gw_antenna_one_statement
plain-language theorem explainer
Engineers designing phantom-coupled gravitational wave antennas cite this result for the compact statement that the carrier frequency 5φ lies in (8.05, 8.10) Hz, sensitivity equals h_0 there, and sensitivity is strictly decreasing with frequency. The result assembles the numerical band, the equality at carrier, and the anti-monotonicity property. The proof is a one-line term that directly applies the carrier band theorem, the sensitivity equality lemma, and the strict anti-monotonicity lemma.
Claim. Let $c = 5φ$ where $φ$ is the golden ratio. Then $8.05 < c < 8.10$, the minimum strain sensitivity at frequency $c$ equals the reference value $h_0$, and for all positive frequencies $0 < f_1 < f_2$ the sensitivity at $f_2$ is strictly less than at $f_1$.
background
The carrier frequency is defined as five times the golden ratio in hertz, matching the cortical neuromodulation device carrier. The carrier band theorem establishes the numerical bounds 8.05 to 8.10 using the known inequalities for phi. Sensitivity is defined as $h_0$ times carrier over frequency for positive $f$, with $h_0$ set to one. This module derives the sensitivity curve for a phantom-cavity-coupled gravitational wave antenna, where $h_{min}(f)$ scales as carrier over $f$.
proof idea
The proof constructs the conjunction by taking the two parts of the carrier band theorem, the sensitivity equality at the carrier frequency, and the strict anti-monotonicity lemma for sensitivity.
why it matters
This theorem supplies the single-statement summary of the antenna sensitivity properties in the engineering derivation track. It supports claims about sub-Hz performance at LISA-band frequencies. The module notes the falsifier as a deployed antenna failing to show the 1/f scaling above the noise floor.
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