5:42 PM PT -- TMZ has obtained the mugshot for the Sphere climber ... who happens to have a smile on his face.

12:21 PM PT -- A spokesperson for Sphere Entertainment tells TMZ ... "We are grateful to the local authorities for their support in this matter. The individuals involved are currently in the custody of LVMPD."

The Sphere in Las Vegas got an unexpected visitor Wednesday ... an activist-climber scaled the towering 367-foot-tall structure.

Video of the individual walking around the top of The Strip's newest concert venue started to crop up online shortly after he began ... and the climber -- Maison Des Champs -- also posted to Instagram confirming he was the one who'd made the daring climb.

Maison explained in the short clip that he was doing the climb to raise money for a homeless woman and her unborn child ... asking his 273k followers to donate to the cause while standing on the sphere.

Reporters spoke with Tim Clement, outreach director for Survivors of The Abortion Holocaust ... who said he was told Des Champs was detained after coming off the top of The Sphere.

BTW ... this is sorta Maison's whole gimmick. He climbed the Chase Tower in Phoenix during Super Bowl week last year to protest abortion and pulled off a similar stunt the year before in San Francisco.

Police have reportedly shut down the streets in the area to traffic and have seemingly detained members of Des Champs' activist group as well.

U2's supposed to perform in The Sphere tonight ... unclear if today's stunt will delay or postpone the show.