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Interesting idea!
Thinking out loud... There Doesn't Have To Be One Way To Do It. Piuk (or somebody) should hack together a client or miner that uses a ledger system; it could refuse to relay or include any transactions with inputs smaller than 0.001 BTC, so it only needed a truncated ledger to create new blocks (if it is a miner, maybe it connects to a trusted 'traditional' bitcoin node to make sure it only builds on valid blocks which might contain tiny inputs).