Toward a Synchronization Obstruction Theory for the Collatz Problem: Safe Corridors, 2-adic Hearts, Integer Liftability, and a Finite Arithmetic Witness

We develop a structural obstruction framework for the Collatz conjecture centred on integer liftability: the question of whether an infinite symbolic survival corridor in the 2-adic integers ℤ₂ can correspond to an actual positive integer orbit. Principal results (v2.0) Proved (exact): • Integer-Liftability Necessity Lemma: any integer-liftable corridor must have ρ_L → 0 • Arithmetic Stabilisation Criterion (NEW): ρ_L → 0 ⟺ ξ ∈ ℤ (the 2-adic limit is a rational integer) • All-ones corridor: ξ = −1 ∉ ℕ⁺ (algebraic proof) • Finite Beatty Synchronization Collapse: S₉ = ∅ (mod 2¹⁴), exact exhaustive computation Numerical evidence (not theorems): • Exponential scarcity of positive-drift corridors: P_pos(L) ≈ Ce^{−cL}, c ≈ 0.367 • Typical corridors appear to satisfy ρ_L → 1 (experiments up to L = 100) Open (explicitly stated): • Zero-Tail Exclusion Problem: whether any positive-drift corridor can have ρ_L → 0 Companion paper: Moon, K.-U. (2026). Collatz Normal Form. Zenodo. https://doi.org/10.5281/zenodo.18233316 Related independent work: Chang, E.Y. (2026). arXiv:2603.11066, arXiv:2603.25753. Both frameworks independently encounter the distributional-to-pointwise barrier as the core remaining obstruction. This paper does not claim a proof of the Collatz conjecture.