Quote from: JoelKatz on June 26, 2011, 04:52:20 AM

You can prove the amount of currency has not changed because any change in the amount of currency will require changing one of the private key / balance pairs, which will change the hash in step 4.

This does not cryptographically verify that the sum of the values of all the keys is the same as another hash, of a different distribution of values/currency/funds, sorry for the confusion. The idea is I should be able to compare GETTHEBLOCK_x( (private key₁, balance₁₁), (private key₂, balance₂₁) ) and GETTHEBLOCK_x( (private key₁, balance₁₂), (private key₂, balance₂₂) ), and verify whether or not balance₁₁+balance₂₁ == balance₁₂+balance₂₂ .

The "reference" I'm talking about is the initial input that contains a publicly known private key, and the initial currency. You compare future hashes to this block to verify the sum amount of currency in circulation has not changed.

This does happen to be a bit of a departure from a traditional hash, in that it's supposed to preserve exactly one piece of information information somehow: the sum of the values, even if you can't tell exactly how much, you should be able to compare it to another block.