  This study considers the characteristics of planetary systems with giant
planets based on a population-level analysis of the California Legacy Survey
planet catalog. We identified three characteristics common to hot Jupiters.
First, while not all hot Jupiters have a detected outer giant planet companion
($M \sin i$ = 0.3--30 $M_{\textrm{Jup}}$), such companions are ubiquitous when
survey completeness corrections are applied for orbital periods out to 40,000
days. Giant harboring systems without a hot Jupiter also host at least one
outer giant planet companion per system. Second, the mass distributions of hot
Jupiters and other giant planets are indistinguishable. However, within a
planetary system that includes a hot Jupiter, the outer giant planet companions
are at least $3\times$ more massive than the inner hot Jupiters. Third, the
eccentricity distribution of the outer companions in hot Jupiter systems (with
an average model eccentricity of $\langle e\rangle=0.34\pm0.05$) is different
from the corresponding outer planets in planetary systems without hot Jupiters
($\langle e\rangle=0.19\pm0.02$). We conclude that the existence of two gas
giants, where the outermost planet has an eccentricity $\ge0.2$ and is
$3\times$ more massive, are key factors in the production of a hot Jupiter. Our
simple model based on these factors predicts that $\sim$10\% of warm and cold
Jupiter systems will by chance meet these assembly criteria, which is
consistent with our measurement of $16\pm6\%$ relative occurrence of hot
Jupiter systems to all giant-harboring systems. We find that these three
features favor coplanar high-eccentricity migration as the dominant mechanism
for hot Jupiter formation.
