dft8Fundamental
plain-language theorem explainer
Recognition Science Fourier analysis sets the DFT-8 fundamental frequency to five times the golden ratio divided by eight. Workers establishing the eight-tick harmonic comb at D=3 cite this constant when counting modes and checking positivity. The value enters as a direct constant definition drawn from the spectral signature.
Claim. The fundamental frequency of the eight-point discrete Fourier transform is given by $f_0 = 5φ/8$, where $φ$ is the golden ratio.
background
The FourierAnalysisFromRS module treats Fourier analysis as decomposition into frequency components inside the Recognition Science framework. The DFT-8 mode structure equals the 8-tick harmonic comb that follows from the eight-tick recognition period, which produces eight Fourier modes equal to $2^D$ at spatial dimension D=3. The fundamental is fixed at 5φ/8 Hz, with five canonical operations (DFT, FFT, convolution, correlation, power spectrum) matching configDim D=5.
proof idea
The definition is a direct assignment of the expression five times phi divided by eight. No lemmas or tactics are invoked; the declaration simply binds the constant for use in downstream statements.
why it matters
This constant supplies the fundamental frequency field inside the FourierCert structure, which also records five operations and eight DFT-8 modes. It completes the DFT-8 fundamental step in the module's account of Fourier analysis from RS and connects to the eight-tick octave (T7) and D=3 (T8) in the forcing chain. The value is imported from DFT8SpectralSignature.lean and anchors the harmonic comb at the recognition period of $2^3$.
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