The Stack is a multiverse consisting of an infinite number worlds, each of a different topology. The worlds can be referred to as "geometries" when "dimension" would be too confusing. Usually there is one universe per Thurston geometry (or the equivalent in higher dimensions), but there are some exceptions. The stack contains all Thurston geometries of space-time combined with all selections of space dimensions vs. time dimensions. Most of the interaction between dimensions only happens from 4 dimensions up, with 1 Euclidean time dimension.
Interaction
Across the various universes in the stack, there is one very important constant: All of them (except for E0 and E1 where no life can exist) are populated with variations of a species of people known as Endbeings (short for N-dimensional being). The Endbeings have set up a global internet between dimensions, and can travel across dimensions. Traveling between geometries of the same number of spacial dimensions is usually easy, but travelling across different numbers means one will either be flat or not fit, so systems exist to transfer consciousness onto a robot with a different number of dimensions, then transfer back into one's original body when returning.
E3/Tuxe
Our dimension, known as E3/Tuxe, is actually a computer simulation running in the E4 dimension (which is 4D Euclidean space), as an experiment to see if expanding interaction downwards into 3D dimensions is possible. Thus it is not part of the stack, and humans are not Endbeings. This computer simulation is live broadcasted on the cross-dimensional internet. Also, the universe is not fully constructed. Originally it was just Earth and a sky dome, but larger and larger structures (such as the Solar System and other galaxies at a low level of detail) had to be constructed as humanity explored them.
The computer simulation is run at Tuxe Labs and is overseen by a pair of 4D Endbeings (Uncovesseltuxe and Thaneophyros) along with a previous transfer from E3/Tuxe into E4 (Ievokt).