Over the last decade, much of the progress in the classification and regularity theory of simple, nuclear C*-algebras has made direct use of von Neumann algebraic techniques. A common theme in these results is a careful study of the “trace-kernel ideal” consisting of the tracially null elements of the norm-ultrapower. In the presence of mild regularity conditions (such as a weak form of comparison), this trace-kernel ideal admits certain extension-theoretic rigidity properties. I’ll discuss this idea and explain how this leads to an extension-theoretic proof of the Elliott Conjecture.