Mathematical modeling reveals dual-fractal structures and inverse-growth constraints in Collatz sequences, suggesting alternative slow trajectories to traditional benchmarks.
This paper investigates the structural properties of the Collatz (3n+1) system. Starting from the principle of "No Overlap, No Omission", this work introduces a dual‑fractal framework for Collatz iteration. We analyze inverse‑growth constraints and explore the boundedness behavior of iteration sequences. Numerical verification is performed to examine special slow‑lane trajectories, including the 91‑dominated slow‑channel, and revise the viewpoint that 27 is the global slowest trajectory. This preprint provides new observational structures and numerical evidence for studying the Collatz conjecture, without claiming a complete mathematical proof of the conjecture.
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Ruijie Qin (2026) studied this question.
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