  The 3D index of Dimofte-Gaiotto-Gukov a partially defined function on the set
of ideal triangulations of 3-manifolds with $r$ torii boundary components. For
a fixed $2r$ tuple of integers, the index takes values in the set of $q$-series
with integer coefficients.
  Our goal is to give an axiomatic definition of the tetrahedron index, and a
proof that the domain of the 3D index consists precisely of the set of ideal
triangulations that support an index structure. The latter is a generalization
of a strict angle structure. We also prove that the 3D index is invariant under
3-2 moves, but not in general under 2-3 moves.
