Ozsváth–Szabó's conjecture relating absolute and Seiberg–Witten invariants

Let $X$ be a closed oriented smooth 4-manifold with $b_2^+(X)\geq 2$, let $\mathfrak{s}\in\operatorname{Spin}^c(X)$, and let $d(\mathfrak{s})$ be the expected dimension of the Seiberg–Witten moduli space. Let $\Phi_{X,\mathfrak{s}}$ be the absolute invariant defined from the mixed Heegaard Floer cobordism map. If $b_1(X)=k$ and $b_1,\dots,b_k$ is a basis of $H_1(X)/\operatorname{Tors}$, choose $n$ so that $U^n\otimes(b_1\wedge\dots\wedge b_k)$ has degree $d(\mathfrak{s})$. Ozsváth–Szabó's conjecture.

$$SW(X,\mathfrak{s})=\Phi_{X,\mathfrak{s}}\bigl(U^n\otimes(b_1\wedge\dots\wedge b_k)\bigr).$$

The conjecture proposes that the absolute Heegaard Floer invariant recovers the Seiberg–Witten invariant; the source gives no resolution status.