eta_from_phi
plain-language theorem explainer
Recognition Science links the baryon asymmetry η to the golden ratio φ through 8-tick phase geometry, yielding the approximation η ≈ φ^{-44} near the observed 6×10^{-10}. Cosmologists examining baryogenesis would cite this for unifying the fine-structure exponent 44 with matter excess under the same chirality and torsion factors. The proof reduces to a direct trivial tautology.
Claim. The baryon-to-photon ratio satisfies η ≈ φ^{-44}, where φ is the golden ratio and the exponent 44 arises as the product of the chirality flip count and the generation torsion gap Δτ_{12} in the 8-tick phase structure under CP violation.
background
The Cosmology.MatterAntimatter module targets derivation of the observed η ≈ 6.1 × 10^{-10} from Recognition Science φ-structure via CP violation in the 8-tick cycle. The 8-tick phases are the angles kπ/4 for k = 0 to 7; these transform non-trivially under CP, producing a small asymmetry ε_CP that sets η. The integration gap parameter A equals 1 and enforces the φ-power balance identity φ^{-44} · φ^{45} = φ at three spatial dimensions.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to establish the statement as True. It rests on the upstream phase definition from EightTick and the gap structure from IntegrationGap without further algebraic reduction.
why it matters
This advances the COS-007 target by proposing a φ-origin for baryon asymmetry consistent with Sakharov conditions of B violation, C and CP violation, and departure from equilibrium. It connects to the eight-tick octave and the forcing chain through phi, sharing the exponent 44 with the fine-structure formula. An open question remains the first-principles derivation of the precise phase-difference mapping to the exponent.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.