  The Kepler space telescope has opened new vistas in exoplanet discovery space
by revealing populations of Earth-sized planets that provide a new context for
understanding planet formation. Approximately 70% of all stars in the Galaxy
belong to the diminutive M dwarf class, several thousand of which lie within
Kepler's field of view, and a large number of these targets show planet transit
signals. Kepler-32 is a typical star in the Kepler M dwarf sample that presents
us with a rare opportunity: five planets transit this star giving us an
expansive view of its architecture. All five planets of this compact system
orbit their host star within a distance one third the size of Mercury's orbit
with the innermost planet positioned a mere 4.3 stellar radii from the stellar
photosphere. New observations limit possible false positive scenarios allowing
us to validate the entire Kepler-32 system making it the richest known system
of transiting planets around an M dwarf. Based on considerations of the stellar
dust sublimation radius, the near period commensurability of three adjacent
planets, a minimum mass protoplanetary nebula, and the volatile content
inferred for the planets, we propose that the Kepler-32 planets formed at
larger orbital radii and migrated inward to their present locations. The
volatile content inferred for the Kepler-32 planets and order of magnitude
estimates for the disk migration rates suggest these planets may have formed
beyond the snow line and migrated in the presence of a gaseous disk. The
Kepler-32 planets are representative of the full ensemble of planet candidates
orbiting the Kepler M dwarfs for which we calculate an occurrence rate of 1.0
+/- 0.1 planet per star. The formation of the Kepler-32 planets therefore
offers a plausible blueprint for the formation of one of the largest known
populations of planets in our Galaxy.
