Is there such a thing as pigul for half of the offering? It's a machloket! And a further development of Rabbi Yosei's position, which doesn't presume karet and whether some amount of pigul intent contaminates everything - for example, the 2 loaves of lechem ha-panim. What is the smallest unit, so to speak, that can become a problem of pigul? Or can it be in parts at all? Also, what about mitigating factors against the phenomenon of pigul - to make an offering permitted, when it might have become pigul? Also, delving into the position of Rabbi Yehudah HaNasi, regarding combining intents and whether pigul results. Plus, the implications of a communal offering (vs. a personal one), with regard to purity/impurity.