Is the compact-object lower mass gap a threshold? A logistic-gate description, a Bayesian assessment with current events, and a discrimination forecast

The dearth of compact objects between ~2.5 and ~5 solar masses (the "lower mass gap") is modelled phenomenologically as the transition region of a soft threshold, using a logistic three-state gate. With public LVK posterior samples of three firmly in-gap objects (GW190814, GW200210_092254, GW230529), a hierarchical Bayesian comparison yields a Bayes factor of approximately 3.9 favouring a monotonically decreasing gap profile over a flat one, after including a real, nearly-flat selection function computed from the official O3 injection campaign. The central result is negative and quantitative: at the data-implied steepness, roughly 1600 in-gap events would be needed to distinguish the gate from an ordinary falling power-law mass function at 3 sigma. Current data are consistent with, but cannot establish, a threshold structure; the required event count is reported as an honest testability forecast.