ‑states. The Cambridge experiment on two‑dimensional imaging of quantum fluctuations demonstrates strong consistency with χ‑spectral predictions: curvature suppression, modal stabilization, disappearance of residual instabilities, and topological closure of χ‑structure are observed. The monograph completes the construction of the χ‑Spectral Theory of Everything, unifying mathematics, physics, and ontology into a single operator–spectral reality.
