Many talk about the first coins mined by Satoshi "lost" unless he comes back around and still has the wallet.dat or private key info.
Presumed lost, sure. Provably lost, nope.
Others say that if an owner can't recover password info for their .dat file and sell it, and it's on the open market, they are lost.
Again, there is no proof these coins are lost. They could have set a password they know would be impossible to brute force and are scamming users by selling the wallet, which they will sweep at a later date. Or perhaps the wallet doesn't belong to them in the first place.
And some say only the burner addresses are considered "lost" because they can not be recovered because some of the burner addresses are made up and have no checksum and therefore cannot be recovered.
This is probably the closest we can come to coins which are lost for the time being. The chances of anyone currently knowing the private key to burner addresses such as 1BitcoinEaterAddressDontSendf59kuE is so astronomically small as to essentially be zero. However, these coins are still not
provably lost, as there exists a chance, however small, that someone could stumble upon or brute force the private key to these addresses as some point in the future.
If you had to come up with set criteria for deeming coins "lost", what would it be?
The only coins which are provably lost are ones which cannot be spent. Such an example would be coins sent to OP_RETURN outputs. But if they cannot be spent, then that defeats the purpose of what you are trying to do.