untagged – Bitcoin: How does Proof of Work and single transactions align?

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I am studying papers since hours and nonetheless do not get one factor:
A bitcoin transaction is an data like “Bob sends 2 BTC to Alice”. This message is signed with Bobs non-public key and must be added to the blockchain that’s distributed to each participant. I additionally obtained that you must calculate a Proof of Work to have the ability to add one thing to the chain. Or in different phrases: The opposite contributors will not settle for your block with out the proof of labor.

How does Bob get this proof of labor or how does Bobs message went to an individual who has such I proof? I am unable to imagine that each individual making a transaction must calculate it is personal proof. Is it actually like that? If not: How does Bobs “message” is transmitted to an individual who owns such a proof, how can the individual guarantee that Bobs message is a sound transaction (and never solely rubbish) and what the motivation for this individual to course of Bobs message in any respect?



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