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2025
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| Acceso en línea: | https://doi.org/10.5281/zenodo.17667482 |
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| _version_ | 1866902284647006208 |
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| author | Hallman, D. J. |
| author_facet | Hallman, D. J. |
| contents | <p>This work presents a complete, axiomatic resolution to Hilbert’s Sixth Problem using Spatial–Causal Geometry (SCG), a deterministic geometric framework in which all physical phenomena arise from the curvature and topology of a single scalar field, ρ(x). The manuscript introduces the foundational axioms of SCG, derives the universal causal–gradient law and the γ(cause) invariant, and demonstrates how coherent rotational modes of ρ(x) form the structures traditionally known as photons, electrons, nucleons, and large-scale vortices.</p> <p>Transition processes—including photon emission, neutrino release, and beta decay—are unified under a single geometric mechanism using the transition operator T(x). Statistical mechanics emerges from curvature degeneracy across ensembles, and probability theory (including the Born rule and Kolmogorov structure) is reconstructed from deterministic geometric projection. The metric tensor and spacetime geometry appear as limiting approximations of slowly varying density, reproducing general-relativistic effects without requiring spacetime as a fundamental entity.</p> <p>By deriving mechanics, quantum behavior, thermodynamics, transition dynamics, and probabilistic laws from a single geometric ontology, this work fulfills Hilbert’s program in both form and substance. The result is a structurally unified foundation in which all domains of physics arise from the behavior of ρ(x) and its universal curvature constraints.</p> <h3><strong>Keywords</strong></h3> <p>Spatial–Causal Geometry (SCG); gamma(cause) invariant; causal–gradient law; rotational modes; unified field dynamics; geometric unification; quantum reconstruction; emergent probability; Born rule; projection geometry; curvature degeneracy; emergent thermodynamics; transition operator T(x); neutrinos; photons; vortex coherence; metric limit; emergent spacetime; Hilbert’s Sixth Problem; deterministic physics; unified physics; geometric ontology.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17667482 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hilbert's Sixth Problem Resolved through Spatial-Causal Geometry and the gamma(cause) Invariant Hallman, D. J. <p>This work presents a complete, axiomatic resolution to Hilbert’s Sixth Problem using Spatial–Causal Geometry (SCG), a deterministic geometric framework in which all physical phenomena arise from the curvature and topology of a single scalar field, ρ(x). The manuscript introduces the foundational axioms of SCG, derives the universal causal–gradient law and the γ(cause) invariant, and demonstrates how coherent rotational modes of ρ(x) form the structures traditionally known as photons, electrons, nucleons, and large-scale vortices.</p> <p>Transition processes—including photon emission, neutrino release, and beta decay—are unified under a single geometric mechanism using the transition operator T(x). Statistical mechanics emerges from curvature degeneracy across ensembles, and probability theory (including the Born rule and Kolmogorov structure) is reconstructed from deterministic geometric projection. The metric tensor and spacetime geometry appear as limiting approximations of slowly varying density, reproducing general-relativistic effects without requiring spacetime as a fundamental entity.</p> <p>By deriving mechanics, quantum behavior, thermodynamics, transition dynamics, and probabilistic laws from a single geometric ontology, this work fulfills Hilbert’s program in both form and substance. The result is a structurally unified foundation in which all domains of physics arise from the behavior of ρ(x) and its universal curvature constraints.</p> <h3><strong>Keywords</strong></h3> <p>Spatial–Causal Geometry (SCG); gamma(cause) invariant; causal–gradient law; rotational modes; unified field dynamics; geometric unification; quantum reconstruction; emergent probability; Born rule; projection geometry; curvature degeneracy; emergent thermodynamics; transition operator T(x); neutrinos; photons; vortex coherence; metric limit; emergent spacetime; Hilbert’s Sixth Problem; deterministic physics; unified physics; geometric ontology.</p> |
| title | Hilbert's Sixth Problem Resolved through Spatial-Causal Geometry and the gamma(cause) Invariant |
| url | https://doi.org/10.5281/zenodo.17667482 |