Continuity conjecture for relative symplectic cohomology

Let $(M,bomega)$ be a closed symplectic manifold and let $K_0\subset M$ be a compact subset. The relative symplectic cohomology $SH_M(K;\Lambda_{\geq0})$ is defined for compact subsets $K\subset M$, with restriction maps inducing a directed system over compact $K$ satisfying $K_0\subset\operatorname{Int}(K)$. Continuity conjecture.

$$\underset{\substack{K_0\subset \operatorname{Int}(K) \\ K\text{ is compact}}}{\varinjlim} SH_M(K;\Lambda_{\geq0})=SH_M(K_0;\Lambda_{\geq0}).$$

The paper establishes this identity in the special case of standard toric balls in complex projective space, while the general continuity property for relative symplectic cohomology remains the proposed extension.