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He said the campaign, to be safe, threw away the pages containing about 700 signatures from assistant circulators.

From the dais, Ms. Curry noted several incomplete entries — for instance an illegible signature accompanied by the printed first name “Robert.”

“Did it occur to you to either ask Robert to put his last name in or put in a legible signature?” Ms. Curry said, before pointing to another instance of sloppy record-keeping. “So again, how can the board verify who that is and if the person is a registered voter of the District?”

But math may be on Ms. Alexander’s side. Unless the board finds rampant fraud in the petition process, she will likely have more than enough signatures to meet the threshold of 250 even after numerous signatures that are either incomplete or from unqualified voters are thrown out.

Mr. Ford said the campaign, “as the incumbent,” set out to collect 10 times the required number of signatures.

“We wanted to show force,” he told the board.

Mr. Hughes, who sat beside Ms. Matthews, testified he looked into the Alexander team’s practices based on the volume of signatures that the campaign acquired over a short period of time, from mid-November to early December.

Mr. Ford and Mr. Browne said they were good at what they do, setting out in the morning to Metro stops, fast-food chains and grocery stores along Benning Road and Nannie Helen Burroughs Avenue. Many of the best spots were within walking distance of their homes.

“Within a mile of me, I had a large volume of signatures I could obtain,” Mr. Ford said.

Ms. Nichols, the board’s chairman, said it will issue a ruling to the involved parties by email before the close of business on Monday.