On the 3n+1 Problem: Binary Carry Dynamics, Pipeline Model, and a Reduction of the Collatz Conjecture to a Combinatorial Hypothesis

This manuscript provides a rigorous combinatorial reduction of the Collatz conjecture via original binary carry dynamics and pipeline orbit decomposition. We construct a state potential function governed by bit-level carry propagation parameters P and M, and prove that the entire 3n+1 conjecture reduces to a single local contraction hypothesis on finite pipeline units. All previous definitional errors and logical ambiguities are fully corrected in this refined version.