IndisputableMonolith.Physics.InflationEfoldsFromGap45
The module derives the e-fold count in inflation from Recognition Science as N_e = 44 obtained by subtracting one from the gap-45 parameter. Cosmologists matching RS predictions to early-universe observables would cite it when fixing the duration of inflation. The module consists of a collection of direct definitions and arithmetic relations among Nefolds, gap45 and related quantities with no lemmas or complex proofs.
claim$N_e = 44 = \text{gap}_{45} - 1$, where gap_{45} denotes the gap parameter at the indicated rung on the RS ladder and N_e is the number of e-folds.
background
The module imports Constants, which supplies the fundamental RS time quantum τ₀ = 1 tick. Recognition Science obtains all physical scales from the forcing chain and the Recognition Composition Law; the present module specializes this structure to inflationary cosmology by expressing the e-fold number directly in terms of the gap parameter. Sibling definitions include Nefolds, gap45, Nefolds_gap45_minus_one, Nefolds_times_gap45, nS_RS and InflationEfoldCert, which together convert the gap choice into the spectral index and related observables.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module supplies the RS-native e-fold count N_e = 44 that enters inflation models, implementing the relation stated in the module documentation. It serves as a foundational block for downstream cosmological quantities such as nS_RS even though the used_by list is currently empty. The construction links the gap parameter on the phi-ladder to the eight-tick octave structure of the forcing chain.
scope and limits
- Does not derive the numerical value of gap45 itself.
- Does not contain the dynamical equations of the inflaton.
- Does not perform comparison with CMB observations.
- Does not address multi-field or non-slow-roll regimes.