[DarylZero]

E.g. right now the social consensus is that the longest chain _minus the top 5_ blocks is the "settled" consensus of committed transactions. If you own the coin in a block 6 deep, then you can prove it.

As the difficulty gets lower, the number of transactions to drop from the top gets higher, and maybe also less certain.

It makes no difference about the mining difficulty in the past. If double-spends are possible _today_ then you can't ever prove you own the coin, regardless of whether you could do it in the past.