Argument from the Graphical Properties of Predecessor Tree

-- There is a unique root node for the graph
-- All nodes in abstract predecessor tree are unique (by construction)
     -- each contains dn+c, n=0 ... infinity
     ==> no multiple paths to any integer in a predecessor tree
     ==> no cycles in the graph; it is truly a tree
     ==> Collatz trajectory and predecessor direction are distinct
     ==> Predecessor tree is a directed graph (from state transition diagram)
-- Behavior of every integer in an l.d.a. is known
     -- the Collatz trajectory moves upward (s|b) to an extension
     -- the Collatz trajectory then moves left (e) to an l.d.a.
-- These path elements repeat: l.d.a. to extension to l.d.a. to extension ....
-- Every integer does map into the abstract tree (shown by "counting" and sieving)
-- Every pathway in the predecessor tree is constrained to this same behavior whether observed in the abstract or the binary tree
==> Path is constrained to upwards and leftwards steps, so all trajectories go to the root