Concentration conjecture for the verification decoder's edge-type counts

Let $t$ denote the discrete decoding time, let $R_{i,j,k}(t)$ be the number of edges connected to IVNs of type $r_{i,j,k}$, and let $\bar{R}_{i,j,k}(t)=E[R_{i,j,k}(t)\mid H_t]$, where $H_t$ is the history up to time $t$. Let $\alpha_0 n$ be the lifespan of the random process and let $d_v$ be the maximum variable-node degree. Concentration conjecture.

$$\lim_{n\rightarrow \infty}\Pr\left(\sup_{0\le t\le \alpha_0 n}\left|\bar{R}_{i,j,k}(t)-R_{i,j,k}(t)\right|\ge n^{5/6}\right)=0$$

for all $\{i,j,k:0\le i\le d_v,0\le j\le d_v,0\le k\le d_v,0\le i+j+k\le d_v\}$. This concentration is one of the unproved assumptions needed to establish the correctness of the decoding analysis.