Uniqueness without a hard-core assumption for repulsive Gibbs point processes

Let $\phi$ be a pair potential satisfying assumptions (A2) and (A3), with activity $z$ and inverse temperature $\beta$. A Gibbs measure is a probability measure describing the equilibrium distribution of the point process under the potential $\phi$. Uniqueness conjecture. Under assumptions (A2) and (A3), there is uniqueness of the Gibbs measure when

$$z\ \sup_{x \in \mathbb{R}^d} \ \int_{\mathbb{R}^d} \left(1-e^{-\beta \phi(x,y)}\right)\,dy<1.$$

This would extend the paper's explicit Dobrushin uniqueness region beyond potentials with a hard-core part, including interactions such as the Strauss model. The conjecture is motivated by the fact that, as the discretisation cubes shrink, boundary conditions with more than one point in a cube become increasingly unlikely; deriving the corresponding explicit criterion without the hard-core assumption remains open.