etaBAt_44
plain-language theorem explainer
The declaration fixes the baryon-to-photon ratio at exactly 44 recognition e-folds after the GUT epoch as φ to the power of negative 44. Cosmologists using the Recognition Science phi-ladder would cite this to anchor the present-epoch asymmetry to the equilibrium identity. The proof is a one-line wrapper that unfolds the etaBAt definition and normalizes the integer exponent.
Claim. η_B(44) = φ^{-44}, where η_B(N) is the baryon-to-photon ratio after N recognition e-folds since the GUT epoch.
background
The Baryogenesis Dynamic Trajectory module defines etaBAt(N) as the baryon asymmetry parameter after N recognition e-folds, given explicitly by etaBAt(N) := φ^{-N}. This produces the trajectory η_B(N) = exp(-N log φ), with the 44-rung gap from GUT-scale unity to the present epoch matching the inflation e-fold count N_e = 44 and the equilibrium identity η_B · Θ_crit = φ from the matter-consciousness duality theorem. The upstream definition etaBAt supplies the core recursive step used throughout the module.
proof idea
The proof is a one-line wrapper that unfolds the definition of etaBAt and applies norm_cast to equate the natural-number exponent with its integer form.
why it matters
This supplies the terminal value required by the baryogenesisTrajectoryCert, confirming that η_B reaches φ^{-44} at the present epoch and closes the dynamic trajectory. It realizes the 44 e-fold prediction on the phi-ladder that links the GUT epoch to the observed asymmetry band. The result sits inside the Recognition framework's eight-tick octave and D = 3 spatial structure without introducing new hypotheses.
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