Complete Derivation of Fundamental Constants Prime Number System, BC Algebra, and Verifiable Predictions — Updated to ALO v3 Update note: This article originally presented the ALO v1 derivation of fundamental constants (α⁻¹, α_s, sin²θ_W, quark mass ratios, CKM angles, gauge groups from BC). Since then, the framework was extended (ALO v3) to a full hierarchical reconstruction of the Standard Model…