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This could be a community project:
1 – Create a smart contract that has control over a bitcoin wallet.
2 – Every time someone sends bitcoin to that wallet they include as part of their transaction their EOS address.
3 – The smart contract then creates tokens at a 1:1 ratio of the number of bitcoin that were received in the wallet.
4 – Next the smart contract sends 99% of those tokens to EOS address that was included in the bitcoin transaction.
5 – The remaining 1% is a fee that could be used in a few different ways and may not even be necessary.
6 – If someone sends the token back to the contract with a btc address attached, they will receive an equivalent amount of btc (minus the btc network fee of course).
An EOS token 100% backed by BTC but faster and usable in everyday transactions.
If this were popular enough the btc blockchain may cease to have sufficient transaction volume to support the btc network, especially as the mining reward drops off. In which case, EOS replaces all of BTC with a smart contract
I don't actually know enough about smart contracts to know if this is possible.