The TDRL diagnostic plane. The vertical axis shows the prompt/core radio-loudness ﹩{R}_{\nu }^{{\rm{core}}}﹩, tracing present-day engine activity; the horizontal axis shows the memory/lobe radio-loudness ﹩{R}_{\nu }^{{\rm{lobe}}}﹩, tracing the time-integrated jet history over τ_ν. The dashed diagonal marks approximate quasi-equilibrium between injection and accumulated lobe power; the perpendicular offset defines the mismatch index ﹩{{ \mathcal I }}_{\nu }﹩ (Equation (6)). Four regimes are indicated: triggering or restarting (core bright, lobe faint, ﹩{{ \mathcal I }}_{\nu }\gg 0﹩), sustained activity (both components bright, ﹩{{ \mathcal I }}_{\nu }\simeq 0﹩), remnant or fading (lobe bright, core faint, ﹩{{ \mathcal I }}_{\nu }\ll 0﹩), and quiescent or weak systems (both components faint). The two-dimensional decomposition separates what the engine is doing now from what it has done in the past, a distinction that scalar R cannot make. Orientation-dependent beaming of the core component can shift sources along the vertical axis and must be modeled or controlled for in quantitative applications.