A Geometric Derivation of the Fine Structure Constant from the Gap Labeling Theorem and K-Theory of Quasiperiodic Spectra.
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2026
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| author | Gruia, Alin |
| author_facet | Gruia, Alin |
| contents | <p><span><span class="citation-298">I present a complete, first-principles derivation of the fine structure constant alpha = 1/137.036</span></span><span><span class="citation-298 citation-end-298"><sup class="superscript"></sup></span></span><span>. The derivation is grounded in the algebraic structure of a six-dimensional quasicrystalline compactification and follows five rigorous steps: (1) application of the Gap Labeling Theorem to establish IDS = 1/kappa; (2) derivation of the Drude weight; (3) determination of the 5D gauge coupling based on the D_4 root system of the K-theory lattice K_0 = Z^4; (4) </span><span><span class="citation-297">Kaluza-Klein reduction; and (5) standard gauge normalization</span></span><span><span class="citation-297 citation-end-297"><sup class="superscript"></sup></span></span><span>. </span><span><span class="citation-296">The resulting formula, alpha = lambda^2 / (kappa^8 * pi^2), matches CODATA values within 0.016%, a deviation fully accounted for by one-loop QED running at the Lambda scale</span></span><span><span class="citation-296 citation-end-296"><sup class="superscript"></sup></span></span><span>. </span><span><span class="citation-295">All numerical factors are algebraically fixed by the group-theoretic structure of the compactification</span></span><span><span class="citation-295 citation-end-295"><sup class="superscript"></sup><sup class="superscript"></sup><sup class="superscript"></sup><sup class="superscript"></sup></span></span><span>.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19634134 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Geometric Derivation of the Fine Structure Constant from the Gap Labeling Theorem and K-Theory of Quasiperiodic Spectra. Gruia, Alin fine structure constant Gap Labeling Theorem K-theory quasiperiodic Hamiltonian Kaluza-Klein reduction D_4 root system Gruia Labs <p><span><span class="citation-298">I present a complete, first-principles derivation of the fine structure constant alpha = 1/137.036</span></span><span><span class="citation-298 citation-end-298"><sup class="superscript"></sup></span></span><span>. The derivation is grounded in the algebraic structure of a six-dimensional quasicrystalline compactification and follows five rigorous steps: (1) application of the Gap Labeling Theorem to establish IDS = 1/kappa; (2) derivation of the Drude weight; (3) determination of the 5D gauge coupling based on the D_4 root system of the K-theory lattice K_0 = Z^4; (4) </span><span><span class="citation-297">Kaluza-Klein reduction; and (5) standard gauge normalization</span></span><span><span class="citation-297 citation-end-297"><sup class="superscript"></sup></span></span><span>. </span><span><span class="citation-296">The resulting formula, alpha = lambda^2 / (kappa^8 * pi^2), matches CODATA values within 0.016%, a deviation fully accounted for by one-loop QED running at the Lambda scale</span></span><span><span class="citation-296 citation-end-296"><sup class="superscript"></sup></span></span><span>. </span><span><span class="citation-295">All numerical factors are algebraically fixed by the group-theoretic structure of the compactification</span></span><span><span class="citation-295 citation-end-295"><sup class="superscript"></sup><sup class="superscript"></sup><sup class="superscript"></sup><sup class="superscript"></sup></span></span><span>.</span></p> |
| title | A Geometric Derivation of the Fine Structure Constant from the Gap Labeling Theorem and K-Theory of Quasiperiodic Spectra. |
| topic | fine structure constant Gap Labeling Theorem K-theory quasiperiodic Hamiltonian Kaluza-Klein reduction D_4 root system Gruia Labs |
| url | https://doi.org/10.5281/zenodo.19634134 |