carrier_band
plain-language theorem explainer
The theorem proves that the cortical carrier frequency, defined as five times the golden ratio phi in hertz, lies strictly between 8.05 and 8.10. Neuromodulation device engineers and gravitational-wave antenna designers cite this bound to certify operating parameters in the Recognition Science engineering track. The proof is a term-mode wrapper that unfolds the carrier definition and applies linear arithmetic to the established numerical bounds on phi.
Claim. The cortical-column carrier frequency satisfies $8.05 < 5phi < 8.10$.
background
The module specifies a transcranial neuromodulation device (RS_PAT_025) that operates at cortical-column resonance 5φ Hz ≈ 8.09 Hz, with optimal pulse spacing τ = 1/(5φ) s ≈ 124 ms. Carrier is defined locally as 5 * phi. Upstream lemmas from Constants supply the tight bounds 1.61 < phi and phi < 1.62, obtained by comparing phi to rational approximations of √5.
proof idea
The proof is a term-mode wrapper. It unfolds carrier to 5 * phi, invokes phi_gt_onePointSixOne for the lower bound and phi_lt_onePointSixTwo for the upper bound, then applies linarith to close the target inequality.
why it matters
This bound populates the carrier_band field of CorticalNeuromodulationDeviceCert and is reused verbatim in neuromod_one_statement, PhantomCoupledGWAntennaSensitivity.carrier_band, and AsteroidTrajectoryShapingCert. It implements the frequency specification for the φ-rational pulse schedule in the engineering derivation, anchoring device parameters to the phi-ladder and the eight-tick octave resonance.
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