A condition on the error update

Every time the three colors want a simultaneous update, there must be three times that at least on of the colors want two updates.   This says nothing about how often a color wants more than two updates. However, we are restricted to integer counts, and we assume independent counters.  Thus if the fast rate gets two in a row and another update then is pending, we can be assured it is either the small rate again or the next larger rate, and so on.  Thus, out of four updates, at least one will have one update pending for each color.  This condition is ignored, carried in the error term. Skipping the update when it is ambiguous closes the sphere. Doing each layer gets you an Avogadro as a power series in Phi.

The extra dimensions also have an equivalent surface area to volume which will determine the equivalent Diophantine, I think.  Except there will a new mode of ambiguity for each dimension added. The link shows the recurrence. In all cases we should be reducing a factorial spanning tree to a minimal with equal ambiguities removed.

Updates pending are grouped; (1,0,0), (0,1,0), 0,0,1) are equally likely and ambiguous. They are carried in the error term.  This is the principle of reduction. There are no real quantities, just integer counts. The error processor wants the most likely and least likely.