Universal tightness conjecture for concave neighborhoods of circular spherical divisors

Let $(X,\omega)$ be a closed symplectic $4$-manifold obtained as a symplectic blowup of $\mathbb{CP}^2$ with the standard Kähler form. Let $D=C_1\cup\cdots\cup C_n\subset X$ be a circular spherical symplectic divisor, meaning that the $C_i$ are embedded symplectic $2$-spheres intersecting transversely and positively in a circular configuration, with no three passing through a common point. Suppose that

$$C_i\cdot C_i\in\{0,+1\}$$

for some $i\in\{1,\ldots,n\}$. Universal tightness conjecture. Any contact structure induced on the boundary of a concave neighborhood of $D$ is universally tight. This conjecture extends the uniqueness and universal tightness results for several classes of torus bundles arising as boundaries of symplectic divisors; its general status is not resolved in the supplied source.