The de Finetti theorem tells us that an infinite exchangeable sequence of random variables can be represented as a mixture of independent identically distributed sequences, governed by a so-called mixing measure. The rigidity question asks: if you can only see finitely many coordinates of such a sequence, at what point does the information from those coordinates pin down the entire mixing measure completely? The papers on rigidity of exchangeable sequences probe when the joint distribution of a small number of coordinates forces the mixing measure to be unique, but a sharp general characterization of which sequence families admit this rigidity at small coordinate counts remains unknown.