  M35 is a young open cluster and home to an extensive binary population. Using
Gaia DR3, Pan-STARRS, and 2MASS photometry with the Bayesian statistical
software, BASE-9, we derive precise cluster parameters, identify single and
binary cluster members, and extract their masses. We identify 571 binaries down
to Gaia G = 20.3 and a lower-limit on the binary frequency of f_b = 0.41 +/-
0.02. We extend the binary demographics by many magnitudes faint-ward of
previous (radial-velocity) studies of this cluster and further away from the
cluster center (1.78-degrees, roughly 10 core radii). We find the binary stars
to be more centrally concentrated than the single stars in the cluster.
Furthermore, we find strong evidence for mass segregation within the binary
population itself, with progressively more massive binary samples becoming more
and more centrally concentrated. For the single stars, we find weaker evidence
for mass segregation; only the most massive single stars (> 2.5MSun) appear
more centrally concentrated. Given the cluster age of ~200 Myr, and our derived
half-mass relaxation time for the cluster of 230 +/- 84 Myr, we estimate ~47%
of the binary stars and ~12% of single stars in the cluster have had time to
become dynamically mass segregated. Importantly, when we investigate only stars
with mass segregation timescales greater than the cluster age, we still find
the binaries to be more centrally concentrated than the singles, suggesting the
binaries may have formed with a primordially different spatial distribution
than the single stars.
