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 Deltaₖ to the orbit size nₖ, showing that any divergent orbit must force the absolute value of Deltaₖ to grow proportionally to 2ᵏ times nₖ. 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 Deltaₖ recurrence. This note is not a full unconditional proof, but a complete structural skeleton isolating the final unresolved assumption required for global convergence.