  We present 1.3 millimeter observations of the debris disk surrounding the HR
8799 multi-planet system from the Submillimeter Array to complement archival
ALMA observations that spatially filtered away the bulk of the emission. The
image morphology at $3.8$ arcsecond (150 AU) resolution indicates an optically
thin circumstellar belt, which we associate with a population of dust-producing
planetesimals within the debris disk. The interferometric visibilities are fit
well by an axisymmetric radial power-law model characterized by a broad width,
$\Delta R/R\gtrsim 1$. The belt inclination and orientation parameters are
consistent with the planet orbital parameters within the mutual uncertainties.
The models constrain the radial location of the inner edge of the belt to
$R_\text{in}= 104_{-12}^{+8}$ AU. In a simple scenario where the chaotic zone
of the outermost planet b truncates the planetesimal distribution, this inner
edge location translates into a constraint on the planet~b mass of $M_\text{pl}
= 5.8_{-3.1}^{+7.9}$ M$_{\rm Jup}$. This mass estimate is consistent with
infrared observations of the planet luminosity and standard hot-start
evolutionary models, with the uncertainties allowing for a range of initial
conditions. We also present new 9 millimeter observations of the debris disk
from the Very Large Array and determine a millimeter spectral index of
$2.41\pm0.17$. This value is typical of debris disks and indicates a power-law
index of the grain size distribution $q=3.27\pm0.10$, close to predictions for
a classical collisional cascade.
