  Millimeter very-long baseline interferometry (mm-VLBI) provides the novel
capacity to probe the emission region of a handful of supermassive black holes
on sub-horizon scales. For Sagittarius A* (Sgr A*), the supermassive black hole
at the center of the Milky Way, this provides access to the region in the
immediate vicinity of the horizon. Broderick et al. (2009) have already shown
that by leveraging spectral and polarization information as well as accretion
theory, it is possible to extract accretion-model parameters (including black
hole spin) from mm-VLBI experiments containing only a handful of telescopes.
Here we repeat this analysis with the most recent mm-VLBI data, considering a
class of aligned, radiatively inefficient accretion flow (RIAF) models. We find
that the combined data set rules out symmetric models for Sgr A*'s flux
distribution at the 3.9-sigma level, strongly favoring length-to-width ratios
of roughly 2.4:1. More importantly, we find that physically motivated accretion
flow models provide a significantly better fit to the mm-VLBI observations than
phenomenological models, at the 2.9-sigma level. This implies that not only is
mm-VLBI presently capable of distinguishing between potential physical models
for Sgr A*'s emission, but further that it is sensitive to the strong
gravitational lensing associated with the propagation of photons near the black
hole. Based upon this analysis we find that the most probable magnitude,
viewing angle, and position angle for the black hole spin are
a=0.0(+0.64+0.86), theta=68(+5+9)(-20-28) degrees, and xi=-52(+17+33)(-15-24)
east of north, where the errors quoted are the 1-sigma and 2-sigma
uncertainties.
