SpectralRegion
plain-language theorem explainer
The inductive definition enumerates the five spectral regions used to partition the electromagnetic spectrum in the J-cost derivation of blackbody radiation. Physicists certifying the Planck distribution from the Recognition Composition Law would reference this partition to obtain the finite cardinality in the radiation certificate. The definition is a direct inductive type with five explicit constructors that automatically derives finite-type and equality structures.
Claim. SpectralRegion is the finite inductive type whose elements are the five bands radio, infrared, visible, ultraviolet, and x-ray.
background
The module Blackbody Radiation from J-Cost models each photon mode as a recognition unit with energy ε = hν. The J-cost function (imported from IndisputableMonolith.Cost) satisfies J(1) = 0 at the Rayleigh-Jeans equilibrium hν = kT. Module documentation states that five spectral regions equal configDim D = 5, supplying the concrete enumeration needed for downstream cardinality claims.
proof idea
The declaration is a direct inductive definition that lists the five constructors explicitly and derives DecidableEq, Repr, BEq, and Fintype in one step.
why it matters
This definition supplies the five-region partition required by the BlackBodyRadiationCert structure, which asserts Fintype.card SpectralRegion = 5 together with Jcost 1 = 0 and off-peak positivity. It realizes the module claim that five spectral regions correspond to configDim D = 5 in the Recognition Science treatment of thermal radiation derived from the J functional equation.
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