Fundamental Constants from Logical Geometry: Deriving α, me, and Mp/me from the RTLI Framework
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2025
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| _version_ | 1866901979694891008 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p>This paper presents geometric derivations of three fundamental constants using the Relational Thermodynamic Layered Index (RTLI) framework: the fine structure constant (α⁻¹ ≈ 137.02, accuracy 99.99%), the electron mass (m_e ≈ 0.509 MeV, accuracy 99.6%), and the proton-to-electron mass ratio (M_p/m_e ≈ 1836.15, accuracy >99.99%). All three emerge from the same geometric building blocks—the toroidal phase-space volume N = 4π²/e, the coherence corridor [√e, 7/4], the critical angle θ_c = arctan(1/e), and the torsional coupling cost C = 0.08—with a single empirical input: the recombination energy E_rec ≈ 0.25 eV. The coherence corridor bounds connect to established physics: √e as the duality fixed point from stability axioms, 7/4 as the exact 2D Ising critical exponent, and 1.715 as the AdS/CFT holographic phase transition. These results suggest fundamental constants are constrained by logical geometry rather than being arbitrary parameters.</p> <p> </p> <h3>Related Identifiers:</h3> <ul> <li><a href="https://doi.org/10.5281/zenodo.17930540">https://doi.org/10.5281/zenodo.17930540</a> (λ/e Ratio)</li> <li><a href="https://doi.org/10.5281/zenodo.17946628">https://doi.org/10.5281/zenodo.17946628</a> (Mass and Complexity)</li> <li><a href="https://doi.org/10.5281/zenodo.17934102">https://doi.org/10.5281/zenodo.17934102</a> (Arrow of Time)</li> <li><a href="https://doi.org/10.5281/zenodo.17924917">https://doi.org/10.5281/zenodo.17924917</a> (RTLI Book v2)</li> <li><a href="https://doi.org/10.5281/zenodo.17917603">https://doi.org/10.5281/zenodo.17917603</a> (Three-Angle Recursion)</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17971278 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Fundamental Constants from Logical Geometry: Deriving α, me, and Mp/me from the RTLI Framework De Jesus, Elias logical geometry, fundamental constants, fine structure constant, electron mass, proton-electron ratio, RTLI, coherence corridor, Ising model, AdS/CFT, holography, stability axioms, toroidal geometry, golden ratio, critical angle, phase transitions <p>This paper presents geometric derivations of three fundamental constants using the Relational Thermodynamic Layered Index (RTLI) framework: the fine structure constant (α⁻¹ ≈ 137.02, accuracy 99.99%), the electron mass (m_e ≈ 0.509 MeV, accuracy 99.6%), and the proton-to-electron mass ratio (M_p/m_e ≈ 1836.15, accuracy >99.99%). All three emerge from the same geometric building blocks—the toroidal phase-space volume N = 4π²/e, the coherence corridor [√e, 7/4], the critical angle θ_c = arctan(1/e), and the torsional coupling cost C = 0.08—with a single empirical input: the recombination energy E_rec ≈ 0.25 eV. The coherence corridor bounds connect to established physics: √e as the duality fixed point from stability axioms, 7/4 as the exact 2D Ising critical exponent, and 1.715 as the AdS/CFT holographic phase transition. These results suggest fundamental constants are constrained by logical geometry rather than being arbitrary parameters.</p> <p> </p> <h3>Related Identifiers:</h3> <ul> <li><a href="https://doi.org/10.5281/zenodo.17930540">https://doi.org/10.5281/zenodo.17930540</a> (λ/e Ratio)</li> <li><a href="https://doi.org/10.5281/zenodo.17946628">https://doi.org/10.5281/zenodo.17946628</a> (Mass and Complexity)</li> <li><a href="https://doi.org/10.5281/zenodo.17934102">https://doi.org/10.5281/zenodo.17934102</a> (Arrow of Time)</li> <li><a href="https://doi.org/10.5281/zenodo.17924917">https://doi.org/10.5281/zenodo.17924917</a> (RTLI Book v2)</li> <li><a href="https://doi.org/10.5281/zenodo.17917603">https://doi.org/10.5281/zenodo.17917603</a> (Three-Angle Recursion)</li> </ul> |
| title | Fundamental Constants from Logical Geometry: Deriving α, me, and Mp/me from the RTLI Framework |
| topic | logical geometry, fundamental constants, fine structure constant, electron mass, proton-electron ratio, RTLI, coherence corridor, Ising model, AdS/CFT, holography, stability axioms, toroidal geometry, golden ratio, critical angle, phase transitions |
| url | https://doi.org/10.5281/zenodo.17971278 |