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Aranna, there is no missing dimension. We have both dimensions for a cylinder.
Yes, you are in house rule territory because you are adding rules here.
Adjudication is about determining what rule is correct, house rules are about filling in missing pieces. In this case you are using both, not just adjudication.
You are adjudicating adding a house rule to fill in the missing pieces.
The problem is we do not know it is an empty bag. In fact, it very much behaves as if it were not an empty bag because it is quite heavy for an 'empty bag'.
My adjudication avoids adding house rules.
My adjudication is that the bag is presented as having the dimensions of a cylinder and thus I do not have to add a dimension to the bag. I can look at a non-magical example in Ultimate Equipment if I want to see the size and shape of a sack in Pathfinder, it is a cylinder. Thus I do not have to houserule a third dimension in.
My adjudication is that the bag is heavier by an order of magnitude than a nonmagical empty cloth sack and thus does not behave like an empty sack thus avoiding the houserule of compressing a magic item into a smaller space.