| _version_ | 1866902264454578176 |
|---|---|
| author | Okolo, Hanyelichukwu Paul |
| author_facet | Okolo, Hanyelichukwu Paul |
| contents | <div> <div> <div> <p>This paper presents a complete, five-step proof deriving the value of the fine-structure constant, α, from the first principles of number theory. The proof begins by defining the Harmonic Divisor Fan (HDF) lattice as a dynamical system whose stability is formally characterized by the controlled growth of a prime vorticity function, S(t). We then prove that this dynamic stability is necessarily caused by a geometrically optimal dispersion of divisor points, a state described by phyllotaxis. This necessitates the adoption of the Golden Angle strategy, which in the discrete integer lattice of the HDF, compels the selection of k = 137 via the unique minimization of a derived Arithmetic Cost Function. The final value of α is then calculated from the minimal, non-zero dissonance of this selection, which is arithmetically quantified by a fundamental break in the system’s prime symmetry. The result demonstrates that α is a necessary and calculable constant of a universe governed by the Fundamental Theorem of Arithmetic.</p> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15694456 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Complete Proof for the Derivation of the Fine-Structure Constant from Prime Number Dynamics. Okolo, Hanyelichukwu Paul Physics Physics Mathematical physics Fine Structure Constant Electromagnetism Electromagnetism Prime numbers Prime Numbers Lattice <div> <div> <div> <p>This paper presents a complete, five-step proof deriving the value of the fine-structure constant, α, from the first principles of number theory. The proof begins by defining the Harmonic Divisor Fan (HDF) lattice as a dynamical system whose stability is formally characterized by the controlled growth of a prime vorticity function, S(t). We then prove that this dynamic stability is necessarily caused by a geometrically optimal dispersion of divisor points, a state described by phyllotaxis. This necessitates the adoption of the Golden Angle strategy, which in the discrete integer lattice of the HDF, compels the selection of k = 137 via the unique minimization of a derived Arithmetic Cost Function. The final value of α is then calculated from the minimal, non-zero dissonance of this selection, which is arithmetically quantified by a fundamental break in the system’s prime symmetry. The result demonstrates that α is a necessary and calculable constant of a universe governed by the Fundamental Theorem of Arithmetic.</p> </div> </div> </div> |
| title | A Complete Proof for the Derivation of the Fine-Structure Constant from Prime Number Dynamics. |
| topic | Physics Physics Mathematical physics Fine Structure Constant Electromagnetism Electromagnetism Prime numbers Prime Numbers Lattice |
| url | https://doi.org/10.5281/zenodo.15694456 |