Transience conjecture for self-interacting random walks in dimension at least four

Let $\mu_1,\ldots,\mu_{d-1}$ be $d$-dimensional measures in $\mathbb{R}^d$, with $d\geq 4$, zero mean, and finite $(2+\beta)$-moments for some $\beta>0$, and let $\ell$ be an arbitrary adapted rule. Transience conjecture. The walk $X$ generated by these measures and the rule $\ell$ is transient.

This conjecture proposes transience in dimensions at least four under only moment and zero-mean assumptions, uniformly over adapted rules. The supplied text presents it as an open question; no resolution is given.