The classical fourth-moment phenomenon, originally discovered by Nualart and Peccati for Gaussian limits, says that on Gaussian Wiener chaos, convergence in distribution to a Gaussian is equivalent to just the second and fourth moments converging. A parallel story has now been established for Poisson limits on Poisson and Rademacher chaoses, as in the paper above. The open problem is whether such a four-moment criterion characterizes Poisson convergence on arbitrary discrete chaoses, for instance those built from general independent integer-valued or mixed-type random variables, without requiring the specific combinatorial structure of Poisson or Rademacher inputs.