The large-number Syracuse falling-time conjecture

Let $\operatorname{sft}(n)$ denote the Syracuse falling time of an odd positive integer $n$. Large-number Syracuse falling-time conjecture.

$$\operatorname{sft}(n)\leq 2$$

for all odd $n\geq 2^{5000}$.

This conjecture is the Syracuse analogue of the large-number falling-time bound and is motivated by computational evidence and heuristics for very large odd integers. Its truth beyond the tested finite range is open.