Kozyrev's Active Time Reinterpreted Through the Zero‑Entropy Background Topological Structure (ZEBTS): The First Rigorous Ontological Reconstruction

@misc{mukha2026kozyrevs,
  title = {{Kozyrev's Active Time Reinterpreted Through the Zero‑Entropy Background Topological Structure (ZEBTS): The First Rigorous Ontological Reconstruction}},
  author = {Anatolii Mukha},
  howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
  year = {2026},
  month = aug,
  doi = {10.5281/zenodo.21775584},
  url = {https://doi.org/10.5281/zenodo.21775584},
  note = {CC BY},
}

TY  - UNPB
TI  - Kozyrev's Active Time Reinterpreted Through the Zero‑Entropy Background Topological Structure (ZEBTS): The First Rigorous Ontological Reconstruction
AU  - Anatolii Mukha
PY  - 2026
DA  - 2026/08/03
PB  - Zenodo (CERN European Organization for Nuclear Research)
DO  - 10.5281/zenodo.21775584
UR  - https://doi.org/10.5281/zenodo.21775584
AB  - This article develops a complete operator–spectral reconstruction of physical reality based on the χ‑ontology of time. We demonstrate that χ‑time is not a coordinate, not a thermodynamic parameter, and not a phenomenological construct, but a fundamental operator‑spectral invariant arising from the spectrum of the primary χ‑operator D_χ. The χ‑manifold M_χ is introduced as a non‑metric, non‑probabilistic, spectral–topological substrate of reality, defined by the ordered set of invariants { H_χ , D_χ , S_χ , J_χ , ρχ , Φχ , K_χ , C_nonlocal , E_t }. These invariants collectively generate the full architecture of physical phenomena: causality, interaction, fields, matter, geometry, nonlocality, and evolution. We show that χ‑time t_χ = T( Spec D_χ ) induces an intrinsic causal arrow through monotonic χ‑entropy evolution dS_χ/dt_χ ≥ 0, resolving the long‑standing problem of temporal asymmetry without statistical assumptions. Causality is reconstructed as a vector‑spectral phenomenon governed by the sign of the χ‑gradient projection sgn( J_χ · n_dir ), replacing geometric light‑cone causality with operator‑spectral causality. Interaction is shown to arise from χ‑flow Φχ = ∫ (Jχ · dΣχ), replacing gauge‑field propagation with χ‑transport across χ‑surfaces. All physical fields — electromagnetic, gravitational, quantum, biological — are demonstrated to be projections of χ‑invariants into physical spacetime: F_phys = P{χ→phys}( O_χ ), where O_χ ∈ { J_χ , ρ_χ , δλn , C_nonlocal , Kχ }. This establishes a unified operator‑spectral ontology of fields, replacing the multiplicity of gauge symmetries with a single χ‑projection mechanism. Matter is reconstructed as a spectral projection of Spec D_χ, where particles correspond to eigenvalues λn, atoms to spectral clusters, molecules to χ‑coherent networks, and condensed phases to χ‑density manifolds. Phase transitions arise from χ‑entropy reconfiguration ΔSχ ≠ 0 and spectral shifts δλn ≠ 0. Material properties are shown to be χ‑susceptibility responses χmat = d⟨Oχ⟩/dX̂, linking conductivity, elasticity, magnetism, and optical behavior to χ‑invariants. Biological matter is interpreted as a χ‑coherence amplifier governed by C_bio = Tr( C_metabolic · Π{k0} ), providing a unified operator‑spectral foundation for biological coherence, metabolic gradients, and neural dynamics. The χ‑spectral geometry developed in Section 13 establishes that geometry is spectral rather than metric: distances correspond to spectral gaps |λn − λm|, curvature corresponds to spectral deformation δλn, topology corresponds to χ‑entropy Sχ, directionality corresponds to χ‑gradient Jχ, density corresponds to ρχ = dS_χ/dV_χ, transport corresponds to χ‑flow Φχ, nonlocality corresponds to C_nonlocal, and energy corresponds to E_t = γχ ∫|J_χ|² dV_χ. This yields the first unified operator‑spectral geometry of reality, replacing Riemannian geometry with χ‑spectral geometry. The article integrates Kozyrev’s empirical discoveries — active time, causal asymmetry, rotational anomalies, astronomical nonlocality — into the χ‑operator framework, demonstrating that Kozyrev’s phenomenology corresponds to χ‑gradient dynamics, χ‑curvature modulation, χ‑nonlocal coherence, and χ‑flow transport. A complete experimental program is provided, including χ‑nonequilibrium tests, rotational χ‑curvature tests, χ‑spectral frequency tests, χ‑material susceptibility tests, χ‑geometric focusing tests, χ‑nonlocal correlation tests, and χ‑vacuum tests, each with strict null‑conditions, ensuring full falsifiability. The resulting χ‑framework resolves foundational problems in physics: the origin of time’s arrow, the origin of causality, the origin of interaction, the origin of nonlocality, the origin of matter, and the origin of geometry. It unifies classical mechanics, quantum theory, thermodynamics, relativity, field theory, cosmology, and biophysics into a single operator‑spectral ontology. χ‑Reality emerges as a coherent, mathematically complete, experimentally testable, and conceptually unified foundation for physics beyond classical, quantum, and relativistic paradigms.
ER  -