The bounded enumeration conjecture for induced cuts

For a graph with the parameters and family of cuts defined in Lemma~, let $\mathcal{C}^{\mathrm{ind}}$ denote the corresponding family of induced cuts. Bounded enumeration conjecture. Lemma~ holds with

$$|\mathcal{C}^{\mathrm{ind}}| \leq 2^{O(1/\delta)}.$$

This conjecture proposes that the family of induced cuts can be bounded independently of the graph size, depending only exponentially on $1/\delta$. The supplied text gives no resolution or further evidence for the conjecture.