Frequency-Specific Bounds on ε(ν) for Cosmological Metric Modulation of Electromagnetic Coherence

This technical note evaluates the coupling parameter ε as an explicit function of observing frequency ν for the cosmological metric modulation route identified in Note 2. The central result is ε(ν) ∝ ν^(−6/5), which is structurally distinct from all plasma propagation scaling laws. The mechanism is falsified for propagation distances L < 500 Mpc at all K-band frequencies. A narrow survival window exists at L ~ 1 Gpc, ν ~ 10–15 GHz. FRB multi-frequency coherence statistics are identified as the cleanest near-term observational test. Keywords: Fermi paradox, coherence bandwidth, metric perturbation, coupling parameter, K-band, frequency scaling, fast radio bursts, pulsar timing arrays License: CC BY 4.0 Related works: Note 1 (10.5281/zenodo.18906111), Note 2 (10.5281/zenodo.18906757), USDOP v1.2 (10.5281/zenodo.18721255), SHRF v2 (10.5281/zenodo.18761638), IWC (10.5281/zenodo.18764956), Corpus Baseline-12 (10.5281/zenodo.18899474)