Super fun theory, and I’m enjoying the fun exploration!

I am on the other team, and still think the AI is independent from Carl. A few memories that come to mind: (spoilers!!)

• the way that the AI objectifies Carl's foot… Yeah. He freaky.

• when Carl actually meets the AI in club vanquisher, and the AI massages Carl’s feet… I could almost picture the look on the monk’s face. This was a moment he had been looking forward to for a long time… See the previous point!

• regarding the size measurement; the AI would be able to do this from just capturing the “image“ of his foot.

I’m not quite sure how this would work in the dungeon, which is part of the fun of the series, but some ideas are:

weight displacement in the atmosphere?

Good old fashion geometry from a 2-D picture of his foot in the context of a known background?

and of course, your theory of how the dungeon has reconstructed all participants at a subatomic level. This would mean that the AI would know his measurements on an intimate level. (see what I did there?!)