  Kepler has discovered hundreds of systems with multiple transiting exoplanets
which hold tremendous potential both individually and collectively for
understanding the formation and evolution of planetary systems. Many of these
systems consist of multiple small planets with periods less than ~50 days known
as Systems with Tightly-spaced Inner Planets, or STIPs. One especially
intriguing STIP, Kepler-80 (KOI-500), contains five transiting planets: f, d,
e, b, and c with periods of 1.0, 3.1, 4.6, 7.1, 9.5 days, respectively. We
provide measurements of transit times and a transit timing variation (TTV)
dynamical analysis. We find that TTVs cannot reliably detect eccentricities for
this system, though mass estimates are not affected. Restricting the
eccentricity to a reasonable range, we infer masses for the outer four planets
(d, e, b, and c) to be $6.75^{+0.69}_{-0.51}$, $4.13^{+0.81}_{-0.95}$,
$6.93^{+1.05}_{-0.70}$, and $6.74^{+1.23}_{-0.86}$ Earth masses, respectively.
The similar masses but different radii are consistent with terrestrial
compositions for d and e and $\sim$2% H/He envelopes for b and c. We confirm
that the outer four planets are in a rare dynamical configuration with four
interconnected three-body resonances that are librating with few degree
amplitudes. We present a formation model that can reproduce the observed
configuration by starting with a multi-resonant chain and introducing
dissipation. Overall, the information-rich Kepler-80 planets provide an
important perspective into exoplanetary systems.
