Blondel–Maesumi generic finiteness conjecture for complex matrix families

Let the ambient space consist of finite families of complex square matrices, equipped with its natural measure, and let the finiteness property mean that some finite product attains the joint spectral radius. Blondel–Maesumi generic finiteness conjecture. The finiteness property holds almost everywhere in the space of finite families of complex square matrices; equivalently, the set of families without the finiteness property has measure zero. The source gives no resolution status and motivates the conjecture by the expectation that pathological computational and undecidability phenomena are nongeneric.