The incorrect-path splitting conjecture for polar-code list decoding

Let $u_i$ be an unfrozen bit in a polar code, and consider any incorrect decoding path that survives at $u_i$. Under the Gaussian approximation, the path may continue through subsequent unfrozen bits $u_{i+1},\ldots,u_N$.

Incorrect-path splitting conjecture. Under the Gaussian approximation, for any incorrect path that survives at some unfrozen bit $u_i$, it will split at some stage within $\{i+1,i+2,\ldots,N\}$ with high probability.

This conjecture concerns the behavior of incorrect paths in successive-cancellation list decoding. Together with the preceding conjecture about the correct path, it is intended to describe how splitting and pruning affect path survival, but the source provides empirical evidence rather than a proof.