The Syracuse falling-time conjecture for Mersenne-type integers

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

$$\operatorname{sft}(2^{\ell}-1)=2$$

for all $\ell\geq 4625$.

The assertion agrees with computations through $\ell=500000$, following a finite-range pattern in which the Syracuse falling time equals $2$ for all tested exponents from $4625$ onward. Its validity for all larger exponents is open.