A deterministic framework is developed for excluding the existence of non-trivialcycles in the Collatz map 3n+1 on N. The trajectory is interpreted not asa pseudo-random process, but as an evolution through a hierarchy of 3-adic scalelevels: each odd step necessarily increases the 3-adic denominator depth, forcing thesystem into a finer representational layer. This mechanism is combined with the local2-adic structure, which uniquely determines the sequence of divisions by 2, and withthe global Diophantine constraint given by the cycle equation. A dynamic top-levelcontribution arising at each odd step is identified. Under normalization to depth 3K, the final transition produces a non-removable residue 2^A₊-₁ 3, whereas allpreceding contributions are multiples of 3 and vanish. This residue cannot be cancelledby the nodal term n (2M - 3K), yielding a structural incompatibility between the2-adic determinism of the descent sequence and the topology of the 3-adic scalehierarchy. As a consequence, no non-trivial cycles with K>1 can occur. The analysisplaces the Collatz problem within the framework of deterministic non-Archimedeanarithmetic dynamics, where the 3-adic scale structure acts as a stable invariant of thetransformation.
Eduard Dyachenko (Sun,) studied this question.