The Triviality Pattern of Compensation-Avoiding Towers in Collatz Dynamics: A Profinite-Symbolic Obstruction Framework

Any Collatz counterexample must sustain a compensation-avoiding orbit where v2(3T^j(n)+1) ∈ {1,2} indefinitely. We investigate such towers through two exhaustive tests. Finite Residue Exhaustion: For every M ≤ 21, exhaustive enumeration of all 2^(M-1) odd residues modulo 2^M shows U_M = {1}. Every odd residue except r ≡ 1 receives compensation within 53 steps. Periodic Tower Obstruction: For all primitive words w ∈ {1,2}^p with 2 ≤ p ≤ 21, the divisibility condition 2^A(w) - 3^p | Δ(w) fails. The only solution is w = (2), x = 1. Any remaining counterexample must be a nonperiodic critical balanced {1,2}-tower satisfying global 2-adic compatibility — a highly rigid structure for which no candidate has been observed. Paper D of a four-part series. Paper A: Moon, K.-U. (2026). Zenodo. https://doi.org/10.5281/zenodo.20068553Paper B: Moon, K.-U. (2026). Zenodo. https://doi.org/10.5281/zenodo.20068640Paper C: Moon, K.-U. (2026). Zenodo. https://doi.org/10.5281/zenodo.20068757