| _version_ | 1866901175930978304 |
|---|---|
| author | Муха, Анатолий |
| author_facet | Муха, Анатолий |
| contents | <h1>Abstract</h1> <p>We develop a complete spectral–topological framework for dark matter based on χ‑geometry and the operator–geometric foundations of χ‑QFT. In this approach, dark matter arises not from additional particle species or symmetry‑breaking mechanisms, but from intrinsic χ‑topological defects generated by nontrivial χ‑cohomology classes of the χ‑hypergraph G∗. The χ‑boundary operator Γμ, the χ‑spectral operator D∧, and the χ‑curvature Fχ together define a discrete hierarchy of χ‑monopoles, χ‑vortices, and χ‑domain walls whose stability is ensured by χ‑topological charge and χ‑spectral gaps. We derive χ‑spectral mass formulas showing that the masses of χ‑defects originate from the minimal χ‑spectral displacement required to trivialize their χ‑cohomology classes, yielding a quantized χ‑mass spectrum independent of Higgs‑type mechanisms. Interactions with Standard Model fields arise solely through χ‑curvature mixing, χ‑boundary mixing, and χ‑spectral corrections, all of which are suppressed by the χ‑spectral hierarchy, placing χ‑defects naturally in the class of heavy, weakly interacting dark‑matter candidates. Cosmological production is governed by χ‑phase transitions, χ‑instantons, and χ‑freeze‑in processes, which generate a relic abundance determined by the χ‑spectral structure of the early Universe and predict characteristic gravitational‑wave signatures. The resulting χ‑dark‑matter sector is structurally stable, phenomenologically viable, and experimentally testable, providing a mathematically rigorous alternative to conventional dark‑matter models and establishing χ‑geometry as a unified operator–topological origin of dark matter.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19824021 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dark Matter: Spectral–Topological Origin of Stable χ‑Defects in χ‑Geometry Муха, Анатолий <h1>Abstract</h1> <p>We develop a complete spectral–topological framework for dark matter based on χ‑geometry and the operator–geometric foundations of χ‑QFT. In this approach, dark matter arises not from additional particle species or symmetry‑breaking mechanisms, but from intrinsic χ‑topological defects generated by nontrivial χ‑cohomology classes of the χ‑hypergraph G∗. The χ‑boundary operator Γμ, the χ‑spectral operator D∧, and the χ‑curvature Fχ together define a discrete hierarchy of χ‑monopoles, χ‑vortices, and χ‑domain walls whose stability is ensured by χ‑topological charge and χ‑spectral gaps. We derive χ‑spectral mass formulas showing that the masses of χ‑defects originate from the minimal χ‑spectral displacement required to trivialize their χ‑cohomology classes, yielding a quantized χ‑mass spectrum independent of Higgs‑type mechanisms. Interactions with Standard Model fields arise solely through χ‑curvature mixing, χ‑boundary mixing, and χ‑spectral corrections, all of which are suppressed by the χ‑spectral hierarchy, placing χ‑defects naturally in the class of heavy, weakly interacting dark‑matter candidates. Cosmological production is governed by χ‑phase transitions, χ‑instantons, and χ‑freeze‑in processes, which generate a relic abundance determined by the χ‑spectral structure of the early Universe and predict characteristic gravitational‑wave signatures. The resulting χ‑dark‑matter sector is structurally stable, phenomenologically viable, and experimentally testable, providing a mathematically rigorous alternative to conventional dark‑matter models and establishing χ‑geometry as a unified operator–topological origin of dark matter.</p> <p> </p> |
| title | Dark Matter: Spectral–Topological Origin of Stable χ‑Defects in χ‑Geometry |
| url | https://doi.org/10.5281/zenodo.19824021 |