Exponential mixed-integer lower bound for general binary oracles

Let $n$ be the number of integer variables, let $d$ be the continuous dimension, and let $M$, $R$, $\rho$, and $\varepsilon$ be the problem parameters. A first-order chart $\mathcal{G}$ determines a general binary oracle. Mixed-integer binary lower-bound conjecture. There exists a first-order chart $\mathcal{G}$ such that the general binary oracle based on $\mathcal{G}$ has information complexity

$$\Omega\left(2^n \Big(1+d^2\log\left(\frac{MR}{\rho\varepsilon}\right)\Big)\right).$$

The conjecture transfers the proposed quadratic continuous-case binary-oracle lower bound to mixed-integer convex optimization; the cited continuous-case results motivate it, but it remains open.