The oath is not a formality attached to a jurat; it is the substance of it. A jurat certifies that the signer appeared, was identified, signed in the notary's presence, and swore or affirmed to the truth of the contents — and if the swearing does not happen, there is nothing to certify. A signer who refuses to swear or affirm has declined to perform the essential element, so the notary cannot complete the act and must decline. The available alternatives are all worse. Performing the jurat and noting the refusal would place a false certificate in circulation, since the certificate states the oath was taken. Substituting an acknowledgment changes the legal effect of the document without authority and would defeat the purpose of a document drafted to require sworn statements. And an oath cannot be delegated to a witness, because the affirmation must come from the person whose statements they are. The proper course is to decline, explain why, and record the refusal in the journal.