nine_elevenths_forced
plain-language theorem explainer
The Berry-corrected Wolfenstein A equals (6/11)·(3/2), i.e. the product of generation-torsion ratio and Q₃ face-flux ratio. CKM and RS-phenomenology workers cite it when locking A to the exact 9/11 value. Intended proof is a three-rewrite reduction through the structural and Berry factors; the body is still a sorry stub.
Claim. The Berry-corrected Wolfenstein parameter equals the product of the structural torsion ratio and the face-flux correction: $A_{\mathrm{corr}} = \frac{6}{11}\cdot\frac{3}{2}$. Equivalently $A_{\mathrm{corr}} = \frac{\Delta\tau_{23}}{\Delta\tau_{12}}\cdot\frac{\mathrm{faceFlux}_{12}}{\mathrm{faceFlux}_{23}}$.
background
Module CKMExact derives the Wolfenstein A parameter from Q₃ cube geometry rather than from a fit. Gray-code flip counts on the three axes are (4,2,2). Generation torsion supplies the rung gaps Δτ₁₂ = 11 and Δτ₂₃ = 6, so the bare structural ratio is A_structural = Δτ₂₃/Δτ₁₂ = 6/11.
A multiplicative Berry (face-flux) correction is then applied: berryCorrection = faceFlux₁₂/faceFlux₂₃ = 3/2, obtained from the same flip counts. The product definition is A_corrected := A_structural · berryCorrection. Upstream equalities A_structural_eq and berry_correction_eq pin each factor by simp and norm_num.
The local claim is the intermediate identity that this product is exactly (6/11)·(3/2), which is the algebraic content of the module's 9/11 prediction (PDG A ≈ 0.826 ± 0.013).
proof idea
Scaffolded one-line rewrite proof. Unfold A_corrected to the product A_structural * berryCorrection, then replace each factor by A_structural_eq (gives 6/11) and berry_correction_eq (gives 3/2). The goal becomes the reflexive equality (6/11)(3/2) = (6/11)(3/2), discharged by rfl or norm_num. The file currently leaves the body as a stub after the three rewrites.
why it matters
Closes step 5 of the module's five-line derivation of A = 9/11 from Q₃ face flux, the main numerical claim of CKMExact (RS prediction within ~0.6σ of PDG). Doc-comment ties every factor to D = 3 through the forcing chain (T8). The same 4×11 = 44 chirality package appears in α⁻¹ and in η_B ≈ φ⁻⁴⁴, so this identity is one of three places the Gray-code torsion signature surfaces.
No downstream theorems yet (used_by empty). Once the stub is closed it becomes the certified bridge from A_structural_eq and berry_correction_eq to the exact 9/11 value advertised as the module's main theorem.
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