What is the meaning of "is that of"? How to understand it?

The state si in the global state S corresponding to the cut C is that of pi immediately after the last event processed by pi in the cut.

In all other states in the US, a domestic corporation's legal status is that of a foreign corporation.

The word that is an anaphoric pronoun in these examples. This means that we understand what that refers to through words that occurred earlier in the discourse. The reason it is difficult to decode in the first example is because the noun state is followed by an appositive proper noun, si, and then modified by a very long Prepositional Phrase: in the global ... cut C ’. The word that in the first example should be interpreted as the state:

The state si in the global state S corresponding to the cut C is the state of pi immediately after the last event processed by pi in the cut.

Similarly:

In all other states in the US, a domestic corporation's legal status is the legal status of a foreign corporation.

The word that in each case is just 'referring' back to a previous noun in the sentence. In short ‘is that of ’ should be interpreted as ‘is the X of ’ - where the X is co-referrential with a previous noun in the text.