The one-way crossing conjecture for complex zeros of the partial theta function

Let $\theta(q,x)$ be the partial theta function. For $q\in(0,1)$, the zeros are complex-conjugation invariant, so nonreal zeros occur in complex conjugate pairs; for each $j\in\mathbb{N}$, consider the pair born when $q=(\tilde q_j)^+$. One-way crossing conjecture. For every $j\in\mathbb{N}$, this complex conjugate pair crosses the imaginary axis from left to right for some $q_j^*\in(\tilde q_j,1)$, and no complex conjugate pair crosses the imaginary axis from right to left. The claim specifies the direction and parameter range of every asserted crossing and strengthens the preceding theorem's finiteness statement; the source provides no resolution beyond the stated result.