Athanasiadis's nonnegativity conjecture for local gamma-vectors

Let a simplex be subdivided into a flag vertex-induced homology subdivision, and let its local $\gamma$-vector be the vector obtained from the symmetric local $h$-vector by the usual gamma-vector expansion.

Athanasiadis's local gamma-vector conjecture. The local $\gamma$-vector of a flag vertex-induced homology subdivision of a simplex is nonnegative.

This conjecture concerns nonnegativity phenomena for local gamma-vectors of subdivisions. Athanasiadis disproved it by providing a counterexample.