  An overabundance of single-transiting Kepler planets suggests the existence
of a sub-population of intrinsically multi-planet systems possessing large
mutual inclinations. However, the origin of these mutual inclinations remains
unknown. Recent work has demonstrated that mutual inclinations can be excited
soon after protoplanetary disk-dispersal due to the oblateness of the
rapidly-rotating host star, provided the star is tilted. Alternatively, distant
giant planets, which are common in systems of close-in Kepler planets, could
drive up mutual inclinations. The relative importance of each of these
mechanisms has not been investigated. Here, we show that the influence of the
stellar oblateness typically exceeds that of an exterior giant soon after
planet formation. However, the magnitude of the resulting mutual inclinations
depends critically upon the timescale over which the natal disk disperses.
Specifically, we find that if the disk vanishes over a timescale shorter than
10^(3-4) years, comparable to the viscous timescale of the inner ~0.2AU, the
inner planets impulsively acquire misalignments that scale with the stellar
obliquity. In contrast, if the disk disperses slowly, the inner planets remain
coplanar. They first align with the stellar equator but subsequently realign
with the distant giant's plane as the star spins down. Our findings are
consistent with recent observations that giants tend to be aligned with
close-in multis but misaligned with singles. Stellar obliquity measurements
offer a promising test of our proposed framework.
