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Bitcoin references inputs by transaction hash and an index. What disadvantages are there to referencing inputs by block height?

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The outputs of a block can be summarised as a height and {public keys, values} pairs. If I make a transaction later, I need to include my public key anyway, so I feel I should be able to summarise my inputs as simply a height (or a series of them). I appreciate this isn’t what bitcoin does, but could it? It would compress transaction inputs down to single a number, and UTXO entries down to a public key and a list of {height, value} pairs.

This feels like a good which means I haven’t invented it. Can anyone point me to any information on it or maybe let me know why it doesn’t work?


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