A_corrected_exact
plain-language theorem explainer
The Berry-corrected Wolfenstein A parameter equals exactly 9/11. Anyone citing the RS CKM prediction or the Q₃ face-flux derivation of A will use this identity. The proof unfolds the definition as structural A times Berry correction, substitutes the two exact fractions 6/11 and 3/2, and closes by ring arithmetic.
Claim. The Berry-corrected Wolfenstein parameter equals exactly $9/11$: if $A_{\mathrm{corr}} := A_{\mathrm{struct}} \cdot B$ with $A_{\mathrm{struct}} = 6/11$ (generation-torsion ratio) and $B = 3/2$ (face-flux correction), then $A_{\mathrm{corr}} = 9/11$.
background
In the CKMExact module the Wolfenstein $A$ is built from $Q_3$ cube geometry rather than fit to data. Generation torsion supplies the structural ratio $A_{\mathrm{struct}} = \Delta\tau_{23}/\Delta\tau_{12} = 6/11$. Independently, Gray-code flip counts on the three cube axes give face fluxes whose ratio is the Berry correction $B = \mathrm{faceFlux}(12)/\mathrm{faceFlux}(23) = 3/2$.
The corrected parameter is the product $A_{\mathrm{corr}} := A_{\mathrm{struct}} \cdot B$. Upstream lemmas already pin each factor: A_structural_eq proves the torsion ratio is exactly $6/11$, and berry_correction_eq proves the flux ratio is exactly $3/2$. The present theorem multiplies those two identities.
The same $Q_3$ chirality (Gray code $[4,2,2]$ times generation torsion) also appears in the fine-structure and baryon-asymmetry formulae via the composite $44 = 4 \times 11$, so the CKM $A$ sits in that common geometric package.
proof idea
One short tactic proof. Unfold A_corrected to the product $A_{\mathrm{struct}} \cdot B$, rewrite the two factors by A_structural_eq ($= 6/11$) and berry_correction_eq ($= 3/2$), then finish with ring, which reduces $(6/11)\cdot(3/2)$ to $9/11$.
why it matters
This is the main exact identity of the CKMExact module: $A_{\mathrm{corr}} = 9/11 \approx 0.818$, inside $0.6\sigma$ of the PDG central value $0.826 \pm 0.013$. Downstream positivity, tight-interval, and PDG $1\sigma$ membership theorems all rewrite through it; so do the distance-to-PDG bound, the colour-and-torsion rewrite $A = N_c^2/\Delta\tau_{12}$, the certificate ckmExactCert, and the claim that forty-four governs three constants.
It also feeds the T8-to-gauge/Standard-Model bridge in the unified forcing chain, which routes SM surfaces through the forced $D=3$ cube/spinor skeleton. Within the RS landmarks it realises the eight-tick/$Q_3$ geometry (T7–T8) as a concrete CKM number, and it is one of the three places where the composite $44$ appears (with $\alpha^{-1}$ and $\eta_B$).
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.