s23_w
The declaration supplies the 2-3 CKM sine by direct alias to V_cb. Researchers assembling the Jarlskog invariant from phi-ladder rung differences between quark generations cite this when forming the witness product. It is realized as a one-line alias to the upstream V_cb predicate.
claimLet $s_{23}$ denote the sine of the 2-3 Cabibbo-Kobayashi-Maskawa mixing angle. Then $s_{23}$ equals the Wolfenstein parameter $V_{cb}$.
background
The module derives CKM matrix elements from rung differences on the phi-ladder for up and down quark generations at τ_g = 0, 11, 17. This produces angles θ_ij approximately φ to the minus half the rung difference, with the Jarlskog invariant obtained as a forced dimensionless output from residue asymmetry. V_cb is the real 2-3 element, defined via the predicate V_cb_pred that originates in the geometric proofs of MixingDerivation.
proof idea
The definition is a one-line alias that directly references the V_cb definition from the same module, which itself aliases the Wolfenstein form A λ² from the standard model CKM matrix.
why it matters in Recognition Science
This definition is used to build the jarlskog_witness as the product s12_w * s23_w * s13_w, which approximates the Jarlskog invariant J from the phi-ladder. It supports the module goal of extracting the CP phase without external fitting and aligns with the Recognition Composition Law applied to mixing angles. The construction feeds the positivity theorem jarlskog_witness_pos.
scope and limits
- Does not derive the numerical value of V_cb from the phi-ladder rung formula.
- Does not include radiative corrections beyond the base geometric model.
- Does not specify the full CKM matrix or its unitarity constraints.
formal statement (Lean)
61noncomputable def s23_w : ℝ := V_cb