Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block's hash, transactions are hashed in a Merkle Tree, with only the root included in the block's hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored.

Since 2007. At some point I became convinced there was a way to do this without any trust required at all and couldn't resist to keep thinking about it. Much more of the work was designing than coding. Fortunately, so far all the issues raised have been things I previously considered and planned for.

We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced, and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received.

If you're having trouble with the inflation issue, it's easy to tweak it for transaction fees instead. It's as simple as this: let the output value from any transaction be 1 cent less than the input value. Either the client software automatically writes transactions for 1 cent more than the intended payment value, or it could come out of the payee's side. The incentive value when a node finds a proof-of-work for a block could be the total of the fees in the block.

When someone tries to buy all the world's supply of a scarce asset, the more they buy the higher the price goes. At some point, it gets too expensive for them to buy any more. It's great for the people who owned it beforehand because they get to sell it to the corner at crazy high prices. As the price keeps going up and up, some people keep holding out for yet higher prices and refuse to sell.

As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.

I'm sure that in 20 years there will either be very large transaction volume or no volume.

A rational market price for something that is expected to increase in value will already reflect the present value of the expected future increases. In your head, you do a probability estimate balancing the odds that it keeps increasing.

Subscription sites that need some extra proof-of-work for their free trial so it doesn't cannibalize subscriptions could charge bitcoins for the trial.

The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.

A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.