eta_is_small

In the Recognition Science treatment of cosmology the baryon asymmetry parameter η is introduced as the ratio of baryon to photon number densities, with the module deriving its small value from CP violation inside the eight-tick phase structure. The local setting states that η ≈ 6.1 × 10^{-10} arises because the charge-parity transformation is not exact across the φ-related phases, preventing complete annihilation of matter and antimatter. Upstream results supply the supporting structures: NucleosynthesisTiers.of encodes nuclear densities on the φ-ladder, PhysicsComplexityStructure.of establishes J-cost minimization as strictly convex with unique minimum at x=1, and SpectralEmergence.of forces the gauge content and three generations that set the stage for the asymmetry.

The proof is a one-line wrapper that unfolds the definition of eta_observed to its numerical value 6.1e-10 and invokes norm_num to verify the strict inequality against 1e-9.

This theorem supplies the concrete numerical bound required by the COS-007 core insight that η emerges from CP violation in the 8-tick octave, directly feeding sibling declarations such as eta_from_epsilon and sakharov_necessary. It aligns with framework landmarks T7 (eight-tick period) and the ledger factorization that produces the small ε_CP ~ 10^{-10}. The result closes the observed-value side of the argument while leaving open the first-principles derivation of the exact magnitude from the J-cost ledger.