carrier_band
plain-language theorem explainer
The carrier frequency 5φ Hz lies strictly between 8.05 and 8.10. Engineers certifying phantom-coupled gravitational wave antennas or cortical neuromodulation devices cite this interval to anchor the BIT carrier band. The proof is a term-mode wrapper that unfolds the carrier definition and feeds the known bounds on φ into linear arithmetic.
Claim. Let φ denote the golden ratio. The carrier frequency satisfies 8.05 < 5φ < 8.10.
background
The Phantom-Coupled GW Antenna Sensitivity module treats track J6 of Plan v5 for a phantom-cavity-coupled gravitational wave antenna. Carrier is defined as 5 * phi, the same expression appearing in the sibling CorticalNeuromodulationDevice module. The module derives sub-Hz strain sensitivity scaling linearly above the BIT carrier and inversely below it at LISA-band frequencies.
proof idea
The proof unfolds carrier to 5 * phi. It obtains the upstream lemmas phi_gt_onePointSixOne (φ > 1.61) and phi_lt_onePointSixTwo (φ < 1.62). Refine then builds the conjunction by applying linarith to each side.
why it matters
This theorem supplies the carrier_band field required by PhantomCoupledGWAntennaSensitivityCert and by CorticalNeuromodulationDeviceCert. It also feeds neuromod_one_statement and asteroidTrajectoryShapingCert. The bound connects the engineering claims to the Recognition Science self-similar fixed point φ and the eight-tick octave.
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