  We present an analysis of the quenching of star formation in massive galaxies
($M_* > 10^{9.5} M_\odot$) within the first 0.5 - 3 Gyr of the Universe's
history utilizing JWST-CEERS data. We utilize a combination of advanced
statistical methods to accurately constrain the intrinsic dependence of
quenching in a multi-dimensional and inter-correlated parameter space.
Specifically, we apply Random Forest (RF) classification, area statistics, and
a partial correlation analysis to the JWST-CEERS data. First, we identify the
key testable predictions from two state-of-the-art cosmological simulations
(IllustrisTNG & EAGLE). Both simulations predict that quenching should be
regulated by supermassive black hole mass in the early Universe. Furthermore,
both simulations identify the stellar potential ($\phi_*$) as the optimal proxy
for black hole mass in photometric data. In photometric observations, where we
have no direct constraints on black hole masses, we find that the stellar
potential is the most predictive parameter of massive galaxy quenching at all
epochs from $z = 0 - 8$, exactly as predicted by simulations for this sample.
The stellar potential outperforms stellar mass, galaxy size, galaxy density,
and S\'ersic index as a predictor of quiescence at all epochs probed in
JWST-CEERS. Collectively, these results strongly imply a stable quenching
mechanism operating throughout cosmic history, which is closely connected to
the central gravitational potential in galaxies. This connection is explained
in cosmological models via massive black holes forming and growing in deep
potential wells, and subsequently quenching galaxies through a mix of ejective
and preventative active galactic nucleus (AGN) feedback.
