carrierFreq
Carrier frequency is set to 5φ to anchor the DFT-8 spectrum in the theta band near 8.09 Hz. RS brain-rhythm researchers cite it as the base for the eight-mode frequency comb ν_k = k·5φ/8. The declaration is a direct definition with no computational content.
claimThe carrier frequency is defined as $5φ$, where $φ$ is the golden ratio.
background
The module defines the DFT-8 Harmonic Spectrum as eight modes with frequencies ν_k = (k · 5φ / 8) Hz for k = 0 to 7, one per Q₃ vertex. The carrier 5φ ≈ 8.09 Hz places the comb in the theta band and supplies the scaling for all harmonics. Phi is the self-similar fixed point from upstream Constants and the forcing chain T6.
proof idea
One-line definition that directly assigns the product 5 * phi to carrierFreq.
why it matters in Recognition Science
This supplies the base frequency used by DFTHarmonicSpectrumCert to certify eight modes, theta-band bounds, and non-negative harmonics. It realizes the C24 structural claim in the module documentation for RS_PAT_026 and RS_PAT_025. It instantiates the eight-tick octave from the Recognition Science framework.
scope and limits
- Does not derive the numerical factor 5 from prior axioms.
- Does not compute explicit decimal approximations.
- Does not connect to external brain-wave data.
- Does not specify physical units beyond the Hz label.
formal statement (Lean)
38noncomputable def carrierFreq : ℝ := 5 * phi
proof body
Definition body.
39