Baryogenesis: η_B = α·ι_τ¹⁵·(5/6) at −1%
The baryon-to-photon ratio η_B is derived as α·ι_τ¹⁵·(5/6) at −1%, with the three Sakharov conditions satisfied structurally.
Overview
V.T188 derives the baryon asymmetry parameter η_B = n_B/n_γ = α·ι_τ¹⁵·(5/6) at −1% from observation. The formula arises from the SA-i (self-adjoint admissibility) mod-5 structure of the baryogenesis process. The three Sakharov conditions (baryon number violation, C and CP violation, deviation from thermal equilibrium) are each derived from the τ-structure. The ι_τ¹⁵ factor equals (ι_τ³)^(W₃(4)) = (ι_τ³)^5, a structural decomposition via Window Universality.
Detail
The baryon asymmetry of the universe — the fact that there is approximately one baryon per billion photons (η_B ≈ 6 × 10⁻¹⁰) — is unexplained in the Standard Model without a specific baryogenesis mechanism. Sakharov’s 1967 conditions for baryogenesis are: (1) baryon number violation, (2) C and CP violation, (3) departure from thermal equilibrium. Book V derives η_B from the τ-framework. The SA-i (self-adjoint admissibility) condition on the η-sector operates mod-5 in the baryogenesis context: five is the Window number W₃(4) = 5, and mod-5 counting of η-winding determines the net baryon number. The formula η_B = α·ι_τ¹⁵·(5/6) can be decomposed as: ι_τ¹⁵ = (ι_τ³)^5 = (ι_τ³)^(W₃(4)) using the Window Universality structure. The factor (5/6) = W₃(4)/(2·sectors) = 5/6. The three Sakharov conditions are satisfied: baryon number violation from the SA-i mod-5 structure (net winding is non-zero), CP violation from the strong-sector parity (connected to θ_QCD = 0 via the same SA-i admissibility), and thermal non-equilibrium from the τ-phase transition at E₁. The Sakharov bridge from τ-derivation to orthodox baryogenesis mechanism remains conjectural.
Result Statement
V.T188: η_B = α·ι_τ¹⁵·(5/6) at −1%. ι_τ¹⁵ = (ι_τ³)^(W₃(4)) via Window Universality. Three Sakharov conditions structurally satisfied. Sakharov bridge conjectural.