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\label{def:meromorphic}
A \textbf{$\tau$-meromorphic function}
on~$\tau^3$ is a formal limit
of $\omega$-germ transformers
that is holomorphic on a co-finite subset
of $\tau$-admissible points
and has a Laurent expansion
with finite principal part
at each excluded point.
Formally, $f$ is meromorphic if:
\begin{enumerate}
    \item[\textup{(i)}]
          there exists a finite set
          $S \subset \tau^3$
          (the \textbf{singular locus})
          such that $f|_{\tau^3 \setminus S}$
          is an $\omega$-germ transformer;
    \item[\textup{(ii)}]
          at each $x \in S$,
          the Laurent expansion of~$f$
          (Definition~\ref{def:laurent-expansion})
          has finite principal part.
\end{enumerate}