Monograph ZEBTS‑∞: χ‑Ontology of Infinite Structures

ZEBTS‑∞: χ‑Ontology of Infinite Structures presents a unified operator‑spectral framework in which geometry, information, computation, and ontology emerge from infinite χ‑spectral foundations. χ‑ontology defines the primitive layer of reality through infinite spectral modes, correlation kernels, localization functionals, and hyperbolic curvature. These elements generate χ‑spectral geometry, providing metric, curvature, boundary, and manifold structures that extend naturally into the infinite domain. The theory develops χ‑anomaly analysis, including χ‑anomaly geometry, χ‑anomaly dynamics, and χ‑anomaly collapse, describing how infinite systems maintain structural consistency under spectral deviations. χ‑computational structures formalize the operator‑algebraic substrate of computation, defining χ‑machines, χ‑automata, χ‑networks, χ‑graphs, χ‑circuits, and χ‑pipelines as spectral‑hyperbolic devices capable of universal computation in infinite χ‑spaces. χ‑complexity classes classify computational objects by spectral dependence, correlation structure, localization filtering, boundary support, hyperbolic weighting, χ‑∞ projection, and universal reachability. The monograph integrates external foundations from spectral geometry, operator theory, information theory, algorithmic complexity, Ricci flow, optimal transport, invariant set theory, structural realism, and quantum foundations. These sources provide structural constraints and ontological justification for the infinite χ‑framework. χ‑operator cosmology describes boundary‑driven expansion, modular operator reality, and the emergence of matter from infinite relational geometry. ZEBTS‑∞ establishes a complete hierarchy of infinite χ‑structures and demonstrates how physical law, spacetime, matter, and information arise from χ‑spectral relations. It provides a coherent operator‑spectral ontology unifying mathematical physics, geometry, computation, and metaphysics.