More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]

In [ref 1] apparently published in 2006 professor Cadogan presents an interesting function that maps natural numbers into a two dimensional array based on how many ones the number trails off with. The length of trailing one's is said to be the row index. The rest of the number, divided by 2, is the column index. He then shows that applying the Collatz function reduces the ending string of ones by one causing it to drop down a row. At the bottom of the table are odd numbers ending in 'xxx..01' a tail length of one. He reports that a restart function and continued iteration then causes a to monotonic reduction in column indexes, and the existence of this algorithm proves the conjecture.