A Dissipative Attractor Approach to the Collatz Problem: Non-Divergence, Cycle Constraints and Diophantine Obstructions

This work presents an analytical approach to the Collatz problem (3n+1 problem) based on a dissipative dynamical systems framework. The proposed framework combines three complementary components: a non-divergence analysis based on negative bit-length drift, constraints on possible non-trivial cycles through logarithmic and arithmetic relations, and Diophantine considerations involving primitive prime divisors. Computational experiments performed using CUDA parallel processing are included as supplementary material to investigate the numerical behaviour of Collatz trajectories and the proposed dissipative structure. The manuscript is intended to provide a mathematical framework for further analysis and independent verification of the presented arguments.