"arbitrarily" is doing some heavy lifting!
I'm not sure that two concurrent harmonious answers constitutes a "fixed" coin or a diagnosis of a fixed coin.
This scheme will be rubbish with a one sided coin ie the limit for "arbitrary fixed coin".
How is that "heavy lifting"? It's perfectly reasonable for any real-world "coin".
How is that "heavy lifting"? It's perfectly reasonable for any real-world "coin".