corticalResonance_band
plain-language theorem explainer
The theorem proves that 5φ lies strictly between 8.05 and 8.10. Recognition Science calibrators cite it to anchor the cortical alpha resonance prediction at approximately 8.09 Hz from the phi-ladder alone. The proof is a one-line wrapper that unfolds the definition of corticalResonance5phi and applies linear arithmetic to the established bounds 1.61 < φ < 1.62.
Claim. $8.05 < 5phi < 8.10$
background
The Tau-Zero Calibrator module treats τ₀ as the single scalar that fixes the RS time unit, from which all frequencies in Hz are derived. The sibling definition corticalResonance5phi is the real number 5 * phi, where phi is the golden ratio. The module states that this places 5φ ≈ 8.09 Hz inside the cortical alpha band and also inside the Fifth Mode prediction interval (7.5, 8.1).
proof idea
The proof unfolds corticalResonance5phi to 5 * phi. It then invokes linarith on the two upstream lemmas phi_gt_onePointSixOne (phi > 1.61) and phi_lt_onePointSixTwo (phi < 1.62) to obtain the strict two-sided inequality.
why it matters
The result is packaged directly into tauZeroCert, which bundles the cortical band, the fifth-mode band, and the existence of tauZero. It supplies the numerical verification step for the RS time-unit calibration, confirming consistency with the phi-ladder and the self-similar fixed point phi without invoking the Recognition Composition Law or spatial dimension forcing.
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