  Embedded, Class 0/I protostellar disks represent the initial condition for
planet formation. This calls for better understandings of their bulk properties
and the dust grains within them. We model multi-wavelength dust continuum
observations of the disk surrounding the Class I protostar TMC1A to provide
insight on these properties. The observations can be well fit by a
gravitationally self-regulated (i.e., marginally gravitationally unstable and
internally heated) disk model, with surface density $\Sigma \sim 1720
(R/10au)^{-1.96} g/cm^2$ and midplane temperature $T_{mid} \sim 185
(R/10au)^{-1.27} K$. The observed disk contains a $m=1$ spiral substructure; we
use our model to predict the spiral's pitch angle and the prediction is
consistent with the observations. This agreement serves as both a test of our
model and strong evidence of the gravitational nature of the spiral. Our model
estimates a maximum grain size $a_{max}\sim 196(R/10au)^{-2.45} \mu m$, which
is consistent with grain growth being capped by a fragmentation barrier with
threshold velocity $\sim 1 m/s$. We further demonstrate that observational
properties of TMC1A are typical among the observed population of Class 0/I
disks, which hints that traditional methods of disk data analyses based on
Gaussian fitting and the assumption of the optically thin dust emission could
have systematically underestimated disk size and mass and overestimated grain
size.
