Integer Stabilization and the 2-adic Digit Tower in Collatz Valuation Dynamics

This is a clean-rewrite replacement for an earlier draft ("Integer Realizability and Carry Dynamics in the Collatz Valuation Tower") that contained a definitional collapse: the earlier draft's two central quantities, the tower carry b_k and the tower quotient q_k, are identical by definition (b_k ≡ q_k), which invalidated the earlier draft's central "Zero-Carry Congruence" and everything built on it (an error coordinate, two "counterexample" theorems, and an "Arithmetic Boundary" conjecture). This collapse is recorded explicitly in the paper, together with a full diagnosis of the earlier draft's error, rather than silently corrected. What remains, once the invalid apparatus is removed, is elementary: the quantity q_k is simply the next block of α_k bits in the 2-adic binary expansion of the valuation address x_w, and a valuation address is realized by a genuine positive odd integer if and only if this digit expansion is eventually all-zero — an accelerated-coordinate restatement of the elementary fact that a 2-adic integer is an ordinary non-negative integer exactly when its digit expansion terminates. This equivalence holds unconditionally, with no bounded-drift hypothesis needed. The paper is explicit that this does not distinguish a terminating realized orbit from a divergent one: a divergent orbit of a genuine positive integer N still has x_w = N, hence the digit tower still vanishes eventually, regardless of termination. 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" (DOI: 10.5281/zenodo.21468492), "Tail Dependence and Finite-Address Obstructions in Collatz Valuation Dynamics" (DOI: 10.5281/zenodo.21468378), and "Ghost Languages and Unbounded Prefix Memory in Collatz Realizability."