Tail Dependence and Finite-Address Obstructions in Collatz Valuation Dynamics

We establish a finite-address obstruction to integer realizability in Collatz valuation dynamics. A valuation address w = (α_j)j≥0 is realizable if the associated 2-adic limit x_w = -Σ 2A_j/3ʲ⁺¹ lies in the positive odd integers. We prove that every finite valuation prefix admits both a realizable and a non-realizable infinite extension (Tail Dependence Theorem), from which it follows that no coordinate determined by any fixed finite prefix depth can decide realizability on the full address space (Internal Coordinate Obstruction, Fixed-Depth Faithfulness Obstruction). This paper concerns positive-integer realizability of valuation addresses, not termination or divergence among already-realized orbits: if a Collatz counterexample exists, its valuation address is itself positive-integer-realizable, so the obstruction proved here does not by itself distinguish a terminating realized orbit from a nonterminating one. This paper does not prove the Collatz conjecture. Part of a four-paper program on Collatz valuation realizability, together with "The Dual Automaton Structure of Collatz Realizability," "Integer Stabilization and the 2-adic Digit Tower in Collatz Valuation Dynamics," and "Ghost Languages and Unbounded Prefix Memory in Collatz Realizability."