Meng–Lin–Yang's optimal-query conjecture for the Rényi-Ulam game

Let $k\ge 1$ and $a,b\ge 0$ satisfy $2k>a$ and $a+b\ge 2$. Define

$$ch(a,b)\coloneqq\min\big\{q:(q+1)a+b\le 2^q\big\}.$$

Set

$$C\coloneqq\max\big\{ch(a,b),RU_0^k(2a+b)\big\},$$ $$\chi_0\coloneqq\max\big\{x:RU_1^k(x,a-x)\le C-1,\ x\le a,\ x\le k\big\},$$ $$\chi_1\coloneqq\max\big\{y:RU_1^k(\chi_0,y+a-\chi_0)\le C-1,\ y\le b,\ y\le k-\chi_0\big\}.$$

Meng–Lin–Yang's conjecture. With these definitions,

$$RU_1^k(a,b)=\max\big\{C,1+RU_1^k(a-\chi_0,b-\chi_1+\chi_0)\big\}.$$

This conjecture concerns the optimal query in the Rényi-Ulam game with restricted-size queries, where $RU_1^k(a,b)$ denotes the relevant one-lie query complexity and the parameters describe the current state. The paper presents it as a conjecture about optimal play; no resolution is given in the supplied text.