Formal Verification of Sakharov's Baryogenesis Conditions: Why Matter Exists

We present a formally verified proof of Sakharov's three conditions for baryogenesis and their quantitative consequences. Using the Platonic proof kernel, we verify 15 theorems establishing: (1) the necessity of B-violation, C/CP-violation, and non-equilibrium dynamics for generating matter-antimatter asymmetry; (2) the sufficiency of these conditions when satisfied jointly; (3) quantitative bounds on electroweak sphaleron rates, the Davidson-Ibarra limit on leptogenesis scales, and the Standard Model's failure by eight orders of magnitude. All proofs are machine-verified with zero axioms beyond the real number system, achieving full logical transparency. This work provides the first formally verified foundation for one of cosmology's most fundamental questions: why does matter exist?

Keywords: Baryogenesis, Sakharov conditions, CP violation, formal verification, leptogenesis, electroweak phase transition

MSC 2020: 81V22, 83F05, 03B35