faceFlux_12

This module derives the Wolfenstein $A$ parameter from first-principles $Q_3$ geometry. The three cube axes carry Gray-code flip counts $(4,2,2)$: axis 0 is dominant (four flips), axes 1 and 2 are minor (two flips each). Generation torsion supplies the complementary integers $\Delta\tau_{12}=11$ and $\Delta\tau_{23}=6$.

Face flux on a generation face is the sum of the flip counts of the two axes that span it. The 1→2 face therefore mixes the dominant axis with a minor axis, while the 2→3 face mixes the two minors. The module records the five-line chain from these integers to $A_{\mathrm{corrected}}=9/11$, matching PDG within $0.6\sigma$.

The same $[4,2,2]$ chirality appears in the fine-structure and baryon-asymmetry sectors through the composite $44=4\times 11$, so the face-flux integers are not CKM-local bookkeeping; they are shared $Q_3$ data.

Term-mode rfl. By definition, face flux on axes $i,j$ is the sum of the two Gray-code flip counts. Those counts are already fixed at $(4,2,2)$ for axes $(0,1,2)$, so the pair $(0,1)$ reduces definitionally to $4+2=6$. No lemmas are invoked; the equality is computational.

This is step 4 of the module's five-line derivation of Wolfenstein $A$. Together with the companion face-flux value 4 on axes $(1,2)$, it supplies the Berry correction factor $6/4=3/2$. Multiplying the structural ratio $A_{\mathrm{structural}}=\Delta\tau_{23}/\Delta\tau_{12}=6/11$ by that factor yields $A_{\mathrm{corrected}}=9/11$.

Downstream, ckmExactCert packages the structural identity, the corrected value, the Berry factor, its square, and the PDG $1\sigma$ membership into a single certificate. The same integers reappear in the "44 connection": $\alpha^{-1}$ and $\eta_B$ are governed by $4\times 11$, while $A$ is the cross-ratio of torsion gaps against these face fluxes. Closing the flux values is therefore what lets the CKM sector sit on the same $Q_3$ chirality as the gauge and cosmological sectors.