Spencer's conjecture on infinitely recurring bin orderings

Consider a balls-in-bins process $(I_m(i))_{i\in[B],m\geq 0}$ with feedback function $f$ in the almost-balanced regime. Here $[B]=\{1,\ldots,B\}$, and $\Pi$ ranges over all permutations of $[B]$. Spencer's conjecture. For every permutation $\Pi$ of $[B]$ and every initial condition, with probability $1$ there are infinitely many $m\geq 0$ such that

$$I_m(\Pi(1))<I_m(\Pi(2))<\dots<I_m(\Pi(B)).$$

Equivalently, every possible ordering of the bins occurs infinitely often almost surely. The conjecture concerns the almost-balanced regime and asks whether the process visits every strict ordering infinitely often, regardless of its initial state; the supplied text gives no resolution.