is there a way to verify a note was sent exactly on the time stamp that is in the note?

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Not really. Maybe a trusted relay could attest to it. Or if it was timestamped with OpenTimestamps, you'd know within 10 mins.

i guess we can say note N happened before T, if there are replies/reactions to N after T, that are coming from people that are known to be not back posting.

so "no back posting bots" that react to things could be a service. or a relay that does not allow back posting could be a differentiating feature.

this could be important for forecasters to be recorded well. forecasters should have more value if their accuracy is high and time difference between prediction and actual event is longer. a bad forecaster could claim they sent the note a lot earlier but if there are services, it would be harder to claim that.

WUT?

no, but you can use NIP-03 for a form of attestation to prove the note was created before a relative point in time.