berry_sq_eq

The module derives the Wolfenstein $A$ parameter of the CKM matrix from the geometry of the cube graph $Q_3$. Gray-code flip counts on the three axes are $(4,2,2)$; generation torsion differences are $\Delta\tau_{12}=11$ and $\Delta\tau_{23}=6$. The bare structural ratio is therefore $A_{\mathrm{structural}}=\Delta\tau_{23}/\Delta\tau_{12}=6/11$.

The Berry correction is the ratio of face fluxes seen by the mixing amplitudes $V_{us}$ ($1\to 2$) and $V_{cb}$ ($2\to 3$). By definition it equals $\mathrm{faceFlux}(1,2)/\mathrm{faceFlux}(2,3)$. The upstream identity already proves this ratio is exactly $3/2$ (from flip counts $6$ and $4$). Squaring that factor is the present claim; the doc-comment flags the link $(3/2)^2=9/4$ to the colour factor $N_c=3$.

One-line term-mode wrapper. Rewrite the goal by the upstream equality that the Berry correction equals $3/2$, then discharge $ (3/2)^2 = 9/4 $ by norm_num. No further geometric reasoning is needed at this step.

This identity is packaged into the certificate record that assembles every exact CKM claim in the module, and it appears as the middle conjunct of the theorem that $44$ governs three constants: the same integer $4\times 11$ that enters $\alpha^{-1}$ and $\eta_B$ also organises $A_{\mathrm{corrected}}=9/11$ once the squared Berry factor $9/4$ is in place. The module result is $A_{\mathrm{corrected}}=(6/11)\times(3/2)=9/11\approx 0.818$, within $0.6\sigma$ of the PDG value $0.826\pm 0.013$. The colour-factor reading of $9/4$ ties the flux correction to $N_c=3$, consistent with the eight-tick $Q_3$ geometry (T7) that forces three spatial axes (T8).