unitarity_triangle_valid
plain-language theorem explainer
The Wolfenstein parameters satisfy ρ̄² + η̄² < 1, confirming closure of the unitarity triangle for the CKM matrix. Flavor physicists verifying Standard Model consistency with Recognition Science derivations would cite this result. The proof is a direct term-mode reduction that unfolds the two parameter definitions and evaluates the resulting numerical inequality.
Claim. $ {¯ρ}^2 + {¯η}^2 < 1 $
background
The module derives CKM matrix elements from φ-quantized mixing angles tied to the eight-tick phase structure of Recognition Science. Wolfenstein rho and eta are the standard reparametrization coordinates of the CKM matrix that encode the CP-violating phase and the deviation from the Cabibbo angle hierarchy. Upstream definitions supply the explicit CKM elements V_ud, V_us, V_ub, V_cd, V_cb as real numbers obtained from the φ-ladder and 8-tick neutrality conditions.
proof idea
The proof is a one-line term wrapper. It unfolds the definitions of wolfenstein_rho and wolfenstein_eta, then applies norm_num to reduce the resulting arithmetic expression to a concrete numerical comparison that holds.
why it matters
The declaration closes the unitarity requirement for the CKM matrix constructed from φ-angles in the eight-tick octave. It supplies the geometric consistency check needed before any downstream use of the full 3×3 unitary matrix in weak-interaction calculations. No parent theorem is listed among the used-by edges, and the result touches no open scaffolding.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.