This work presents a unified structural proof framework for the Collatz Conjecture,combining geometric intuition (Vacuum Funnel) with rigorous arithmetic constraints (Δₖ Automaton, Residue Mixing Lemma, Structural Decay Principle). The paper establishes:• non-existence of infinite k=1 sequences• positive density of collapse events (k ≥ 2)• strictly negative drift in logarithmic potential (εₖ > 0) These combined mechanisms force global convergence for all trajectories. This is the closed formal version used for the public release of“The Unified Theory of Collatz Dynamics (Closed Proof Attempt) — Part 5” posted on Reddit r/Collatz on December 4, 2025.
Moon， Kyung-Up (2025) studied this question.