regimeCount
plain-language theorem explainer
The declaration fixes the number of heat transfer regimes at five in the Recognition Science thermodynamics layer. Researchers certifying Nusselt ratios or thermoelectric effects from the phi-ladder would reference this count to anchor the configDim D = 5 claim. The proof is a one-line decision procedure that enumerates the constructors of the derived Fintype instance.
Claim. The set of heat transfer regimes consisting of pure conduction, mixed convection, forced convection, natural convection, and radiative modes has cardinality five: $5$.
background
The HeatTransferRegime inductive type lists exactly the five modes pureConduction, mixedConvection, forcedConvection, naturalConvection, and radiative, each equipped with a Fintype instance. The module document states that these regimes realize configDim D = 5 and that adjacent-regime Nusselt numbers scale by phi squared. The same pattern appears in the upstream ThermoelectricEffectFromJCost.regimeCount theorem, which likewise fixes five thermoelectric regimes by direct cardinality computation.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the automatically generated Fintype instance of HeatTransferRegime, which returns the integer 5.
why it matters
The result supplies the five_regimes field of heatTransferCert and is reused inside thermoelectricCert. It completes the configDim D = 5 step inside the thermodynamics tier of the Recognition framework, consistent with the phi-ladder scaling and the eight-tick octave structure. No open scaffolding questions are attached to this declaration.
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