When his grievance hearing scheduled to start Tuesday gets going, star tight end Jimmy Graham will carry the burden of proof as he argues that he is actually a wide receiver worth about $5 million more than what the Saints want to pay him under a franchise tag for the 2014 season, according to the NFL’s collective bargaining agreement.

There’s a possibility it doesn’t go this far; but if it gets to the point that a ruling comes down either for or against Graham, the losing side will then have up to 10 days to serve notice of an appeal.

Much has been written about the merits of Graham’s and his representatives’ arguments, and those the NFL’s Management Council will use to counter them. But the hearing that could last through Wednesday might bring the Saints and their followers into close proximity with the specifics of a process not often initiated.

To prevent Graham from becoming the most-sought unrestricted free agent when his contract expired in March, the Saints handed him a one-year franchise tag that was worth $7.035 million and classified him as a tight end — the position at which he was drafted, at which he has been selected for two Pro Bowls, and which he lists on his Twitter bio.

But the CBA adopted in 2011 states that the kind of tag Graham was given should pay out the average of the five largest salaries from the previous season given to players at the position at which the player participated in the most plays during the previous season.

About two out of every three snaps Graham logged for the Saints in 2013, Graham lined up out wide, leading New Orleans with 1,215 receiving yards and the NFL with 16 touchdown grabs. Therefore, through the league players union, he filed a grievance in May arguing that he deserves a franchise tag that considers him a wide receiver and would pay him $12.3 million.

If Graham succeeds in his hearing, that entire amount would count against the Saints’ 2014 salary cap. New Orleans was about $1.72 million under the salary limit Monday counting Graham’s tight-end tag, meaning the team would have to create cap space. That can be achieved by restructuring deals on the books, terminating players under contract or trading them.

Taking the side opposite Graham, the NFL Management Council is expected to contend he was merely utilized in a manner consistent with how tight ends have been used in the modern NFL: as hybrid blockers and pass receivers.

The franchise-tag battle would become irrelevant and end the moment the Saints and Graham hammered out a long-term deal to replace the expired one. But any ruling that might come on whether Graham should be considered a receiver or a tight end for tag purposes would give significant leverage to the winning side in negotiations about how much money he should make annually under his new deal.

There have been similar disputes in the past concerning tight ends Jermichael Finley and Jared Cook — both prolific pass receivers — and outside linebacker Terrell Suggs, a productive pass rusher who sought more money by arguing that he was used more as a defensive end. All were settled before an arbitrator issued a ruling.

If Graham’s case doesn’t follow that route, a ruling in the matter will come from the NFL’s system arbitrator, Stephen Burbank, who has been involved in resolving CBA-related disputes between league management and the players union since 2002.

A couple of high-profile cases Burbank has heard recently have essentially gone against the Saints. In one, Burbank — a University of Pennsylvania Law School professor — ruled a franchise tag the Saints used on quarterback Drew Brees in 2012 was the second of the player’s career, not his first, as the league argued. A third tag applied in 2013 would’ve represented a 144 percent raise for Brees, who eventually signed a long-term deal and never played under the franchise tender.

In another case, Burbank ruled that NFL Commissioner Roger Goodell was acting within his authority disciplining Saints players in the wake of the bounty scandal. The players union challenged that. Ultimately, asked to review the matter, former NFL Commissioner Paul Tagliabue vacated all bounty-related player penalties.

Burbank took six days to issue his ruling in the Brees case. He took five days in the bounty case.

The CBA mandates that a system arbitrator’s determinations “upon their issuance be binding upon and followed by the parties unless stayed, reversed, or modified” by a three-person appeals panel, one member of which is a former judge.

Unless otherwise agreed to, aside from serving notice, anyone seeking review of a system arbitrator’s determinations would have at least 15 days and no more than 25 from the date of a decision to lodge a brief in support of an appeal.

The opposite side would have as much time to respond in writing to any appellate brief. Oral arguments would follow between five and 10 days after that. And a written decision on the appeal would be issued within 30 days of oral arguments, unless the schedule is accelerated for “good cause,” according to the CBA.