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Thanks for your answer, but this is really bad news. I obtained most of my bitcoin before the split off of etherium years ago, and held it in a different e-wallet app, which is now defunct. I really don’t think there is a record of my original purchase transactions, except in the blockchain.  Can you help me trace that back?    

If not, I think you have confirmed my worst fears: I will have to use a basis of $0 when I eventually sell it.