I don't need to answer 1,000 lines of a questionnaire where you only talk about the hashes themselves.
RIPEMD-160 was purely an example. What stops you from simply using the first 58 bits instead (let's call this a hash prefix)? What stops you from using just the first bit of the hash? They're all uniform, independent bits, or are they not?
Let's talk a bit about Poisson, since you brought it up. It is used to estimate the CDF when the number of possibilities is extremely large (hence, it's an estimated probability, not an exact one, careful). Using Poisson, can you please tell us, if we want a degree of confidence of let's say >= 90%, how many hashes in a 66-bit range start with some whatever 10-prefix base58?
It's a simple question, that might reveal how far away from the "average" the amount of prefixes are likely to be.
Obviously, the answer is somewhere between 0 and 2**66 included, because that is the only interval where the confidence reaches 100%. I am really interested on what you come up with as a result.
And yes, before you search in AI, two independent events, unrelated to each other, each maintains their own identical probabilities. But they change like when you flip 2 or more coins trying to get both heads.
Unfortunately, unlike many others around here, I'm not using any AI to produce crap statements or crackpot theories.
Exercise:
Two subjects head to a casino, subject A called 'Near' bets with subject B that we will call 'Far'.
Far bets Near $1000 that he won't flip 3 coins and have all of them result in heads. Who has a higher probability of winning, Near or Far?
I thought we were talking about having some estimated amount of prefixes in some range, and whether it's more or less likely for them to be close to each other, rather than semi-arbitrarily spaced through the range. Pardon me, what do Near or Far have to do about this?