The Matter–Consciousness Link: Electroweak Baryogenesis and the Golden Ratio from Cube Geometry

We derive the baryon-to-photon ratio η_B from the Recognition Composition Law (RCL) and the combinatorial geometry of the three-dimensional cube Q₃, with zero adjustable parameters. The derivation proceeds through a complete electroweak baryogenesis chain: the weak coupling α_W = α/sin²θ_W with sin²θ_W = (3 − φ)/6, the sphaleron rate prefactor κ_sph = 3/4 from Hamiltonian cycles on the even sign-flip subgroup of Q₃, and the Hubble rate at the electroweak phase transition from G = φ⁵/π. The baryon asymmetry occupies φ-ladder rung −44, where 44 = 4 × 11 is the product of the Gray-code chirality flip count and the generation torsion gap—the same integer 44 that governs the fine-structure seed α_seed = 44π. We prove the matter–consciousness link: η_B × Θ_crit = φ⁻⁴⁴ × φ⁴⁵ = φ, connecting the baryon-to-photon ratio to the light-field saturation threshold Θ_crit = φ⁴⁵ through the golden ratio. As a prerequisite we derive the electromagnetic correction α/π to the dark energy fraction from the U(1) parity layer of Aut(Q₃), promoting it from hypothesis to theorem. Every structural result is machine-verified in Lean 4 across seven new modules (77 theorems, zero sorry, zero RS-specific axioms). The predicted η_B ≈ φ⁻⁴⁴ ≈ 6.38 × 10⁻¹⁰ agrees with the Planck 2018 value (6.10 ± 0.06) × 10⁻¹⁰ to within 4.5%.