So, there is a series of dophatine equations

In ascending order which tell us the finite number of updates needed to maintain a M partitions of  N things.  That is the same as telling us the residual error after packing. The exact number of updates, and how to make them white.  There should be a finite coloring algorithm for unlimited dimension. It is really a light thing, the implicit assumption is that light is adjusting the queues, and is always fixed in number of steps to completion.