inflationModelCount
plain-language theorem explainer
The Recognition Science framework enumerates exactly five inflation models compatible with the J-cost threshold and baryon rung at 44. Cosmologists working on RS-derived inflation would cite this count when verifying the five-model taxonomy against the config dimension D=5. The proof is a one-line decision procedure that exhausts the finite inductive type.
Claim. The finite set of canonical inflation models in the Recognition Science framework has cardinality five: $|M| = 5$, where $M$ consists of the Starobinsky, natural, Higgs, chaotic, and axion-monodromy models.
background
In the module on Inflationary Cosmology from RS, the inductive type InflationModel enumerates five specific models: starobinsky, natural, higgs, chaotic, and axionMonodromy. This count is tied to the configuration dimension D=5, as noted in the module documentation stating five models equal configDim D=5. Upstream results include the definition baryonRung := 44 from BaryonAsymmetryFromPhiLadder, which sets the e-folds N_e = 44, and the similar inflationModelCount in CosmicInflationFromJCost that also yields 5. The E function from SpectralEmergence defines the number of edges in the D-cube as D * 2^(D-1), providing the combinatorial background for dimensional counting in the framework. The local setting is that these five models are backed by RS, with inflation ending when J-cost crosses the canonical threshold.
proof idea
The proof is a one-line term proof using the decide tactic. This tactic computes the cardinality of the Fintype instance automatically derived from the inductive definition of InflationModel, which has exactly five constructors, confirming the equality to 5 without further lemmas.
why it matters
This theorem supplies the five_models field in the inflationaryCosmCert definition within the same module and is referenced by cosmicInflationCert in CosmicInflationFromJCost. It directly implements the claim from the module documentation that five models correspond to configDim D=5, closing the enumeration step in the inflationary cosmology derivation from Recognition Science. It touches the broader question of how the phi-ladder and J-cost dynamics select the discrete set of viable models, consistent with the eight-tick octave and D=3 spatial dimensions in the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.