BCT Appendices Collection — Vol. AD: Unitarity Triangle, Biology Theorems, and Protein Folding (Appendices AD3–AD5)

Companion appendices to BCT Letters Collection Vol. 4 (Letters 89–95). Three formal technical derivations. Appendix AD3 — BCT Unitarity Triangle Theorem: complete algebraic derivation of all Wolfenstein CKM parameters in closed form (in √2, √6, and π only). Full 3×3 CKM matrix. Jarlskog invariant J = 3. 07×10⁻⁵ (error −0. 3%). Companion to Letter 90. Appendix AD4 — BCT Biology Theorems: formal proofs of the BCT DNA Complementarity Theorem (Chargaff's rules from net Hopf charge = 0), the hydrogen bond count theorem (bonds = |H|), and the chirality energy formula ΔE = 2α₀rₜet·Ebond ≈ 1. 67×10⁻³·Ebond. Unified BCT structural biology hierarchy from Letter 80 through Letter 92. Companion to Letter 92. Appendix AD5 — Protein Secondary Structure Derivations: formal derivation of the double-winding mechanism (n = 2rₒct/rₜet = 3. 686) ; Farey sequence lock-in analysis identifying 18/5 as the commensurate state; exact algebraic forms for all α-helix and collagen parameters. Companion to Letter 93. All derivations: zero free parameters. Closed algebraic forms in √2, √6, and π throughout.