Check out these photos that were taken Friday, which show KK heading into a meeting in Beverly Hills ... with something of note in her arm. That would be the script for the new 'American Horror Story' season, in which Kim has been cast as a major character.

BTW, it doesn't just look like a generic script or outline ... this appears to be the script for a specific episode in the upcoming 12th entry of the series, which has been dubbed 'Delicate.'

On a zoomed-in shot, you can see it's been watermarked as Kim's copy -- and you can even make out a bit of the title of this episode. To us, it seems to read ... "When the Bough Breaks," and it has the lead writer's name featured (Halley Feiffer), as well as the director.

As we reported ... Kim was announced as being attached to 'AHS' last month, and she'll be acting opposite Emma Roberts ... among other cast members. Her exact role hasn't been declared just yet -- but there's a hint based on the source material, a forthcoming novel.

The book that this season is said to be based on is called "Delicate Condition," by Danielle Valentine. It's described as a story about an expecting mother who becomes convinced evil forces are trying to torpedo her pregnancy ... almost in the vein of "Rosemary's Baby."

Some have speculated Kim might be playing the pregnant mom, and that Emma could perhaps play another villain-adjacent character. Cara Delevingne was also recently cast.

BTW, if you're wondering how 'AHS' is moving forward amid the writers' strike ... it would appear Ryan Murphy and co. might already have some scripts in the can. When Kim was first tied to the new season, the word at the time was production was scheduled to begin shortly thereafter ... and that a summer premiere was likely, with an exact date upcoming.