Conjecture on limit points of zeros of exponential-integral sections

Let $F$ be an exponential integral function as defined in the paper, and let $s_n[F](nz)$ denote its normalized sections. Let $D_{a,b}$ and $D_\text{imag}$ be the curves introduced in the paper as the candidate limit curves for the zeros of these sections. Limit-curve conjecture. All limit points of the zeros of $s_n[F](nz)$ lie on

$$D_{a,b}\cup D_\text{imag}.$$

The conjecture asserts that the exceptional countable set allowed by the paper's general theorem is always empty. Numerical examples studied by the author exhibit no limit points outside these curves, but a proof that this holds for every exponential integral function remains open.