There is actually a reason to claim that have read and accept may be preferable.
Note that the established facts are in the past, but the situation being described is present. This is the reason it is called present perfect, and this is why you can't add any time-indicating adverb like "yesterday" or "earlier".
However, it can be claimed that the facts that need to be established are instead that
Compare this to another sentence which use the verb "be" in the present simple: "You certify that you have studied and are proficient in English".