Today's filing was the last step in the dance of written documents that each side files in an appeal. That means the case is moving along to oral arguments before the Minnesota Supreme Court June 1.
Coleman wants the state Supreme Court to order the three-judge panel that decided Franken won to go back and open 4,400 rejected absentee ballots or, rule that no candidate won the race, presumably to prompt a revote.
Coleman's lawyers contend that counties applied different rules in deciding which absentee ballots met the state's requirements for legal votes. As a result, some counties rejected ballots that other counties opened and counted.
In a brief Monday, Franken's side called these variations minor. But Coleman attorney Ben Ginsberg said the variations could have changed the result of the election, given the small margin by which Coleman trails Franken.
"The math for that is pretty self-explanatory: the margin is 312, there are 4,400 votes that are in dispute," Ginsberg said. "That is more than enough to affect the outcome of the election."
Franken is 312 votes ahead. Coleman said he can take the lead if justices deem more ballots legitimate.
"Applying the standard used on election night to all remaining rejected absentee ballots does not mean the court would be turning a blind eye to the statutory requirements," the former senator's lawyers wrote.
Instead, they said it would acknowledge that some election officials were looser in their application of state law.
Minnesota has four reasons for rejecting an absentee ballot: the voter wasn't registered, they failed to sign the ballot, their witness wasn't qualified and they cast another ballot.
Coleman wants the court to presume that a voter who got an absentee ballot was registered, their witness was authorized and they put their genuine signature on it.
He has long contended that officials in some places took a harder reading of the law than others, meaning ballots ruled eligible in one county would be disqualified in another.
"In sum, the record confronts the court with indisputable evidence that this deliberate, disparate treatment of voters was significant enough to affect the outcome," Coleman's brief said.
Coleman's side said more outstanding ballots are from areas Coleman won than areas where Franken prevailed, although they haven't offered anything other than a geographical analysis.
There is no deadline for the state Supreme Court to rule after the June 1 oral arguments.
Coleman could try to take his case to the U.S. Supreme Court if he loses this round.
A Franken win would give Democrats and aligned independents 60 votes in the Senate. That's the number needed to cut off unfettered debate known as filibusters.
Franken asked the high court to instruct Republican Gov. Tim Pawlenty to issue an election certificate, the gateway document needed to fill the vacant seat.
Coleman's brief did not address Franken's request.
The governor has hedged on whether he's required to sign the certificate if the loser goes on to appeal to the U.S. Supreme Court or files another election lawsuit in federal court.
(The Associated Press contributed to this report.)