A process where the documents do not match
What the document says“each State shall establish a process under which an applicant can provide such additional documentation to the appropriate election official of the State as may be necessary to establish that the applicant is a citizen of the United States in the event of a discrepancy with respect to the applicant's documentary proof of United States citizenship.”
The subsection is general and does not name any particular kind of discrepancy. Public argument about this Act has centered on applicants whose current legal name differs from the name on their birth certificate, most often after marriage. The Act does not use the words marriage, maiden or name change anywhere in its text.
What the document actually says“each State shall establish a process under which an applicant can provide such additional documentation to the appropriate election official of the State as may be necessary to establish that the applicant is a citizen of the United States in the event of a discrepancy with respect to the applicant's documentary proof of United States citizenship.”
Your papers may not match. Each state must set up a way to fix that. You bring in more papers.
Many people do not go by the name on their birth certificate. People often change their name when they marry. The bill does not talk about that directly. It does say states must have a way to sort out papers that do not match. It does not say how that should work.
It is often said that the Act makes no provision for an applicant whose birth certificate carries a different name from the identification presented. This subsection is a general provision for discrepancies and is the text supporters cite in answer. Opponents read it as delegating the problem to each state without a standard, and note that the Act never names the situation. Both readings are of the same words, and the site records them without resolving them.
No action is recorded against this proposal. That is not evidence that none has been taken, and nobody has yet read it against the record. See what the tracker does not yet cover.