IndisputableMonolith.Cosmology.CosmicInflationFromJCost
This module certifies cosmic inflation termination when J-cost crosses the canonical threshold using the six-clause template. Cosmologists in Recognition Science cite it to derive early-universe dynamics from the J functional equation. The module structures its argument via definitions of the inflation model followed by a certification theorem that applies matched-zero and nonnegativity.
claimCosmic inflation terminates when the recognition cost $J(r)$ on the expansion ratio $r$ crosses the canonical threshold, satisfying the band conditions $J(1)=0$ and $J(r)≥0$ for $r>0$.
background
The module imports the CanonicalJBand template, which supplies a reusable six-clause structure for J-cost on ratios. That template proves matched-zero $J(1)=0$ and nonnegativity $J(x)≥0$ for $x>0$, drawn from the Recognition Composition Law. The cosmology module applies this template to the scale-factor evolution governed by the phi self-similar fixed point.
proof idea
This is a definition module, no proofs. It organizes content as definitions for InflationModel and inflationModelCount, the threshold lemma inflation_ends_at_threshold, and the CosmicInflationCert theorem that instantiates the J-band clauses.
why it matters in Recognition Science
This module supplies the CosmicInflationCert that completes the cosmology domain opening in the master cert chain. It fills the B-tier slot by showing inflation ends at J-cost threshold crossing, consistent with the forcing chain T5 J-uniqueness through T8 D=3.
scope and limits
- Does not derive the Friedmann equations or metric dynamics.
- Does not compute e-fold numbers or power spectra.
- Does not address reheating or post-inflationary evolution.