dftModes_8
plain-language theorem explainer
The declaration confirms that the DFT modes count equals 8, matching the 2^3 structure required for the phi-harmonic sound therapy model. Acoustics researchers working from Recognition Science would cite this result to anchor the eight-tick octave in acoustic certification. The proof applies a direct decision procedure to the equality drawn from the upstream definition of the mode count.
Claim. The number of DFT modes equals eight.
background
The Acoustics from RS module links five canonical acoustic phenomena to configuration dimension D = 5 and introduces DFT modes to support the phi-harmonic sound therapy framework under RS_PAT_026. The upstream definition states that DFT-8 modes equal 2^3, supplying the mode count for the overtone series built on the fundamental frequency 5φ Hz in the theta band. This setting treats the eight modes as the discrete Fourier transform basis for envelope targeting in the Recognition Science acoustics derivation.
proof idea
The proof is a one-line wrapper that applies the decide tactic to verify the equality directly from the definition of the DFT modes as 2 raised to 3.
why it matters
This supplies the eight_modes field inside the acousticsCert definition that certifies the full set of acoustic phenomena. It completes the RS_PAT_026 requirement for DFT-8 modes and aligns with the eight-tick octave step in the forcing chain. No open questions or scaffolding remain in this declaration.
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