The “underlying crime(s) were not charged, so the prosecution has no burden to prove them. This is all about intent. Many crimes are “general intent crimes” which means simply committing the act is sufficient to prove intent.
Do you even know what the “underlying crime” was supposed to be? Do you know if it was a crime, or do you take Merchan’s word? Sounds like nonsense.
How is Trump signing checks to Cohen proof that he intended to falsify records? He had nothing to do with the record-keeping. And - as he did with paying for the pollster - he paid what Cohen said he owed.
This whole thing is just asinine.