FourierOperation
plain-language theorem explainer
FourierOperation enumerates five operations (DFT, FFT, convolution, correlation, power spectrum) that Recognition Science associates with the configuration dimension at D=3. A mathematician deriving QFT modes from the 8-tick octave would reference this inductive type to obtain the Fintype instance needed for cardinality statements. The declaration is a direct inductive enumeration whose only content is the five named constructors plus the derived instances.
Claim. The inductive type whose constructors are the discrete Fourier transform, the fast Fourier transform, convolution, correlation, and the power spectrum $P(k)∝(H^2/φ̇)^2$.
background
The module states that Fourier analysis decomposes functions into frequency components and that the 8-tick recognition period supplies exactly 8=2^D modes when D=3. Five canonical operations are identified with configDim D=5. The upstream powerSpectrum definition supplies the concrete expression $P(k)∝V^3/(V')^2$ used as one of the constructors.
proof idea
Inductive definition that introduces the five constructors DFT, FFT, convolution, correlation, powerSpectrum and immediately derives DecidableEq, Repr, BEq and Fintype.
why it matters
The type is the source of the equality Fintype.card FourierOperation=5 proved in fourierOperationCount and recorded in the structure FourierCert. It therefore supplies the concrete link between the five operations and configDim D=5, closing the module claim that DFT-8 modes equal the 8-tick harmonic comb at D=3.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.