  Many discovered multiplanet systems are tightly packed. This implies that
wide parameter ranges in masses and orbital elements can be dynamically
unstable and ruled out. We present a case study of Kepler-23, a compact
three-planet system where constraints from stability, transit timing variations
(TTVs), and transit durations can be directly compared. We find that in this
tightly packed system, stability can place upper limits on the masses and
orbital eccentricities of the bodies that are comparable to or tighter than
current state of the art methods. Specifically, stability places 68% upper
limits on the orbital eccentricities of 0.09, 0.04, and 0.05 for planets $b$,
$c$ and $d$, respectively. These constraints correspond to radial velocity
signals $\lesssim 20$ cm/s, are significantly tighter to those from transit
durations, and comparable to those from TTVs. Stability also yields 68% upper
limits on the masses of planets $b$, $c$ and $d$ of 2.2, 16.1, and 5.8
$M_\oplus$, respectively, which were competitive with TTV constraints for the
inner and outer planets. Performing this stability constrained characterization
is computationally expensive with N-body integrations. We show that SPOCK, the
Stability of Planetary Orbital Configurations Klassifier, is able to faithfully
approximate the N-body results over 4000 times faster. We argue that such
stability constrained characterization of compact systems is a challenging
"needle-in-a-haystack" problem (requiring removal of 2500 unstable
configurations for every stable one for our adopted priors) and we offer
several practical recommendations for such stability analyses.

Earth and Planetary Astrophysics