Pesahim 19a and Pesahim 19b, how we know R. Yose and R. Akiva disagreed about whether there was a concept of a shelishi, a third extension of ritual impurity, for non-sanctified materials (with ramifications for whether there might a revi’i or hamishi, fourth or fifth level extensions for terumah and/or sacrificial foods); the idea of containers combining foods for ritual impurity purposes, what rabbinic decrees of ritual impurity (and doubts about ritual impurity) applied in the Temple and/or in Jerusalem.
