Unconditional Collatz Via 2-Adic Normalization, Stopping-Time Invariance, Backward Growth, and Induced Density.

We study the Collatz dynamics through a single-rule 2-adic normalization that encodes bothparity and halving structure without case distinctions. We prove that the resulting normalizedmap is orbit-wise injective, with strictly increasing forward orbits, and show that this injectivitytransfers canonically to the accelerated odd Collatz map. As a consequence, distinct backwardtrajectories in the accelerated dynamics cannot collide, yielding a rigid binary backward growthstructure with explicit polynomial lower bounds on basin size. This establishes a structuralobstruction: any divergent accelerated orbit would necessarily generate a basin of positive log-arithmic density. This rigidity yields an exact inductive partition of the odd integers at everydyadic scale, ruling out divergent accelerated orbits without appeal to probabilistic density ar-guments. The contribution of this paper is the explicit derivation of orbit-wise injectivity andits transfer to the accelerated dynamics, together with the resulting rigidity of backward growth;no new probabilistic or heuristic assumptions are introduced.