Dexter Lawrence of the Giants celebrates a defensive stop during the third...

Dexter Lawrence of the Giants celebrates a defensive stop during the third quarter against the Texans at MetLife Stadium on Sunday. Credit: Jim McIsaac

When this new Giants regime rolled into the building at the start of this year, they lumped the players they inherited into three pretty clear categories.

There were the ones they wanted to shed if at all possible. Some were expelled from the roster because of their paychecks (such as James Bradberry) and others for locker- room politics (Logan Ryan). There were ones they tried to move who took a little while (Kadarius Toney) and others they just could not pass off to anyone else (Kenny Golladay).

Then there was the wait-and-see list. The Giants weren’t quite ready to make any long-term commitments to Daniel Jones or Saquon Barkley, and although they have carried the offense almost entirely with their play this season, ambiguity remains about their futures here. They will be addressed at a later date.

And then there was the very small portion of the team they were all in on. The no-doubters. The immediate yeses.

Really, there was only one of those guys. It was Dexter Lawrence.

He was the only player whose contract they added seasons to, picking up the fifth-year option for 2023 on his rookie deal faster than it took them to find a comfortable height on their new office chairs.

All those other decisions may or may not wind up working out for them. The Lawrence call could not be going any better.

“He’s definitely the core of our defense,” linebacker Jihad Ward said. “The big, bad [expletive] core.”

Lawrence proved that again on Sunday with one of his most dominant performances of the season. The defensive lineman had a hand in two sacks (bringing his team-leading total to five on the season; no one else has more than two), had another five quarterback hits (including one that led to Dane Belton’s interception), batted down a pass, had a tackle for a loss and drew two holding penalties (one of them enforced that took a Texans touchdown off the scoreboard).

And he did it in a game in which the other supposed long-term cornerstone of the defense, safety Xavier McKinney, was sidelined by a hand injury he suffered in an ATV accident during the bye week.

As the game was going through its paces, he even became something of a running joke between Leonard Williams and Kayvon Thibodeaux. They would rush the quarterback with varying degrees of success, and once the ball came out, they would pursue the play . . .  and then peek back at the pocket.

There they’d see Texans quarterback Davis Mills and, more often than not, their buddy getting up off of him.

“Almost every time I saw Dex hitting the quarterback or in his face or something,” Williams said. “All day. We were laughing and joking about it.”

Thibodeaux said he has yet to see Aaron Donald play in person, but as far as he is concerned, they are the top interior defensive linemen in the league.

It was Lawrence who found that funny.

“I just want to keep dominating and keep proving myself to him and to whoever else,” he said.

For a player known as Sexy Dexy whose sack dances and gyrations during pregame introductions bring smiles from the entire team, Sunday was a chance to see him at his most alluring and seductive. And he figures to only get better.

Lawrence turned 25 years old on Saturday. This is his nascent form.

“It’s just all coming to fruition right now,” he said. “Each year, my goal is to grow in my position, learn in my position, and this year everything is kind of slowing down for me. It’s making sense.”

Lawrence has been overlooked for most of his career. Even when the Giants selected him 17th overall in 2019, he was an afterthought. He arrived on the same night the Giants selected Jones as their quarterback to replace Eli Manning and came in with the pick the Giants had acquired in the blockbuster trade of Odell Beckham Jr. It’s hard to break through that double-team block of the spotlight on draft night, even for a 350-or-so-pounder.

This season, Lawrence is overshadowed by no one.

“He hasn’t been talked about enough over the last few years,” safety Julian Love said. “He’s able to shine now that we’re winning and you can see his game really taking over. We know he’s an All-Pro, Pro Bowl-level player. It’s just that those nose tackles don’t get as much love as they should. But we’re lucky to have him.”

Said Williams: “If no one has noticed him yet, they must not be watching football.”

The Giants’ front office noticed him. They decided they wanted him to stick around, too. He’s turned out to be just as important to the team’s success as Barkley and Jones on the other side of the line of scrimmage.

The only difference between them and him is no one has to fret one bit about what uniform Lawrence will be wearing next year. It’ll still be the Giants.

And, chances are, it’ll be sexier than ever.

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