What question did this study set out to answer?

To formally state and prove the BCT Cabibbo Theorem and explore its implications in particle physics.

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March 22, 2026Open Access

Appendix AD1 — BCT Cabibbo Theorem

Key Points

To formally state and prove the BCT Cabibbo Theorem and explore its implications in particle physics.
Derived a closed-form algebraic expression for sin(θC) using √2, √6, and π without numerical inputs.
Conducted a full derivation of the CKM block based on unitarity principles.
Identified structural parallels between the Weinberg and Cabibbo angles.
Established sin(θC) = 2r_tet(1+3α0/8) with r_tet defined as (√6−2)/4.
Proposed a candidate for the Wolfenstein A parameter as A ≈ 1/(1+r_oct) with a margin of error at +0.56%.
Outlined the NLO factors of α0 in relation to both angles.

Abstract

Companion appendix to BCT Letter 86. Provides the formal statement and proof of the BCT Cabibbo Theorem: sin (θC) = 2rₜet (1+3α0/8), where rₜet = (√6−2) /4 is the tetrahedral void radius and α0 = rₒct·rₜet/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+rₒct), error +0. 56%, formal derivation deferred to Appendix AD2.

Appendix AD1 — BCT Cabibbo Theorem

Key Points

Abstract

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