Alright, I'm putting up a 10 BTC bounty for anyone who can find such a function OR prove that it doesn't exist, with a reasonable description of what combination of features makes is making it impossible.

All it has to do is this: Define a hashing function GETTHEBLOCK_1( inputs ) which takes a map of (private key, balance) pairs, and produces a very large number based on it, in such a way that any pairs with a balance of zero passed to the input does not affect the output, and additionally such that an examination of the hash can securely prove that the amount of currency embodied within it has not changed from a reference.