Transfer from full-information first-order to general binary oracles

Let $u(n,d,R,\rho,M,\mathcal{G})$ denote the worst-case information complexity of a query strategy under the full-information first-order oracle based on a first-order chart $\mathcal{G}$. Binary-oracle upper-bound transfer conjecture. If there exists such a query strategy with worst-case information complexity $u(n,d,R,\rho,M,\mathcal{G})$, then there exists a query strategy under the general binary oracle based on $\mathcal{G}$ with worst-case information complexity bounded by

$$u(n,d,R,\rho,M,\mathcal{G})\cdot O\left((n+d)\log\left(\frac{MR}{\rho\varepsilon}\right)\right).$$

This would transfer upper bounds from full-information first-order oracles to general binary oracles. In particular, it could yield improved binary-oracle upper bounds if the full-information mixed-integer upper bound is improved.