When no active edges remain in the root, the Turing machine stops and its tape represents the PKM output. TM cannot outperform Bubble Sort. Silicon parameters double almost annually. Centuries may turn them into a Dyson Sphere enveloping the solar system. Faster PPM Simulations.
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. Batcher-Merge combines two sorted lists in parallel log time.