The nonisolating contact invariant conjecture over the integers

Let $K$ be a dividing set, let $c(K)$ be its contact invariant, and work with $\mathbb{Z}$-coefficients. A nonzero element is primitive if it is not a nontrivial integer multiple of another element. The dividing set $K$ is nonisolating when every region of the complement satisfies the nonisolating condition used in the paper.

Nonisolating contact invariant conjecture. Over $\mathbb{Z}$-coefficients, the following are equivalent:

1. $c(K)\not=0$;
2. $c(K)$ is primitive;
3. $K$ is nonisolating.

This conjecture proposes that nonvanishing and primitivity of the contact invariant exactly characterize nonisolating dividing sets. The source presents it as an expected statement and gives no resolution.