Interesting Russell; be interested in your response to "Could someone please try this" post below.
On slices: If what is being sliced is not specified; a series of slicing operations might be a self-referent construct with "space" defined only by "hollow number". E.g. how do you know each side of the slice is equal size? Slice again and you have "three" parts; two divisions cutting; but to assume now all three pieces are equal sized requires "going back in time" and re-defining where the first cut was made by reference to the most recent cut.
Further slicings will require further trips back in time to "supposedly re-write history" if equal-spaced pieces are assumed to come from the slicing operations.
If "space" is defined by assumed equal sized pieces (fixed grid) then "time" is getting "condensed" out of all this re-juggling of defining of slicing cut locations; so a particular definition of "time" gets tied to a particular number of slices.
Note that this look at "slicing" paints it as a self-referent continuum.
"The slices must be in Planck units" sounds like "they must be in units of "relativity" or "threes" as it is when you slice a second time and get "3" you get the juggling effect on "where was the first slice made". If this "3-ness" is generalised into "relativity theory" you have a generalised quantum "2-ness" from juggling say "which way do you get 2 in 3?" connected to a "three-ness".
If you assume a quantum (2-ness) changes (has 2-ness or possibility of observability say?) and if you generalise this as 4-ness geometry; you have a means to say juggle relativity and quanta?
As the wavefronts intersect (as three-ness meets new-three-ness) your implicit 2-ness expands 2 to power 2 to power 2 to power 2 etc.
The information density of this space increases?