  KOI-152 is among the first known systems of multiple transiting planetary
candidates (Steffen et al. 2010) ranging in size from 3.5 to 7 times the size
of the Earth, in a compact configuration with orbital periods near a 1:2:4:6
chain of commensurability, from 13.5 days to 81.1 days. All four planets
exhibit transit timing variations with periods that are consistent with the
distance of each planet to resonance with its neighbors. We perform a dynamical
analysis of the system based on transit timing measurements over 1282 days of
\textit{Kepler} photometry. Stellar parameters are obtained with a combination
of spectral classification and the stellar density constraints provided by
light curve analysis and orbital eccentricity solutions from our dynamical
study. Our models provide tight constraints on the masses of all four
transiting bodies, demonstrating that they are planets and that they orbit the
same star. All four of KOI-152's transiting planets have low densities given
their sizes, consistent with other studies of compact multiplanet transiting
systems. The largest of the four, KOI-152.01, has the lowest bulk density yet
determined amongst sub-Saturn mass planets.
