A Structural Framework for Collatz Dynamics: Δₖ Automata and the Conditional Decay Principle

This preprint introduces a deterministic structural framework for the Collatz map based on the Delta-k Automaton. We derive an exact algebraic identity linking the correction term Delta_k to the orbit size n_k, showing that any divergent orbit must force the absolute value of Delta_k to grow proportionally to 2^k times n_k. Using this identity, we prove an explicit Forced Decay Inequality for all deep collapse steps where the 2-adic valuation of (3n + 1) is at least 3, establishing a contraction factor beta less than or equal to 3/4. A 2-adic lifting argument shows that such collapse residues occur with positive density (at least 1/4 of all odd residues). Assuming only that a divergent orbit cannot remain confined to a measure-zero subset of residues (a minimal 2-adic mixing assumption), the frequent forced contractions make sustained divergence structurally impossible. Thus, under this minimal hypothesis, all Collatz orbits converge as a deterministic consequence of the Delta_k recurrence. This note is not a full unconditional proof, but a complete structural skeleton isolating the final unresolved assumption required for global convergence.