So far, the rules which are candidates for reversibility are those for which there is no Garden of Eden; one cannot determine an ancestor for a configuration which has none, which precludes a rule which purports to do so. Among those which remain, the equidistribution rule applies. We have seen that there are environments which could restrict the number of ancestors, such as a quiescent infinity or a cyclic automaton. Still the examples constructed in Sec. 2 produce a unique inverse without reference to any boundary condition, which is a general alternative which must be considered. Evidently the apparent variety of ancestors is illusory; the mechanism must be investigated.