inflationModelsCert
The definition inflationModelsCert packages the enumerated count of five inflation models into the required certificate structure for configDim equal to five. Cosmologists verifying A2-depth predictions in Recognition Science would cite it to confirm the complete set of canonical inflaton families before computing slow-roll observables. The construction is a direct one-line record assignment that inserts the decidable cardinality theorem into the structure field.
claimLet $C$ be the structure whose sole field requires that the cardinality of the set of inflation models equals five. Then inflationModelsCert is the instance of $C$ whose five_models component is the theorem establishing that cardinality.
background
The module treats inflation models derived from configuration dimension five, listing five canonical inflaton-potential families: the chaotic $m^2 phi^2$ form, the new-inflation plateau, the hybrid model, the natural axion-like potential, and the alpha-attractor conformal family. Each family produces distinct slow-roll predictions for the scalar spectral index and tensor-to-scalar ratio. The local setting is the A2 depth classification in Recognition Science cosmology, where configDim equals five fixes the number of models under examination.
proof idea
The definition is a one-line wrapper that constructs the InflationModelsCert record by assigning the result of the inflationModel_count theorem to the five_models field.
why it matters in Recognition Science
This definition supplies the certified enumeration of the five inflation models required for the A2 depth analysis. It closes the model-count step whose slow-roll observables are later compared with observations. No downstream uses appear yet, leaving open its integration into derivations of cosmic microwave background parameters from the Recognition Composition Law.
scope and limits
- Does not compute slow-roll parameters n_s or r for any model family.
- Does not derive the five potential families from the Recognition Composition Law.
- Does not address the transition from inflation to reheating or post-inflationary dynamics.
formal statement (Lean)
31def inflationModelsCert : InflationModelsCert where
32 five_models := inflationModel_count
proof body
Definition body.
33
34end IndisputableMonolith.Cosmology.InflationModelsFromConfigDim