If someone challenges his interpretation of the 3 requirements in court, then presumably he'd have to explain why he believed that to be the case[1], but he does not have to prove this certainty ex ante in order for the 90-day extension to be valid.
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[1]: IANAL but whether he can successfully prove it or not is also ultimately irrelevant given the SCOTUS recent interpretation of presidential power. If he's found "guilty" of making a bad interpretation of the certainty of the 3 requirements, what is really going to be his punishment? There's really nothing you can do against a sitting president with regards to the exercise of their executive power...