Approximate minimum path-metric conjecture for SCL decoding with list size at least 8

Let $L=2^m$ with $m\ge 3$, and let ${{\mathsf L}_{k-m}}$ denote the log-likelihood ratio at bit position $k-m$. For each ${\bf v}_{k-m+1}^k\in\{0,1\}^m$, let $P_{v_{k-m}=1,\,{\bf v}_{k-m+1}^k}$ be the path metric of the path beginning with $v_{k-m}=1$ and continuing with ${\bf v}_{k-m+1}^k$, and let $P_1$ be the corresponding aggregate path metric. Approximate minimum path-metric conjecture. When ${{\mathsf L}_{k-m}}\ge 0$, we assume

$$\min_{{\bf v}_{k-m+1}^k\in\{0,1\}^{m}}\left\{P_{v_{k-m}=1,\,{\bf v}_{k-m+1}^k}\right\}\approx\frac{P_1}{L}.$$

This extends the preceding approximation to successive cancellation list decoding with $L=2^m\ge 8$ and is used to estimate decoding performance. The supplied text gives no evidence that the conjecture has been proved or disproved.