The diameter conjecture for powers-of-two Bell-type Riordan graphs

Let $CG_{2^k}$ be the relevant io-decomposable Riordan graph of the Bell type, and let $\operatorname{diam}(G)$ denote graph diameter. Diameter conjecture.

$$\operatorname{diam}(CG_{2^k})=k$$

and there are no io-decomposable Riordan graphs $G_{2^k}\not\cong CG_{2^k}$ of the Bell type satisfying

$$\operatorname{diam}(G_{2^k})=k$$

for all $k\geq 1$.

This conjecture is presented as a corrected direction after the preceding diameter conjecture was disproved. The supplied text gives no resolution, so its status remains open.