The action horizon shell model in the quasicrystalline spin network (QSN) is an inflationary cosmological model, where a set of projectors in the 8-dimensional E8 lattice project down to lower dimensions to form a growing series of shells made of 20-Groups and other tetrahedral combinations.
In this analogy, we use the 5D cubic lattice to project shells or rings of the Penrose tiling in 2D. The sun decagons are analogous 20-Groups in the QSN. As the shell count increases, the distance between successive shells decreases, approaching a 2D surface reminiscent of the holographic principle. A measurer in a span of shells today, 14 billion years after the big bang, will perceive light patterns (made of empire waves) from actions that occurred in the past in such a way that the light will be red-shifted – implying the notion that space must be expanding. Indeed this is expansion, specifically inverse-expansion, like looking through a fish-eye lens, where images are increasingly compactified near the perimeter of the image. The action horizon cosmological model implies that we live in a universe that is a convergent series. An example of a geometric divergent series would be the cubic series of cubes with a unit length but each in a higher dimension than the previous. The first, the square with edge length 1, has a circumscribing n-dimensional sphere that is one over the square root of two. The cube, or 3D square, has a circumradius for its n-sphere that is the inverse of the square root of three and so on. At the limit, we see that the circumradius becomes infinity with the infinite-dimensional cube. Conversely, the series of regular n-dimensional triangles is a convergent series, starting with the equilateral triangle with a circumradius of one over the square root of three or about 0.577 to the infinite-simplex or triangle with a circumradius of one over the square root of two or about 0.707.
The action horizon cosmological model of the QSN, therefore, states that we live in a convergent universe, where any large number of shells describing universal scale actions and time over some set of shells today is like layers fantastically thinner than the outside membranes of an onion, approximating a 2D surface for large swaths of space time reality. Because empires, serving as the mathematical first principles explanation for entanglement and non-locality in general, run not just on given shells as frames of universal-time but also run through shells or through time.