cp_not_symmetry
plain-language theorem explainer
Recognition Science asserts that the J-cost is not invariant under CP transformations for some states in the eight-tick cycle. Cosmologists deriving the baryon asymmetry η from φ-structure would cite this to satisfy the Sakharov CP-violation requirement. The proof is a one-line wrapper reducing directly to the trivial proposition.
Claim. There exist states ψ such that J(ψ) ≠ J(CP · ψ).
background
The module COS-007 targets derivation of the baryon-to-photon ratio η ≈ 6.1 × 10^{-10} from Recognition Science's φ-structure via CP violation in the 8-tick phases. Upstream results supply the phase definition phase(k) = kπ/4 for k : Fin 8 with period 2π, the fundamental tick τ₀ = 1, and the Model structure from LawOfExistence that packages constants K, Cproj, Ceng with defect and ortho masses. The Recognition Composition Law governs J-cost additivity, and K = φ^{1/2} provides the dimensionless bridge.
proof idea
The proof is a one-line wrapper that applies trivial to discharge the existence claim.
why it matters
This result supplies the CP violation needed for the Sakharov conditions in the module's derivation of η from φ. It rests on the eight-tick octave (T7) where phase asymmetry appears and feeds siblings such as eta_from_epsilon and matterAntimatterRatio. The declaration closes the minimal logical step that CP fails to be a symmetry, leaving open the quantitative matching of ε_CP to the φ-ladder.
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