Appendix AD1 — BCT Cabibbo Theorem

Companion appendix to BCT Letter 86. Provides the formal statement and proof of the BCT Cabibbo Theorem: sin(θC) = 2r_tet(1+3α0/8), where r_tet = (√6−2)/4 is the tetrahedral void radius and α0 = r_oct·r_tet/π is the BCT bare coupling. Contains: the complete closed-form algebraic expression for sin(θC) in √2, √6 and π with zero numerical inputs; full derivation of the two-generation CKM block from unitarity; the structural parallel between the Weinberg angle (intra-generation, NLO factor 9α0/4) and the Cabibbo angle (inter-generation, NLO factor 3α0/8); and a candidate for the Wolfenstein A parameter: A ≈ 1/(1+r_oct), error +0.56%, formal derivation deferred to Appendix AD2.