AcousticsCert
plain-language theorem explainer
AcousticsCert packages the assertions that the set of acoustic phenomena has cardinality five and that the DFT mode count equals eight. Researchers modeling phi-harmonic sound therapy cite the certificate when anchoring the five classical wave effects to the eight-tick octave. The structure is assembled directly from the Fintype instance on the five-element inductive type and the constant definition dftModes := 2^3.
Claim. Let $P$ be the set consisting of reflection, refraction, diffraction, absorption, and interference. The structure AcousticsCert asserts that the cardinality of $P$ equals 5 and that the number of DFT modes equals 8.
background
The module AcousticsFromRS develops acoustic phenomena directly from Recognition Science. It enumerates five canonical effects—reflection, refraction, diffraction, absorption, and interference—as the complete set whose cardinality matches configDim D = 5. The DFT mode count is fixed at eight by the definition dftModes := 2^3, corresponding to the eight-tick octave in the forcing chain T7.
proof idea
The declaration is a structure definition with two fields. The first field records the cardinality equality obtained from the Fintype derivation on AcousticPhenomenon. The second field records the equality dftModes = 8 taken directly from the upstream definition dftModes := 2^3. No tactics or lemmas are applied beyond the built-in cardinality computation.
why it matters
This certificate supplies the two numerical invariants required by the acousticsCert construction, which in turn supports RS_PAT_026 on phi-harmonic sound therapy. It closes the link between the five acoustic phenomena and the eight DFT modes that arise from the period-2^3 octave in the UnifiedForcingChain. The structure therefore anchors the acoustic sector of the Recognition Science derivation at the level of the eight-tick periodicity.
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