suppression_12
plain-language theorem explainer
The 1–2 generation CKM suppression exponent equals −11, so the mass-basis overlap scales as φ^{−11}. Anyone extracting Cabibbo-scale mixing from Q₃ torsion would cite this evaluation. The proof is a one-line native_decide check of the absolute torsion gap between generations 0 and 1.
Claim. The $\varphi$-suppression exponent between the first and second quark generations equals $-11$: if $\tau$ denotes generation torsion, then $-|\tau_0-\tau_1|=-11$, so the mass-basis off-diagonal amplitude scales as $\varphi^{-11}$.
background
In the CKM-from-cube module, mass eigenstates on the three-generation space carry fixed torsions (CW coupling levels): generation 1 has torsion 0, generation 2 has torsion 11, and generation 3 has torsion 17. Off-diagonal mass-basis overlaps are J-cost suppressed by the absolute torsion difference: $\langle\mathrm{mass}_i|\mathrm{mass}j\rangle\propto\varphi^{-|\Delta\tau{ij}|}$.
The integer suppressionExponent packages that exponent as $-(|\tau_i-\tau_j|)$ for indices in $\mathrm{Fin},3$. The companion gap values come from the generation torsion set ${0,11,17}$ forced by the Q₃ edge/face dressing structure. Weak eigenstates are separate (even-sign-flip SU(2) generators on the cube); the present fact only fixes the mass-sector $\varphi$ power that later multiplies flip-count ratios in $\sin^2\theta_{ij}$.
proof idea
One-line computational proof. Unfold the definition of the suppression exponent as the negated absolute torsion gap between indices 0 and 1, then discharge the resulting integer equality by native_decide. No algebraic lemmas are invoked beyond the in-module gap data that native_decide evaluates.
why it matters
This pins the 1–2 entry in the documented exponent triple (1–2: $\varphi^{-11}$, 2–3: $\varphi^{-6}$, 1–3: $\varphi^{-17}$) that feeds the CKM overlap law $\sin^2\theta_{ij}\propto(\mathrm{flip_count_ratio})\times\varphi^{-|\Delta\tau_{ij}|}$. It is the mass-sector half of the Cabibbo-scale mixing amplitude in the Q₃ derivation: torsion gap 11 between the ground and edge-dressed generations. Downstream mixing-angle constructions that assemble $V_{us}$ (or related 1–2 blocks) rely on this exact power. Within the broader RS chain it sits on the $\varphi$-ladder and J-cost suppression already fixed by T5–T6, specialized here to Standard Model flavor geometry rather than forcing $\varphi$ itself.
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