ClimateFeedback
plain-language theorem explainer
Climate physicists cite this inductive enumeration of the five canonical feedback mechanisms when counting channels in energy-balance models derived from Recognition Science. The type equips the feedbacks with decidable equality and finite cardinality for direct computation of the feedback count. The definition proceeds by direct inductive listing of the constructors waterVapor, iceAlbedo, planck, lapseRate, and cloud, with automatic derivation of the required typeclass instances.
Claim. The climate feedback mechanisms form the finite inductive type whose five constructors are water-vapor feedback, ice-albedo feedback, Planck feedback, lapse-rate feedback, and cloud feedback.
background
In the Recognition Science treatment of climate the energy balance condition is expressed by the vanishing of the J-cost function, J = 0. The module introduces five standard feedback processes whose number equals the configuration dimension D = 5. These feedbacks respond to any sustained positive J arising from external forcing such as increased CO2 concentration, with the forcing magnitude given as approximately 0.011 in RS-native units.
proof idea
The declaration is an inductive definition that directly lists the five constructors and derives the DecidableEq, Repr, BEq, and Fintype instances by standard Lean automation.
why it matters
This definition supplies the discrete set of five feedbacks required by the climate equilibrium certificate. It is used to establish that the feedback cardinality equals 5, which in turn populates the ClimatePhysicsCert structure asserting both the count and the balance condition Jcost 1 = 0. Within the framework the construction realizes the configDim D = 5 for the climate sector, linking the general Recognition Science forcing chain to the specific energy-budget imbalance.
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