numericalMethodCount
plain-language theorem explainer
The theorem proves that the set of canonical numerical methods recognized in Recognition Science has cardinality exactly five. Researchers certifying numerical schemes within the RS framework would cite this count to confirm alignment with configDim D=5. The proof is a direct decision on the Fintype instance of the five-constructor inductive type.
Claim. The finite set of canonical numerical methods has cardinality five: $|$ {Newton's method, Euler integration, Runge-Kutta, Gaussian elimination, FFT} $| = 5$.
background
The module defines NumericalMethod as an inductive type with five constructors (newton's method, Euler integration, Runge-Kutta, Gaussian elimination, FFT) and derives Fintype, DecidableEq, and related instances. The module doc states that these five methods equal configDim D=5, with DFT-8 supplying the canonical 8=2^3 modes and FFT requiring 24=3×8 operations per tick. Upstream, the modes definition supplies the finite set of truncated 2D modes that connects to the eight-mode DFT here.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate Fintype.card on the NumericalMethod inductive type, whose five constructors yield cardinality 5 by the derived Fintype instance.
why it matters
This result supplies the five_methods component to the numericalAnalysisCert definition, which assembles the full numerical analysis certificate together with eight modes and 24 FFT operations. It fills the module claim that five methods match configDim D=5 and links to the eight-tick octave (T7) where 8=2^3 modes appear. No open scaffolding remains.
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