I absolutely have no way to trace where the 20$ in my wallet came from.
However, I can trace a satoshi all the way back to its generation.
1. There is a serial number on it, so i guess it's possible
2. You can trace that satoshi, but you can't prove ownership at each address in that timeframe, meaning that you cant prove anything really.
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How can you tell from serial number who gave you that $
Serial numbers served the different purpose you cant trace the owner from it