So I understand how blockchains work. I understand how proof-of-work works. And I understand how they work together. I also understand (or at least I think I do :) how transactions work (A block can contain arbitrary data inside of it, so it can contain a message signed by A that he transfers 5 btc to B).
But where does the bitcoin itself fit in this picture?
Is it a recalculated number every time (so if A gives 1 btc to B, then if I want to confirm, I verify that A has 1 btc to give away by checking who sent him anything, and make sure that he has what to give away, etc. up until the miner's bounty)? If so, this would have to be done whenever a block is mined (if not, I (who have 0 btc in my "wallet") can certify that I give B 100 btc, mine a block, and include that transaction. And while the blockchain on its own would still work (meaning that the hashes work out and solve the proof-of-work), the accounting wouldn't).
Am I making sense or am I totally off?
. It's a linked list, but instead of linking-by-address, it's a link-by-hash.
. Change a part of the Node so that the node's hash would start with 100 zeros, for example.