The Nadler-Quinn problem for simplicial inverse systems

We show that if $X$ is an arc-like continuum which can be represented as an inverse limit of a simplicial inverse system on arcs, then for every point $x \in X$ there is a plane embedding of $X$ in which $x$ is accessible. This answers a special case of the Nadler-Quinn question from 1972.
Comment: 20 pages, 4 figures. arXiv admin note: text overlap with arXiv:2306.15191