predictions
The definition enumerates four explicit predictions for baryogenesis drawn from the Recognition Science φ-structure: η ≈ φ^{-47} ≈ 4×10^{-10}, CP violation tied to the eight-tick phase, baryogenesis during reheating, and correlations among φ-derived cosmological quantities. A cosmologist comparing RS outputs to Planck data on the baryon-to-photon ratio would reference this list. The declaration is a direct string enumeration with no further computation.
claimThe Recognition Science predictions for baryogenesis are: the baryon-to-photon ratio satisfies η ≈ φ^{-47} ≈ 4×10^{-10}; CP violation is intrinsic to the eight-tick structure; baryogenesis occurs during reheating; and the asymmetry correlates with other φ-derived cosmological parameters.
background
The module COS-007 targets derivation of the observed baryon-to-photon ratio η = n_B / n_γ ≈ 6.1×10^{-10} from the Recognition Science φ-ladder and eight-tick phase structure. In this setting the eight-tick octave supplies an intrinsic CP asymmetry ε_CP ~ 10^{-10} that directly sets η, satisfying the Sakharov conditions of baryon-number violation, C and CP violation, and departure from equilibrium. Upstream results supply supporting structure: PrimitiveDistinction.from extracts four substantive conditions from seven axioms, while EdgeLengthFromPsi.is confirms algebraic consistency of the underlying ledger distances.
proof idea
The declaration is a direct definition that enumerates the four prediction strings; no lemmas or tactics are applied beyond literal construction of the List String.
why it matters in Recognition Science
This definition collects the observable outputs of the baryogenesis derivation and points to the target paper proposition 'Baryogenesis from Recognition Science'. It rests on the eight-tick octave (T7) and the self-similar fixed point φ (T6) from the forcing chain, together with the Recognition Composition Law that governs the underlying J-cost. The open question flagged in the module comment is whether the precise exponent n ≈ 44-48 can be derived from first principles rather than fitted to the observed η.
scope and limits
- Does not derive the numerical value of η from the forcing chain axioms.
- Does not prove any of the listed predictions.
- Does not incorporate Planck error bars or dilution factors.
- Does not address reheating dynamics or Sakharov condition verification.
formal statement (Lean)
283def predictions : List String := [
proof body
Definition body.
284 "η ≈ φ^(-47) ≈ 4 × 10⁻¹⁰",
285 "CP violation fundamental to RS",
286 "Baryogenesis during reheating",
287 "Correlations with other cosmological parameters"
288]
289
290/-- The key test: if η = φ^(-n), what is n?
291 n ≈ log(1/η) / log(φ) = log(1.6 × 10⁹) / log(1.618) ≈ 44-48
292
293 If we can derive n from first principles, this would be huge! -/