Do Shannon capacity and its reversible variant coincide?

2403.10985 introduced the notion of reversible capacity of a graph and showed that it is at most the Shannon capacity. It is conjectured there that the two values are equal.

At the finite-length level, it is known to fail: the maximum independent set of $C_7^3$ is strictly larger than the maximum multirectangular independent set (corresponding to reversible capacity sets). However, it remains possible that in the large-n limit they converge.