corticalResonance5phi
plain-language theorem explainer
Definition of the cortical resonance frequency as 5φ Hz in RS-native units. Physicists calibrating τ₀ to match alpha-band brain rhythms or plasma control frequencies would cite this value when deriving all Hz-scale predictions from the single calibration scalar. It is introduced as a direct noncomputable abbreviation that multiplies the golden ratio constant by five.
Claim. The cortical resonance frequency is defined as $5φ$ Hz, where $φ$ is the golden ratio.
background
The Tau-Zero Calibrator module treats τ₀ as the single calibration scalar that fixes the RS time unit at approximately 7.3 × 10^{-15} s. From this scalar the module derives the cortical resonance at 5φ Hz, which lies in the alpha band after conversion to SI units, together with Schumann resonances at integer multiples of φ Hz. The definition therefore supplies the base frequency that converts every RS prediction into observable hertz values once τ₀ is fixed.
proof idea
Direct definition: corticalResonance5phi is set equal to five times the golden ratio constant phi, serving as a one-line abbreviation with no further reduction.
why it matters
The definition supplies the numerical base for the theorems corticalResonance_band and corticalResonance_fifth_mode_band, which place 5φ inside the intervals (8.05, 8.10) Hz and (7.5, 8.1) Hz respectively; both results are then packaged inside the TauZeroCert structure that certifies the overall calibration. Within the Recognition Science framework it realizes the 5φ prediction on the phi-ladder, consistent with the self-similar fixed point T6 and the eight-tick octave T7 that together generate the D = 3 spatial structure and the alpha-band constants.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.