And so is it sort of like you send these private coins off chain per se, and then where does the nullifier come into it?

Yeah, so the observation of these client-side validated protocols is when I give you a payment, I can give you the history of that point.

that allows you to check that all the payments in the history of that coin are valid.

But what it does not allow you to check is that I haven't double spent you.

So I could send you a coin off-chain, I could send somebody else a coin off-chain, and they might conflict.

So what the nullifier allows us to do is like a deterministic, random-looking quantity, derivable, from each coin.

So if I tried to double spend, I'd have to put the nullifier on chain twice.

So you might be an operator of that bridge? We could