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To answer this question, it needs to be more specific, because by the expression "surpass paper money" everyone can understand completely different actions. Bitcoin has long outnumbered every state currency in value. It is unlikely that he is capable of anything else. Even comparing bitcoin and paper money of states by other criteria does not make any sense.
This is true that Bitcoin will surpass the fiat money becasue soon the crypto market is going to be legal and that time the crypto market almost all coins touches the sky and that time the BTC touches the millions of dollars of just 1 coin price.