  We observed Kepler-421 during the anticipated third transit of the snow-line
exoplanet Kepler-421b in order to constrain the existence and extent of transit
timing variations (TTVs). Previously, the Kepler Spacecraft only observed two
transits of Kepler-421b leaving the planet's transit ephemeris unconstrained.
Our visible light, time-series observations from the 4.3-meter Discovery
Channel Telescope were designed to capture pre-transit baseline and the partial
transit of Kepler-421b barring significant TTVs. We use the light curves to
assess the probabilities of various transit models using both the posterior
odds ratio and the Bayesian Information Criterion (BIC) and find that a transit
model with no TTVs is favored to 3.6-sigma confidence. These observations
suggest that Kepler-421b is either alone in its system or is only experiencing
minor dynamic interactions with an unseen companion. With the Kepler-421b
ephemeris constrained, we calculate future transit times and discuss the
opportunity to characterize the atmosphere of this cold, long-period exoplanet
via transmission spectroscopy. Our investigation emphasizes the difficulties
associated with observing long-period exoplanet transits and the consequences
that arise from failing to refine transit ephemerides.
