Assignment 2: Identity

We have agreed that VP Ellipsis depends on some sort of identity between the
elided phrase and an antecedent phrase to permit recovery of the interpretation
of the elided phrase.  This assignment is about the nature of that identity.
Considering

(1)   Bill washed his car, and Harvey did ___ too.
(2)   I washed my car, and Harvey did ___ too.
(3)   Harvey washed his car, and I did ___ too.
(4)   Harvey hurt himself, and I did ___ too.
(5)   I hurt myself, and Harvey did ___ too.
(6)   Every member of the polo team was supposed to wash his/their socks,
      	... but Harvey didn't.
      	... but I didn't.
(7)   A: Did Harvey see you?  B: Yes, he did.
(8)   A: Did you call me?     B: No, I didn't.

and others resulting from your own investigation, what is the identity condition?

Having examined this question for VPE, you may extend your investigation to
other ellipsis phenomena.