If a selected candidate or an unselected candidate files with the Secretary of State, no later than the time specified in Section 6042, an affidavit stating without qualification that he or she is not now a candidate for the office of President of the United States, and stating that similar documents, also without qualification, have been or will be timely filed, where applicable, with the appropriate public election official in all other states holding open presidential primaries, that candidate’s name shall be omitted from the list of names certified by the

Secretary of State to the county elections officials for the ballot and his or her name shall not appear on the ballot.