Ah, the brain of Perseus.

If, as you were replacing neurons, you put them together in the same arrangement in the jar next door so you had 2 exact copes, which one is your brain?

At the exact point 50% of your neurons are copied, which one is your brain?

The best question is : does it matter?

These are similar to the contemplations that resulted in 'cogito ergo sum', being that all you can prove is that you have thoughts, so on some level, somewhere there is something having those thoughts : "I think, therefore I am"