Now each pointer, located at source, has its copy near its sink. The re-coloring stage is straightforward, as all relevant pointers have the same source and are located together. When no active edges remain in the root, the Turing machine stops and its tape represents the PKM output. Silicon parameters double almost annually. Centuries may turn them into a Dyson Sphere enveloping the solar system.
All steps are straightforward to do locally in parallel polylog time except sorting of pointers.
We need to create a fixed connection sorting network. Sophisticated networks sort arbitrary arrays of integers in log time. We need only a simpler polylog method. Merge-Sort splits an array of two or more entries in two halves and sorts each recursively. We merge sorted arrays by appending the reversed second one to the first, considering the last and first entries as neighbors, and sorting the resulting bitonic cycle.