Project T Volume XI Baryogenesis Why Matter Exists: The Three Sakharov Conditions from Algebra

This volume demonstrates how baryogenesis — the creation of the matter-antimatter asymmetry — emerges from the H₀(Ã₂) structure. We show that all three Sakharov conditions are satisfied algebraically:● B-violation: Through trefoil T(3,2) transitions● CP-violation: Through braid chirality (aba = bab is asymmetric)● Departure from equilibrium: Through the Ã₂ → A₃ collapse Complete numerical simulations verify each mechanism. We derive the baryon-to-photon ratio: η_B = (19/42) × (3/61) × (2/24) ≈ 6 × 10⁻¹⁰ This matches the observed value and explains why matter exists from algebraic principles alone.