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Hi A-J!

I've read your scribbles, and I think I understood them (except: what is
an injection?).

Dom d is the X' from your theorem section, i.e. the set of cells which
have posward connections along d, right?

Mostly, it makes sense, just the last section is problematic. The
important thing about clone dimensions is not simply that the contents
are equal; the important thing is they *stay* equal. I.e., I'd say:

    If d is a clone dimension, then for all ZigZag spaces
    Z = (X, c, C) for which d element of X, it holds for
    every x element of Dom d in that space that c(x) = c(Dim{d}(x)).

(By your definition, not only all dimensions where cells have the same
content by chance would be clone dimensions, but also *all cells not
used as dims*! So, each non-dimension cell would be a clone dimension ;).)

- Benja