dftModes
plain-language theorem explainer
Recognition Science acoustics sets the number of DFT modes to eight by defining dftModes as two raised to the power three. Researchers working on phi-harmonic sound therapy cite this constant when certifying the DFT-8 envelope under RS_PAT_026. The definition is a direct assignment that matches the eight-tick octave period without further computation.
Claim. The number of discrete Fourier transform modes in the eight-tick octave is given by $2^3$.
background
The AcousticsFromRS module links five canonical acoustic phenomena (reflection, refraction, diffraction, absorption, interference) to configDim D = 5. It introduces the DFT-8 framework with fundamental frequency 5φ Hz and overtone series 5φ, 10φ, 15φ, … to realize RS_PAT_026 precision sound therapy via DFT-8 envelope targeting. The definition supplies the concrete integer value for the eight-tick octave (period 2³) in this setting.
proof idea
This is a direct definition that evaluates the power 2^3 in the natural numbers. No lemmas are applied and no tactics are used; the value is assigned by the constant expression itself.
why it matters
The definition supplies the eight_modes field required by the AcousticsCert structure, which also records five_phenomena equal to 5. It realizes the T7 eight-tick octave step of the forcing chain and anchors the phi-harmonic sound therapy claim in RS_PAT_026. The downstream theorem dftModes_8 later confirms the equality by decision procedure.
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