Force Unification from the Minimal Discrete Épure to the Standard Model
Abstract
We relate the minimal discrete épure G■=(Z²,d■) to the Standard Model gauge structure. We establish six theorems (T1–T6) on the algebraic invariants and the causal vertex Θ■=arctan(2). Status of the gauge-coupling predictions: the stable-mode geometric identity (I4) has its two factors anchored in the causal angle (√5=sec Θ■; 4=tan²Θ■=|D₂|, with N=2 fixed by Fourier consistency), but the specific power form is not proved canonical and its derivation from a Yang–Mills action is an open problem (P3). Consequently the gauge-coupling values (1/α_EM≈137.036, 1/α_w, 1/α_s) are presented as predictions conditional on (I4), not as parameter-free derived consequences. SU(5) is geometrically excluded. Results verified in Python 3.
Fields of Study & Subjects
Noncommutative and Quantum Gravity Theories
Black Holes and Theoretical Physics
Relativity and Gravitational Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 21 April 2026
- Language
- EN
- Document type
- Preprint