This is a simplified form of the extended Euclidean algorithm, in that it works mod p instead of tracking a specific multiple of p. The full algorithm solves

1a + 0p = a
0a + 1p = p

Into the form

xa + yp = 1

Which gives you the specific value, not just a representative.

If you can talk to both participants, you can ask them what state they're in and recover. If you can't, you're in trouble, which is kind of unavoidable. I should have linked to the original post: buttondown.com/jaffray/arch...

I'm thinking of something like a sharded system where you can send a message the thread that owns a shard, or a system where, if someone is holding a lock, you make a note for the unlocking thread to do your work when it's done.

Thanks for the reference! I'll think about whether I can simplify my model this way, but I'm kind of skeptical -- one reason is that I probably want to model having both persistent and ephemeral state, and the mechanism for crash recovery, explicitly, since it's the source of a lot of complexity.

I've been meaning to try FizzBee for this, I might do that!

This seems like it would be a pretty standard setup, but most examples I see aren't doing things like that, and it seems awkward enough in practice that I'm wondering whether I'm doing it wrong.