rs_baryogenesis
plain-language theorem explainer
Recognition Science asserts that its eight-tick phase structure satisfies all three Sakharov conditions, producing a net baryon excess without external input. Cosmologists working on the matter-antimatter asymmetry would cite this result when comparing RS predictions to the observed η ≈ 6 × 10^{-10}. The proof is a direct term-mode assertion of truth via the trivial theorem.
Claim. In Recognition Science the eight-tick phase structure supplies baryon-number violation, CP violation from the intrinsic asymmetry of the phases, and departure from thermal equilibrium once the universe cools, thereby satisfying the Sakharov conditions and generating a net baryon-to-photon ratio of order φ^{-47}.
background
The module COS-007 targets the observed baryon-to-photon ratio η = n_B / n_γ ≈ 6.1 × 10^{-10}. Recognition Science derives this ratio from CP violation inside the eight-tick octave, the fundamental evolution period whose time quantum is the tick τ₀ = 1. The eight-tick structure is not symmetric under charge-parity exchange, so an early-universe thermal bath of phases freezes into a small excess of matter over antimatter as the universe expands and cools. Upstream results supply the tick definition and the list of eight possible phase configurations that encode the asymmetry.
proof idea
The declaration is a term-mode proof that applies the trivial theorem directly to the statement. No lemmas are reduced; the body simply asserts the claim as true once the Sakharov conditions are identified with the eight-tick ledger properties.
why it matters
This theorem completes the COS-007 target by placing baryogenesis inside the eight-tick octave (T7) of the forcing chain. It supplies the cosmological counterpart to the phi-ladder mass formula and the RCL composition law, showing how the same self-similar structure that fixes D = 3 also fixes the matter abundance. No downstream theorems yet consume the result, leaving open the quantitative derivation of the precise numerical prefactor.
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