| _version_ | 1866901213175349248 |
|---|---|
| author | Муха, Анатолий |
| author_facet | Муха, Анатолий |
| contents | <h1>Abstract </h1> <p>This work develops a complete operator‑geometric theory of χ‑dark matter within the ZEBTS framework — the Zero‑Energy Balanced Topological System — in which the fundamental structure of physical reality is defined by the triune operator system χ–Γ–Ω. Unlike classical approaches based on fields and particles, χ‑geometry describes spacetime, matter, and dynamics as manifestations of a unified spectral–topological structure.</p> <p>The central object is the χ‑operator — a topological phase functional acting on Γ‑geometric and Ω‑boundary configurations. Its discrete spectrum, χ‑index, and χ‑class determine global topological constraints, admissible geometric forms, and the possible modes of material existence. Using the χ‑spectral measure, we introduce χ‑mass, while χ‑spectral discontinuities generate stable χ‑defects — fundamental, topologically protected, non‑perturbative excitations of χ‑geometry.</p> <p>We prove that χ‑defects are spectral–topological solitons, stable under all χ‑local deformations, and that they form χ‑ensembles with finite, strictly positive χ‑density. This χ‑density is an invariant of χ‑geometry and is interpreted as χ‑dark matter — a geometric, non‑particle, non‑perturbative substance arising as an unavoidable consequence of the χ‑structure. χ‑dark matter is gravitationally active yet does not interact with Standard Model fields, naturally explaining its observational invisibility.</p> <p>Explicit χ‑models are constructed and analyzed: the minimal χ‑defect, the χ‑monopole in R3, the χ‑domain wall in R4, χ‑lattice defects, and χ‑cosmological transitions. These examples demonstrate the universality of χ‑geometry and reproduce key astrophysical and cosmological phenomena traditionally attributed to dark matter.</p> <p>We show that χ‑geometry is quantum‑consistent, renormalizable, and UV‑complete: the χ‑spectrum provides a natural ultraviolet regularization, the χ‑index eliminates anomalies, and χ‑dynamics generates unitary evolution. In the low‑frequency limit, χ‑geometry reduces to general relativity, and in the small‑gap limit to quantum field theory, ensuring compatibility with observed physics.</p> <p>The results demonstrate that dark matter, geometry, and matter itself are manifestations of a single χ‑spectral structure. χ‑geometry emerges as a fundamental operator‑geometric foundation of physical reality, in which spacetime, particles, and interactions arise as spectral–topological effects of a single operator.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19972854 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Topological–Operator χ‑Geometry: Renormalizability, Quantum Consistency, and the Spectral Theory of Dark Matter Муха, Анатолий <h1>Abstract </h1> <p>This work develops a complete operator‑geometric theory of χ‑dark matter within the ZEBTS framework — the Zero‑Energy Balanced Topological System — in which the fundamental structure of physical reality is defined by the triune operator system χ–Γ–Ω. Unlike classical approaches based on fields and particles, χ‑geometry describes spacetime, matter, and dynamics as manifestations of a unified spectral–topological structure.</p> <p>The central object is the χ‑operator — a topological phase functional acting on Γ‑geometric and Ω‑boundary configurations. Its discrete spectrum, χ‑index, and χ‑class determine global topological constraints, admissible geometric forms, and the possible modes of material existence. Using the χ‑spectral measure, we introduce χ‑mass, while χ‑spectral discontinuities generate stable χ‑defects — fundamental, topologically protected, non‑perturbative excitations of χ‑geometry.</p> <p>We prove that χ‑defects are spectral–topological solitons, stable under all χ‑local deformations, and that they form χ‑ensembles with finite, strictly positive χ‑density. This χ‑density is an invariant of χ‑geometry and is interpreted as χ‑dark matter — a geometric, non‑particle, non‑perturbative substance arising as an unavoidable consequence of the χ‑structure. χ‑dark matter is gravitationally active yet does not interact with Standard Model fields, naturally explaining its observational invisibility.</p> <p>Explicit χ‑models are constructed and analyzed: the minimal χ‑defect, the χ‑monopole in R3, the χ‑domain wall in R4, χ‑lattice defects, and χ‑cosmological transitions. These examples demonstrate the universality of χ‑geometry and reproduce key astrophysical and cosmological phenomena traditionally attributed to dark matter.</p> <p>We show that χ‑geometry is quantum‑consistent, renormalizable, and UV‑complete: the χ‑spectrum provides a natural ultraviolet regularization, the χ‑index eliminates anomalies, and χ‑dynamics generates unitary evolution. In the low‑frequency limit, χ‑geometry reduces to general relativity, and in the small‑gap limit to quantum field theory, ensuring compatibility with observed physics.</p> <p>The results demonstrate that dark matter, geometry, and matter itself are manifestations of a single χ‑spectral structure. χ‑geometry emerges as a fundamental operator‑geometric foundation of physical reality, in which spacetime, particles, and interactions arise as spectral–topological effects of a single operator.</p> <p> </p> |
| title | Topological–Operator χ‑Geometry: Renormalizability, Quantum Consistency, and the Spectral Theory of Dark Matter |
| url | https://doi.org/10.5281/zenodo.19972854 |