Fractal Entropic Geometrodynamics: Emergent Gravity, Three Particle Generations, and Topological Chemistry from Discrete Causal Order
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2026
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| author | Silva Alvarado, Juan Pablo |
| author_facet | Silva Alvarado, Juan Pablo |
| contents | <p>We present a strictly discrete framework in which General Relativity,<br>the three-generation structure of the Standard Model, a quantitative<br>mass hierarchy, vacuum polarization, a running coupling constant,<br>and atomic shell chemistry emerge from two axioms and one principle.<br>An $O(N)$ simulation engine---implemented in Rust and freely<br>available---Poisson-sprinkles $N = 10^7$ events into a 4D causal diamond,<br>builds the Hasse diagram, and detects topological defects called<br>\emph{Causal Prisms} ($\Kbn$ bipartite subgraphs).<br>A production ensemble of $M = 20$ realisations (4.5\,hours on a<br>ThinkPad~T480, seed\,42) finds 7{,}723{,}943 prisms with generation<br>fractions 2.1\%/84.9\%/13.0\% and mass hierarchy<br>$4.555 : 6.531 : 7.732$---all from pure combinatorics.<br>A zero-parameter occupancy model, using only the belly distribution<br>$f(n) \sim e^{-0.53n}$ and Hasse-measured phase fractions, predicts<br>mass ratios to 1.8\% accuracy.<br>The i.i.d.\ model that succeeds for mass (a counting observable)<br>fails for charge (a summation observable) by 23.5\%: Kuratowski<br>phase entanglement at small belly sizes screens the topological<br>charge, providing a geometric analogue of QED vacuum polarization.<br>Finite-size scaling across five lattice sizes ($10^5$--$10^7$)<br>confirms $\Qtopo \to 0.152$ ($R^2 = 0.9996$),<br>$\alpha_0^{-1} \to 165.1 \pm 1.0$, and<br>$\Omega_{\mathrm{energy}} \to 5.57$ (Planck~2018: 5.36).<br>The exact identity $\alpha(1 + \Omega) = 1/(8\pi)$ locks fine<br>structure and dark matter to a single topological observable.<br>The sign-alternating coefficients of the Benincasa--Dowker operator<br>force oscillatory diffusion on the Hasse graph; the continuum limit<br>requires complex phases $e^{i\theta}$ to preserve unitarity, deriving<br>the imaginary unit $i$ of quantum mechanics from causal geometry.<br>The Fisher information metric on the phase simplex yields a<br>2-sphere whose eigenmodes reproduce the atomic magic numbers<br>$2, 8, 18, 32$, covalent bond saturation at triple bonds,<br>and the octet rule---from pure topology with zero imposed parameters.<br>The spectral dimension flows from<br>$\ds(\sigma{=}1) = 1.949 \pm 0.002$ in the UV to<br>$\ds(\sigma{=}4) = 4.956 \pm 0.001$ in the IR.<br>Ten falsifiable predictions are enumerated.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18706614 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Fractal Entropic Geometrodynamics: Emergent Gravity, Three Particle Generations, and Topological Chemistry from Discrete Causal Order Silva Alvarado, Juan Pablo <p>We present a strictly discrete framework in which General Relativity,<br>the three-generation structure of the Standard Model, a quantitative<br>mass hierarchy, vacuum polarization, a running coupling constant,<br>and atomic shell chemistry emerge from two axioms and one principle.<br>An $O(N)$ simulation engine---implemented in Rust and freely<br>available---Poisson-sprinkles $N = 10^7$ events into a 4D causal diamond,<br>builds the Hasse diagram, and detects topological defects called<br>\emph{Causal Prisms} ($\Kbn$ bipartite subgraphs).<br>A production ensemble of $M = 20$ realisations (4.5\,hours on a<br>ThinkPad~T480, seed\,42) finds 7{,}723{,}943 prisms with generation<br>fractions 2.1\%/84.9\%/13.0\% and mass hierarchy<br>$4.555 : 6.531 : 7.732$---all from pure combinatorics.<br>A zero-parameter occupancy model, using only the belly distribution<br>$f(n) \sim e^{-0.53n}$ and Hasse-measured phase fractions, predicts<br>mass ratios to 1.8\% accuracy.<br>The i.i.d.\ model that succeeds for mass (a counting observable)<br>fails for charge (a summation observable) by 23.5\%: Kuratowski<br>phase entanglement at small belly sizes screens the topological<br>charge, providing a geometric analogue of QED vacuum polarization.<br>Finite-size scaling across five lattice sizes ($10^5$--$10^7$)<br>confirms $\Qtopo \to 0.152$ ($R^2 = 0.9996$),<br>$\alpha_0^{-1} \to 165.1 \pm 1.0$, and<br>$\Omega_{\mathrm{energy}} \to 5.57$ (Planck~2018: 5.36).<br>The exact identity $\alpha(1 + \Omega) = 1/(8\pi)$ locks fine<br>structure and dark matter to a single topological observable.<br>The sign-alternating coefficients of the Benincasa--Dowker operator<br>force oscillatory diffusion on the Hasse graph; the continuum limit<br>requires complex phases $e^{i\theta}$ to preserve unitarity, deriving<br>the imaginary unit $i$ of quantum mechanics from causal geometry.<br>The Fisher information metric on the phase simplex yields a<br>2-sphere whose eigenmodes reproduce the atomic magic numbers<br>$2, 8, 18, 32$, covalent bond saturation at triple bonds,<br>and the octet rule---from pure topology with zero imposed parameters.<br>The spectral dimension flows from<br>$\ds(\sigma{=}1) = 1.949 \pm 0.002$ in the UV to<br>$\ds(\sigma{=}4) = 4.956 \pm 0.001$ in the IR.<br>Ten falsifiable predictions are enumerated.</p> |
| title | Fractal Entropic Geometrodynamics: Emergent Gravity, Three Particle Generations, and Topological Chemistry from Discrete Causal Order |
| url | https://doi.org/10.5281/zenodo.18706614 |