efolds_typical
plain-language theorem explainer
efolds_typical binds the conventional count of inflationary e-folds to the fixed real 57 inside the Recognition Science derivation of the primordial power spectrum. Cosmologists computing the spectral index from J-cost fluctuations would cite this value to recover n_s ≈ 0.9655 via the supplied alternative formula. The definition is a direct numerical assignment with no reduction or lemma application.
Claim. Let $N$ be the number of e-folds during inflation. Then $N = 57$.
background
The module derives the CMB power spectrum from J-cost quantum fluctuations during inflation, with the φ-ladder fixing the spectral tilt. Upstream, cost denotes the J-cost of a recognition event (ObserverForcing.cost) or the derived cost of a multiplicative recognizer comparator (MultiplicativeRecognizerL4.cost). The local setting states that these fluctuations freeze out and seed density perturbations, yielding a nearly scale-invariant spectrum with n_s slightly below 1.
proof idea
One-line definition that directly assigns the real constant 57.
why it matters
The constant supplies the input N for the alternative spectral-index formula n_s = 1 - 2/(N + 1) and supports the paper proposition on the CMB spectral index from the golden ratio. It sits inside the eight-tick octave structure (T7) and the φ-ladder of the forcing chain, touching the open question whether N equals φ^8 - 1 or an exact multiple of the octave period.
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