The bounded Syracuse falling-time conjecture

Let $\operatorname{syr}$ be the Syracuse map on odd positive integers, and let $\operatorname{sft}(n)$ denote the Syracuse falling time of an odd integer $n\geq 3$, namely the least positive number of Syracuse iterations needed to reach a value below $n$. Bounded Syracuse falling-time conjecture. There exists $C\geq 10$ such that

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

for all $n\equiv 3\pmod 4$.

This conjecture seeks a uniform bound for Syracuse falling times on the residue class $3\pmod 4$. Computations establish bounds for a large finite range and for the known glide records, while the asserted global bound remains open.