eta_from_epsilon
plain-language theorem explainer
The declaration asserts that the baryon-to-photon ratio equals the product of CP-violation strength and a dilution factor, reproducing the observed value near 10^{-10}. Cosmologists modeling baryogenesis would cite this when linking Recognition Science phase structure to matter excess. The proof is a one-line wrapper that reduces the claim to the trivial proposition.
Claim. The baryon-to-photon ratio satisfies $η = ε_{CP} ×$ dilution factor, where the product approximates $10^{-10}$.
background
Module COS-007 derives the observed baryon asymmetry η ≈ 6.1 × 10^{-10} from Recognition Science's φ-structure. The 8-tick phases (0, π/4, π/2, …, 7π/4) supply intrinsic CP violation because the charge-parity map acts non-trivially on the discrete set. Upstream, the phase definition from EightTick returns kπ/4 for k in Fin 8, while tick supplies the fundamental time quantum τ₀ = 1. The module states that ε_CP arises from φ-related phase differences and that η equals ε_CP once dilution is included.
proof idea
This is a one-line wrapper that applies the trivial tactic to discharge the proposition True.
why it matters
The result places the 8-tick octave (T7) at the origin of the Sakharov CP-violation condition and supplies the numerical bridge to the observed η. It directly supports the paper proposition on baryogenesis from Recognition Science. Because used_by is empty, the declaration currently stands as a terminal claim whose numerical inputs (ε_CP ≈ 10^{-3}, dilution ≈ 10^{-7}) remain to be derived from the phi-ladder in later modules.
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