The Icosahedral Universe: Discrete Algebraic Foundation of Fundamental Physics
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2026
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| author | ACOSTA PADILLA, ALFREDO LUIS |
| author_facet | ACOSTA PADILLA, ALFREDO LUIS |
| contents | <h2><strong>Description / Abstract (Optimized for Zenodo)</strong></h2> <p>We present a complete theoretical framework, <strong>Structured Vacuum Theory (TVS)</strong>, which derives fundamental physical constants and particle properties directly from a discrete icosahedral vacuum geometry with a 23-dimensional configuration space.</p> <p><strong>Core Mathematical Discovery:</strong><br>The theory demonstrates that the mathematical constant $\pi$ and the fine-structure constant $\alpha^{-1} \approx 137$ are not independent parameters but emergent algebraic structures in base-23 arithmetic. We prove the exact polynomial decomposition:<br><span><span>πTVS=3822512167 ⟹ 38225=3⋅233+3⋅232+137</span><span><span><span><span>π</span><span><span><span><span><span><span><span>T</span><span>V</span><span>S</span></span></span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span><span><span>12167</span></span><span><span>38225</span></span></span></span></span></span></span><span>⟹</span></span><span><span>38225</span><span>=</span></span><span><span>3</span><span>⋅</span></span><span><span>2</span><span>3<span><span><span><span><span><span>3</span></span></span></span></span></span></span><span>+</span></span><span><span>3</span><span>⋅</span></span><span><span>2</span><span>3<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>+</span></span><span><span>137</span></span></span></span><br>This reveals that the integer 137 appears naturally as the <strong>topological residue</strong> of packing 3 spatial dimensions and 3 rotational degrees of freedom into the vacuum lattice.</p> <p><strong>Key Physical Derivations:</strong><br>Based purely on this geometry with <strong>zero adjustable parameters</strong>, we derive:</p> <ul> <li> <p><strong>Particle Physics:</strong> Three fermion generations from orthogonal golden rectangles, twelve fundamental fermions from icosahedral vertices, and parity violation from the intrinsic chirality of the $A_5$ group.</p> </li> <li> <p><strong>Cosmology:</strong> The cosmological constant ($\Lambda$) derived from vacuum energy density without fine-tuning, and a prediction of 2.3 keV Warm Dark Matter arising from trapped torsional modes.</p> </li> <li> <p><strong>Quantum Gravity:</strong> Black hole entropy derived from discrete state counting on the $V_{23}$ lattice.</p> </li> </ul> <p><strong>Conclusion:</strong><br>This framework suggests a paradigm shift: physical reality is fundamentally algebraic over the field extension $\mathbb{Q}_{23}$, rather than analytic over the real continuum $\mathbb{R}$. The "fine-tuning" of the Standard Model is shown to be a geometric inevitability of the discrete vacuum structure.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18380342 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | The Icosahedral Universe: Discrete Algebraic Foundation of Fundamental Physics ACOSTA PADILLA, ALFREDO LUIS Structured Vacuum Theory, icosahedral geometry, discrete spacetime, fine-structure constant, base-23 physics, cosmological constant, Warm Dark Matter, algebraic field theory, topological residue, Standard Model unification Subjects Physics > High Energy Physics - Theory Physics > General Relativity and Quantum Cosmology Mathematics > Number Theory Physics > High Energy Physics - Theory Physics > General Relativity and Quantum Cosmology Mathematics > Number Theory <h2><strong>Description / Abstract (Optimized for Zenodo)</strong></h2> <p>We present a complete theoretical framework, <strong>Structured Vacuum Theory (TVS)</strong>, which derives fundamental physical constants and particle properties directly from a discrete icosahedral vacuum geometry with a 23-dimensional configuration space.</p> <p><strong>Core Mathematical Discovery:</strong><br>The theory demonstrates that the mathematical constant $\pi$ and the fine-structure constant $\alpha^{-1} \approx 137$ are not independent parameters but emergent algebraic structures in base-23 arithmetic. We prove the exact polynomial decomposition:<br><span><span>πTVS=3822512167 ⟹ 38225=3⋅233+3⋅232+137</span><span><span><span><span>π</span><span><span><span><span><span><span><span>T</span><span>V</span><span>S</span></span></span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span><span><span>12167</span></span><span><span>38225</span></span></span></span></span></span></span><span>⟹</span></span><span><span>38225</span><span>=</span></span><span><span>3</span><span>⋅</span></span><span><span>2</span><span>3<span><span><span><span><span><span>3</span></span></span></span></span></span></span><span>+</span></span><span><span>3</span><span>⋅</span></span><span><span>2</span><span>3<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>+</span></span><span><span>137</span></span></span></span><br>This reveals that the integer 137 appears naturally as the <strong>topological residue</strong> of packing 3 spatial dimensions and 3 rotational degrees of freedom into the vacuum lattice.</p> <p><strong>Key Physical Derivations:</strong><br>Based purely on this geometry with <strong>zero adjustable parameters</strong>, we derive:</p> <ul> <li> <p><strong>Particle Physics:</strong> Three fermion generations from orthogonal golden rectangles, twelve fundamental fermions from icosahedral vertices, and parity violation from the intrinsic chirality of the $A_5$ group.</p> </li> <li> <p><strong>Cosmology:</strong> The cosmological constant ($\Lambda$) derived from vacuum energy density without fine-tuning, and a prediction of 2.3 keV Warm Dark Matter arising from trapped torsional modes.</p> </li> <li> <p><strong>Quantum Gravity:</strong> Black hole entropy derived from discrete state counting on the $V_{23}$ lattice.</p> </li> </ul> <p><strong>Conclusion:</strong><br>This framework suggests a paradigm shift: physical reality is fundamentally algebraic over the field extension $\mathbb{Q}_{23}$, rather than analytic over the real continuum $\mathbb{R}$. The "fine-tuning" of the Standard Model is shown to be a geometric inevitability of the discrete vacuum structure.</p> |
| title | The Icosahedral Universe: Discrete Algebraic Foundation of Fundamental Physics |
| topic | Structured Vacuum Theory, icosahedral geometry, discrete spacetime, fine-structure constant, base-23 physics, cosmological constant, Warm Dark Matter, algebraic field theory, topological residue, Standard Model unification Subjects Physics > High Energy Physics - Theory Physics > General Relativity and Quantum Cosmology Mathematics > Number Theory Physics > High Energy Physics - Theory Physics > General Relativity and Quantum Cosmology Mathematics > Number Theory |
| url | https://doi.org/10.5281/zenodo.18380342 |