V_cd
plain-language theorem explainer
V_cd assigns the CKM down-charm mixing element to the negative of the Wolfenstein lambda parameter. Researchers assembling quark flavor mixing matrices in the Recognition Science framework cite this entry when checking CP violation bounds and unitarity triangles. The assignment is a direct abbreviation of the upstream cabibboAngle definition.
Claim. The CKM matrix element satisfies $V_{cd} = -λ$, where $λ$ is the Wolfenstein parameter equal to the sine of the Cabibbo angle.
background
The StandardModel.CKMMatrix module derives CKM elements from φ-quantized mixing angles linked to the eight-tick phase structure. Wolfenstein lambda is introduced as cabibboAngle, which approximates 0.227 and matches the observed |V_us|. The upstream Physics.CKM module defines an analogous V_cd as the negative of V_us, grounding the Jarlskog invariant in geometric predictions.
proof idea
One-line definition that substitutes the value of wolfenstein_lambda directly into the complex numbers.
why it matters
This supplies the V_cd entry required by the cp_violation_small theorem, the predictions list, and the unitarity_triangle_valid check. It fills the SM-012 paper proposition on CKM Matrix from Golden Ratio Geometry by connecting to the 8-tick octave and φ-ladder in the forcing chain. The definition keeps the matrix construction aligned with observed magnitudes while leaving numerical verification to downstream norm_num tactics.
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