This was a great beginning! When I first read the prompt, I was curious to see how writers would deal with the 4th dimensional aspect of the tesseract. Your description of the room folding into the next plane is fascinating (makes sense since they already occupy three of those four planes). And then what comes after...

They were soon separated, because familiar laws of locomotion and distance did not operate anymore. Would she see Brian again?

They were lost.

That delivers such a punch. She truly loves the guy, and she's determined to see this through with him. But because of his obsession, it feels like he's been drifting away from her for months. Then when they invade the fourth dimension and that separation becomes literal... wow!

I also dig that you turned this into Start the Story! Feels like a nod to the way time and space get distorted inside the story itself. :D Very cool and very much in keeping with the creative spirit of the contest imo!