Ghost Languages and Unbounded Prefix Memory in Collatz Realizability

We study, within the class of Collatz valuation words realized by genuine positive odd integers, whether the exact accelerated digit block q_k at a given position k can be recovered from a bounded local observation: a fixed-width sliding window together with a bounded phase datum. We prove (Unbounded Prefix Memory Theorem) that it cannot: for every window length L, there exist two realized valuation words sharing an identical length-L window and phase at some position k, yet with differing q_k, unconditionally (no bounded-drift hypothesis needed). The construction uses an explicit safe adjacent-symbol swap (odd valuation difference), an exact 2-adic non-integrality argument, and the Backward Lifting construction with an odd-terminal correction to realize both finite truncations by genuine positive odd integers. This is a bounded-local exact-value obstruction, logically distinct from both zero-decision hardness (whether q_k=0 can be decided) and from the fixed-prefix realizability obstruction of the companion Tail-Dependence paper; neither of these stronger claims is established here. A conditional (experimentally supported, not proven) strengthening to explicit on-demand target control, and a conjectural non-ω-regularity of the associated bounded-alphabet ghost language, are also discussed, together with the precise gap remaining to establish them. To the author's knowledge, no prior work establishes a constructive bounded-local separation theorem for the exact accelerated digit block q_k within the class of valuation words realized by positive Collatz integers, of this form; a detailed comparison with the classical parity-vector/2-adic conjugacy literature (Terras, Lagarias, Bernstein, Bernstein-Lagarias), computational-complexity literature (Stérin-Woods), and statistical parity-code literature (Koyuncu et al.) is given in the paper. This paper does not prove the Collatz conjecture. Accompanying code independently re-verifies the paper's explicit 44-symbol / N0 = 89,898,906,153,467,314,169 construction (Section 6) from scratch, and reproduces the qualitative pattern behind the Swap Handle Coverage experimental observation. Part of a four-paper program on Collatz valuation realizability, together with "The Dual Automaton Structure of Collatz Realizability" (DOI: 10.5281/zenodo.21468492), "Tail Dependence and Finite-Address Obstructions in Collatz Valuation Dynamics" (DOI: 10.5281/zenodo.21468378), and "Integer Stabilization and the 2-adic Digit Tower in Collatz Valuation Dynamics" (DOI: 10.5281/zenodo.21468590).