Kronheimer–Mrowka's combinatorial dimension conjecture

Let $\Gamma$ be a planar trivalent graph, let $\langle\Gamma\rangle_0$ be the state space obtained from the specialized foam evaluation over $\mathbb{F}_2$, and let $J^\sharp(\Gamma)$ be the Kronheimer–Mrowka homology. Kronheimer–Mrowka's conjecture.

$$\operatorname{dim}_{\mathbb{F}_2}\langle\Gamma\rangle_0=\operatorname{dim}_{\mathbb{F}_2}(J^\sharp(\Gamma)).$$

The preceding text says that a specialization of the foam construction led to a proof of the combinatorial counterpart conjecture, but it does not explicitly state that this displayed equality is the resolved conjecture itself. The candidate is therefore retained as an open conjecture pending verification of its relation to the proved result.