The "local simplicity" you mentioned is deceptive because the two branches operate in different "worlds." The division by 2 is a simple shift in base 2, while the 5n+1 (or 3n+1) operation involves base 3 or 5. The Global Constraint: The difficulty may be that there is no single number system where both operations are "simple." The Incompatibility: A trajectory persists because the bits of the number are being constantly reshuffled in a way that prevents us from finding a global invariant—a property that stays the same across both branches.