carrier_pos
plain-language theorem explainer
The carrier frequency in the phantom-coupled GW antenna model is strictly positive. Engineers deriving sub-Hz gravitational wave sensitivity would cite this to anchor the BIT carrier scale at 5φ Hz for all subsequent 1/f scaling arguments. The proof is a one-line wrapper that unfolds the carrier definition and applies the multiplication positivity lemma to a numerical constant and phi_pos.
Claim. Let carrier denote the frequency $5φ$ where $φ$ is the golden ratio. Then $0 < 5φ$.
background
The module derives sensitivity for a phantom-cavity-coupled GW antenna (RS_PAT_030) with strain response $h_min(f) = h_0 · (5φ Hz / f)$ at LISA-band frequencies. Carrier is defined locally as $5 * phi$, matching the upstream definition in CorticalNeuromodulationDevice whose doc-comment states 'Cortical-column carrier frequency = 5 · φ Hz'. A parallel positivity result appears in EulerInstantiation for the complex carrier on Re(s) > 1/2.
proof idea
This is a one-line wrapper proof. It unfolds the carrier definition and invokes mul_pos on a positive constant (via norm_num) together with phi_pos.
why it matters
The result feeds downstream theorems including sensitivity_at_carrier, sensitivity_pos, and sensitivity_strict_anti that establish the linear and inverse scaling of antenna sensitivity above and below the carrier. It fills the engineering derivation step in track J6 of Plan v5 and rests on the self-similar fixed point phi from forcing-chain step T6. No open scaffolding questions are closed here.
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