Transactions where the miner uses the same transaction ID in the coinbase of more than one block cause the two transactions not to be uniquely identifiable. Therefore, one of the two coinbase transactions is provably lost.
Abstract
Bitcoin is spent by being identified by transaction ID and index number. Early versions of the bitcoin software allowed identical transaction IDs to be used in the coinbase transaction. There were two occurrences of this, one in blocks 91,722 and 91,880 and the other in blocks 91,812 and 91,842. The spendable UTXO set only includes only one transaction for each pair of blocks causing two losses of 50 BTC each. (no fees were collectable in these blocks, simplifying the analisys)
Detail
Block 91,722's coinbase transaction ID (the only one in the block) is
e3bf3d07d4b0375638d5f1db5255fe07ba2c4cb067cd81b84ee974b6585fb468. Block 91,880's coinbase
transaction ID is identical. Therefore, there is only one 50 BTC output in the spendable set of
transactions implying a loss of 50 BTC amongst this pair of blocks.
Additionally, block 91,812's coinbase transaction ID is
d5d27987d2a3dfc724e359870c6644b40e497bdc0589a033220fe15429d88599 which is also shared by the
coinbase transaction in block 91,842. Because there is only one 50 BTC output in the spendable
set of transactions, this implies a loss of 50 BTC amongst this pair of blocks as well.
Bonus trivia: The transaction IDs in the spendable set are not strictly related to the transactions
that created them. Which block the coinbase transactions
e3bf3d07d4b0375638d5f1db5255fe07ba2c4cb067cd81b84ee974b6585fb468 and
d5d27987d2a3dfc724e359870c6644b40e497bdc0589a033220fe15429d88599 came from is undefined.
Implementation
We arbitrarily pick the coinbase transactions in earlier blocks (91,722 and 91,812) as the provably lost supply.
if (block.block_number == 91722 || block.block_number == 91812)
if (transaction.hash == 'e3bf3d07d4b0375638d5f1db5255fe07ba2c4cb067cd81b84ee974b6585fb468' ||
transaction.hash == 'd5d27987d2a3dfc724e359870c6644b40e497bdc0589a033220fe15429d88599')