  Massive circumstellar disks are prone to gravitational instabilities, which
trigger the formation of spiral arms that can fragment into bound clumps under
the right conditions. Two dimensional simulations of self-gravitating disks are
useful starting points for studying fragmentation, allowing for high-resolution
simulations of thin disks. However, convergence issues can arise in 2D from
various sources. One of these sources is the 2D approximation of self-gravity,
which exaggerates the effect of self-gravity on small scales when the potential
is not smoothed to account for the assumed vertical extent of the disk. This
effect is enhanced by increased resolution, resulting in fragmentation at
longer cooling timescales $\beta$. If true, it suggests that the 3D simulations
of disk fragmentation may not have the same convergence problem and could be
used to examine the nature of fragmentation without smoothing self-gravity on
scales similar to the disk scale height. To that end, we have carried out local
3D self-gravitating disk simulations with simple $\beta$ cooling with fixed
background irradiation to determine if 3D is necessary to properly describe
disk fragmentation. Above a resolution of $\sim 40$ grid cells per scale
height, we find that our simulations converge with respect to the cooling
timescale. This result converges in agreement with analytic expectations which
place a fragmentation boundary at $\beta_\mathrm{crit} = 3$.
