  By proving precisely which singularity index lists arise from the pair of
invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and
Smillie determined a Teichmueller flow invariant stratification of the space of
quadratic differentials. In this paper we determine an analog to the theorem
for $Out(F_3)$. That is, we determine which index lists permitted by the
Gaboriau-Jaeger-Levitt-Lustig index sum inequality are achieved by fully
irreducible outer automorphisms of the rank-$3$ free group.
