I wonder how that giving hope works... do they siphon off your optimism into a little glass bottle, like Skeksis? I'd probably be rejected as a hope donor anyway. The hopes I'd be willing to give up aren't really the sort of things you want people to hope for, generally.
On the bracelet, they abbreviated it as "give time|money|hope", which implies there's some bitfield of all possible things that can be given. We could use this to establish a lower bound for the total addressable heap space available for the universe, if we could list every conceivably option like the celestial programmer certainly must have. But that would be silly, since astrophysicists already calculated it through other means.
2^X = 10^10^100th. X = total bits in the universal heap. X/N = 2^N, where N is the number of bits in a celestial int. I'm pretty sure that at some point I would have been able to solve for N.
Hmm, with various approximations, I get an N of around 300. So most likely, the universe is running on a 512-bit operating system.