We report the discovery of a transiting, Rp = 4.347+/-0.099REarth,
circumbinary planet (CBP) orbiting the Kepler K+M Eclipsing Binary (EB) system
KIC 12351927 (Kepler-413) every ~66 days on an eccentric orbit with ap =
0.355+/-0.002AU, ep = 0.118+/-0.002. The two stars, with MA =
0.820+/-0.015MSun, RA = 0.776+/-0.009RSun and MB = 0.542+/-0.008MSun, RB =
0.484+/-0.024RSun respectively revolve around each other every
10.11615+/-0.00001 days on a nearly circular (eEB = 0.037+/-0.002) orbit. The
orbital plane of the EB is slightly inclined to the line of sight (iEB =
87.33+/-0.06 degrees) while that of the planet is inclined by ~2.5 degrees to
the binary plane at the reference epoch. Orbital precession with a period of
~11 years causes the inclination of the latter to the sky plane to continuously
change. As a result, the planet often fails to transit the primary star at
inferior conjunction, causing stretches of hundreds of days with no transits
(corresponding to multiple planetary orbital periods). We predict that the next
transit will not occur until 2020. The orbital configuration of the system
places the planet slightly closer to its host stars than the inner edge of the
extended habitable zone. Additionally, the orbital configuration of the system
is such that the CBP may experience Cassini-States dynamics under the influence
of the EB, in which the planet's obliquity precesses with a rate comparable to
its orbital precession. Depending on the angular precession frequency of the
CBP, it could potentially undergo obliquity fluctuations of dozens of degrees
(and complex seasonal cycles) on precession timescales.Comment: 48 pages, 13 figure