N_e_is_fibonacci
plain-language theorem explainer
The declaration fixes the e-fold count at 55, expressed as the product 5 times 11 and identified as the tenth Fibonacci number. Inflation modelers in Recognition Science cite it when anchoring spectral-index formulas such as 1 minus 2 over N. The proof is a direct arithmetic check performed by norm_num.
Claim. The number of e-folds satisfies $N_e = 55 = 5 × 11$, where 55 coincides with the tenth Fibonacci number.
background
The JCostInflaton module shows that the Recognition Composition Law forces the inflaton potential to take the form G(t) = cosh(t) − 1 in logarithmic coordinates. Slow-roll parameters ε and η are then obtained from the first and second derivatives of G, with the vacuum at t = 0. The module also records the spectral-index relation 1 − 2/N that follows once N is fixed.
proof idea
The proof is a one-line wrapper that applies norm_num to confirm the numerical identity 55 = 5 × 11.
why it matters
The result supplies the concrete value of N_e required by the master certificate InflationFromJCostCert and by the spectral-index derivation n_s_from_jcost. The identification of 55 with the tenth Fibonacci number aligns with the self-similar fixed point phi (T6) and the phi-ladder structure used for mass assignments. No open questions are closed by this step.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.