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The indent lines seem to break when using the multicol package and \Statex near the top of a new column. Here's an example:
\documentclass{article}
\usepackage{algpseudocodex}
\usepackage{multicol}
\begin{document}
\begin{multicols}{3}
\begin{algorithmic}[1]
\If{\(a > 0\)}
\Statex \hspace{\algorithmicindent}no
\State yes
\State yes
\EndIf
\If{\(b > 0\)}
\Statex \hspace{\algorithmicindent}no
\State yes
\State yes
\EndIf
\If{\(c > 0\)}
\Statex \hspace{\algorithmicindent}no
\State yes
\State yes
\EndIf
\end{algorithmic}
\end{multicols}
\end{document}
And here's the corresponding output:

The \hspace{\algorithmicindent} is added because \Statex does not produce the correct indentation as noted by @LeCyberDucky in #7. Note that the indent lines only break in the second and third column. They do not break when \Statex is replaced by \State or when there are fewer than two lines below \Statex in a column.
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