git remote add my-remote my-super-duper-protocol::some-sort-of-address-thingy
Then pushing/pulling `my-remote` will try to invoke a command called `git-remote-my-super-duper-protocol`, with `some-sort-of-address-thingy` in its arguments. You can implement that however you like.
For example, if aliens claim their machine solves the halting problem, we could test it on millions of inputs whose halting/not-halting behaviour we already know; but even if it works for all of them, there's no way to know that it works for all inputs. For all we know, it might be a huge lookup table which happens to cover all of those inputs we tried.