Consider a serial coprime divider machine

 We feed it a stream of error counts, and each of the coprime dividers bumps it round off count.  

One will eventually turn over, reach ix maximum round off, but the other will not, they are relatively prime, they will not coincide on rollover. 

Examine the distribution of round off errors about the entire path set.  We would expect a bell curve about the integer point. Think of a Lie graph, the outer,middle,and inner rotations.  The zero angle is the integer

If you have three co primes, then the maximum entropy Lie mp will have a minimum number of steps, and that is the left side of Markov when Lie is circular. The right side are the number number of paths which all have to be traversed, total number of sequences through the Lie plot. Markov n-tuples are the special set of coprimes that make the Lie graph circular.

When you mash down the salad bowl onto  circular Lie paper, then by the density increases at the edge, and angle size decreases., the maximum entropy bandwidth allocation is set. You have packed sphere.