efoldCount_eq
The Recognition Science inflaton model fixes the e-fold count at exactly 44 on the gap-45 ladder. Researchers building the inflaton certification object cite this equality to lock in the structural count after reheating transit. The proof is a direct reflexivity reduction to the constant definition of the count.
claimIn the Recognition Science inflaton model the e-fold count satisfies $N_e = 44$.
background
The Inflaton Potential Structural module specifies the RS inflaton potential V(χ) with five canonical regimes (slow-roll plateau, slow-roll slope, hilltop decline, reheating, post-reheating radiation) corresponding to configDim D = 5. Slow-roll parameters are ε = 1/(2φ⁵) and η = 1/φ⁵, yielding n_s - 1 = -2/45 and r = 2/(45 φ²). The e-fold count is introduced as N_e = 44, described as gap-45 minus one tick for reheating transit.
proof idea
The proof is a one-line wrapper that applies reflexivity to the upstream definition efoldCount := 44.
why it matters in Recognition Science
This equality supplies the efolds field inside inflatonCert, which also bundles the five-regime count, the phi5 Fibonacci relation, and positivity of the slow-roll parameters. It realizes the module claim that N_e-fold count = 44 (gap-45 minus one tick for reheating transit). In the Recognition framework it anchors cosmological predictions to the phi-ladder structure and the eight-tick octave.
scope and limits
- Does not derive the value 44 from the J-function or forcing chain T0-T8.
- Does not apply to inflaton potentials outside the five RS structural regimes.
- Does not compute e-fold counts under varying initial conditions or quantum corrections.
- Does not address dependence on spatial dimension D or the alpha band.
Lean usage
efolds := efoldCount_eqformal statement (Lean)
35theorem efoldCount_eq : efoldCount = 44 := rfl
proof body
Term-mode proof.
36
37/-- Slow-roll parameter ε = 1/(2φ⁵). -/