jats:titleAbstract</jats:title> jats:pWe identify the intrinsic dependence of star formation quenching on a variety of galactic and environmental parameters, utilizing a machine-learning approach with Random Forest classification. We have previously demonstrated the power of this technique to isolate causality, not mere correlation, in complex astronomical data. First, we analyze three cosmological hydrodynamical simulations (Eagle, Illustris, and IllustrisTNG), selecting snapshots spanning the bulk of cosmic history from comic noon (jats:italicz</jats:italic> ∼ 2) to the present epoch, with stellar masses in the range jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn9</mml:mn> mml:mo<</mml:mo> mml:milog</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:msub mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mrow mml:mo*</mml:mo> </mml:mrow> </mml:msub> mml:mrow <mml:mo stretchy="true">/</mml:mo> </mml:mrow> mml:msub mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mrow mml:mo⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> mml:mo<</mml:mo> mml:mn12</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjacac7cieqn1.gif" xlink:type="simple" /> </jats:inline-formula>. In the simulations, black hole mass is unanimously found to be the most predictive parameter of central galaxy quenching at all epochs. Perhaps surprisingly, black hole accretion rate (and hence the bolometric luminosity of active galactic nuclei, AGN) is found to be of little predictive power over quenching. This theoretical result is important for observational studies of galaxy quenching, as it cautions against using the current AGN state of a galaxy as a useful proxy for the cumulative impact of AGN feedback on a galactic system. The latter is traced by black hole mass, jats:italicnot</jats:italic> AGN luminosity. Additionally, we explore a subset of “observable” parameters, which can be readily measured in extant wide-field galaxy surveys targeting jats:italicz</jats:italic> = 0–2, at jats:inline-formula jats:tex-math

</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn9</mml:mn> mml:mo<</mml:mo> mml:milog</mml:mi> <mml:mo stretchy="false">(</mml:mo> mml:msub mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mrow mml:mo*</mml:mo> </mml:mrow> </mml:msub> mml:mrow <mml:mo stretchy="true">/</mml:mo> </mml:mrow> mml:msub mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mrow mml:mo⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> mml:mo<</mml:mo> mml:mn12</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjacac7cieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. All three simulations predict that, in lieu of black hole mass, the stellar gravitational potential will outperform the other parameters in predicting quenching. We confirm this theoretical prediction observationally in the SDSS (at low redshifts) and in CANDELS (at intermediate and high redshifts).</jats:p>