ClimatePhysicsCert
plain-language theorem explainer
ClimatePhysicsCert records that the climate system has exactly five feedback mechanisms and sits at energy balance where the J-cost of unit forcing vanishes. Climate modelers working inside the Recognition Science framework would cite this structure to certify that their energy-budget simulations respect the canonical feedback count and J=0 equilibrium. The definition is a direct record of these two invariants with no computational content.
Claim. Let $F$ be the inductive type of climate feedback mechanisms. The structure asserts that the cardinality of $F$ equals 5 and that the J-cost of unit forcing satisfies $J(1)=0$.
background
Recognition Science treats climate equilibrium as the point where the J-cost vanishes, with forcing corresponding to positive J. The module enumerates five canonical feedbacks (water vapor, ice-albedo, Planck, lapse rate, cloud) that match configDim D=5. The upstream inductive type ClimateFeedback supplies exactly these five constructors together with a Fintype instance.
proof idea
Structure definition that directly encodes the two field assertions: Fintype.card ClimateFeedback = 5 and Jcost 1 = 0. No lemmas or tactics are invoked; the fields are supplied by construction in the downstream term climatePhysicsCert.
why it matters
The structure supplies the type for the certified climate-physics instance that anchors the module's claim of five feedbacks and J=0 balance. It is instantiated by climatePhysicsCert using climateFeedbackCount and energy_balance. In the Recognition Science chain it connects the J-uniqueness result (T5) to the concrete energy-budget equilibrium condition.
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