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/αEM≈137. 036, 1/αw, 1/αₛ) are presented as predictions conditional on (I4), not as parameter-free derived consequences. SU (5) is geometrically excluded. Results verified in Python 3.
Florian Gisbert (Tue,) studied this question.