The supercenter conjecture for odd KLR algebras

Let $R_{{\mathfrak{b}}}(\nu)$ be the odd KLR algebra associated with a dimension vector $\nu$, and let $Z(R_{{\mathfrak{b}}}(\nu))$ denote its supercenter. Let $\operatorname{Sym}(\nu)$ be the subring of invariants consisting of symmetric polynomials in dots on vertical strands, and let $\tilde\omega_i^a$ be a floating dot with label $i$ and exponent $a$, placed in the rightmost region. The supercenter conjecture. There is an isomorphism of rings

$$Z(R_{{\mathfrak{b}}}(\nu)) \cong \operatorname{Sym}(\nu) \otimes \bigotimes_{i \in I} \bigwedge^\bullet \langle \tilde\omega_i^{0}, \dots, \tilde\omega_i^{\nu_i-1}\rangle.$$

The preceding inclusion of this tensor product in the supercenter is expected to be exhaustive; proving the equality would determine the supercenter of these odd KLR algebras, extending known calculations in related cases.