Time-domain origin of radio-loudness in the TDRL framework. Panels show: (a) the underlying engine state J(t) modeled as a stochastic on/off process, (b) the prompt compact-core emission modulated by beaming, (c) the lobe emission smoothed by the frequency-dependent fading function for short-memory (high frequency, green) and long-memory (low frequency, red) observations, and (d) the resulting observed scalar radio-loudness R. A single intermittent engine produces either a bimodal or a continuous ﹩p(\mathrm{log}R)﹩ depending on χ_ν = τ_ν/t_switch and on whether the survey recovers diffuse emission.