The enumerable probability coding conjecture for $P^E$

Let $B^{\sharp}$ be the domain of finite binary strings under consideration, and let $P^E(x)$ and $K^E(x)$ denote the corresponding enumerable measure and complexity functions. Write $KP^E(x)$ for the prefix complexity associated with $P^E$. Enumerable probability coding conjecture. For every $x\in B^{\sharp}$ with $P^E(x)>0$,

$$K^E(x)\leq KP^E(x)+O(1).$$

This conjecture proposes removing the small correction term from the corresponding coding bound for the enumerable probability. It is motivated by the discussion of tighter bounds and remains unresolved in the supplied source.