Geometric Proof of Three Fermion Generations from the Bulk Network Root Equation A Unified Theory of Emergent Gravity and Matter v3.0.0
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| Format: | Recurso digital |
| Language: | English |
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2025
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| author | Takahashi, Tamiyuki |
| author_facet | Takahashi, Tamiyuki |
| contents | <p> </p> <p>This paper presents the complete formulation of Emergent Bulk Cosmology (BNC), a unified field theory that resolves the fundamental inconsistencies between General Relativity and the Standard Model, as well as the arbitrariness of physical constants. We postulate a single master action principle, the "Root Equation," which governs the dynamics of a higher-dimensional Bulk Network.</p> <p>From this single equation, we derive a Geometric Duality: the global, continuous "Circle" mode of the bulk generates gravity, while the local, discrete "Square" mode of network defects generates the Higgs field and gauge interactions. The transition between these modes is described as a Geometric Phase Transition via Renormalization Group (RG) flow.</p> <p>The central breakthrough of this work is the rigorous mathematical proof of Fermion Generation Fixation (<span>$N=3$</span>). By applying the Strauss Stability criteria and the Fredholm Index Theorem to the network's topological defects, we demonstrate that stable zero modes are geometrically restricted to three irreducible classes: Equilateral, Isosceles, and Right-Angled Triangles.</p> <p>Finally, we show that Semantic Closure, rooted in the holographic principle, automatically selects the observed cosmological constant as the unique self-consistent solution. We conclude with concrete predictions and explicit falsification criteria.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17680613 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometric Proof of Three Fermion Generations from the Bulk Network Root Equation A Unified Theory of Emergent Gravity and Matter v3.0.0 Takahashi, Tamiyuki Emergent Spacetime Root Equation Higgs-Gravity Dualityx Strauss Problem , Fredholm Index Triangular Stability Semantic Closure <p> </p> <p>This paper presents the complete formulation of Emergent Bulk Cosmology (BNC), a unified field theory that resolves the fundamental inconsistencies between General Relativity and the Standard Model, as well as the arbitrariness of physical constants. We postulate a single master action principle, the "Root Equation," which governs the dynamics of a higher-dimensional Bulk Network.</p> <p>From this single equation, we derive a Geometric Duality: the global, continuous "Circle" mode of the bulk generates gravity, while the local, discrete "Square" mode of network defects generates the Higgs field and gauge interactions. The transition between these modes is described as a Geometric Phase Transition via Renormalization Group (RG) flow.</p> <p>The central breakthrough of this work is the rigorous mathematical proof of Fermion Generation Fixation (<span>$N=3$</span>). By applying the Strauss Stability criteria and the Fredholm Index Theorem to the network's topological defects, we demonstrate that stable zero modes are geometrically restricted to three irreducible classes: Equilateral, Isosceles, and Right-Angled Triangles.</p> <p>Finally, we show that Semantic Closure, rooted in the holographic principle, automatically selects the observed cosmological constant as the unique self-consistent solution. We conclude with concrete predictions and explicit falsification criteria.</p> |
| title | Geometric Proof of Three Fermion Generations from the Bulk Network Root Equation A Unified Theory of Emergent Gravity and Matter v3.0.0 |
| topic | Emergent Spacetime Root Equation Higgs-Gravity Dualityx Strauss Problem , Fredholm Index Triangular Stability Semantic Closure |
| url | https://doi.org/10.5281/zenodo.17680613 |