weatherPhenomenonCount
plain-language theorem explainer
The theorem establishes that the finite type enumerating canonical weather phenomena in the Recognition Science atmospheric model has cardinality exactly five. Atmospheric modelers certifying dimensional consistency between layers and phenomena would cite this result to close the configDim D match. The proof is a direct decision procedure that computes the Fintype cardinality from the inductive definition with five constructors.
Claim. The finite set of canonical weather phenomena has cardinality five: $|$WeatherPhenomenon$| = 5$.
background
The module models atmospheric physics via J-cost balance, with five layers (troposphere through exosphere) fixed by configDim D = 5. The inductive type WeatherPhenomenon lists the five phenomena: high pressure, low pressure, fronts, jet streams, and ENSO, and derives a Fintype instance. Upstream, the equilibrium theorem states that Jcost 1 = 0, supplying the stability condition J = 0 used throughout the module.
proof idea
The proof is a one-line wrapper that applies the decide tactic. This evaluates the Fintype.card computation directly on the inductive type WeatherPhenomenon whose five constructors yield the equality to 5.
why it matters
The result populates the five_phenomena field inside atmosphericPhysicsCert, which assembles the full certification of five layers, five phenomena, and equilibrium. It realizes the module statement that five phenomena equal configDim D, completing the RS derivation of atmospheric structure from J-cost. No open scaffolding remains.
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