\begin{itemize}
    \item Use appropriate notation and terminology consistently throughout the text.
    \item Keep the comments that start with `%' in the document. For example, do not delete ``% We set $\epsilon=0.01$ for sufficient precision in our numerical analysis.'' in the output.
    \item If there are duplicate labels, handle the collision correctly by renaming one of them using a condensed label and adjust accordingly where the labelled items are referenced.
    \item Use $\ldots$ or $\cdots$ rather than $\dots$ or ``...'' to achieve an ellipsis following the best practice of chktex.
    \item Use non-breaking spaces when referencing equations, figures, sections, and references, e.g., use ``Eq.~\ref{eq:label}''; ``see Fig.~\ref{fig:label}''; ``Section~\ref{sec:label}''; ``see Ref.~\cite{AuthorYear}''.
    \item Use either `` or '' as an alternative to `"'.
    \item Put punctuation outside inner math mode.
    \item Use $\tr$ instead of \text{tr} or \textrm{tr}.
    \item If using Dirac notation (e.g., in quantum mechanics), prefer $\bra{...}$ and $\ket{...}$ over $|...\rangle$ and $\langle...|$.
    \item Treat formulas as part of the sentences and add punctuation accordingly in the displayed math environments depending on the next sentence.
    \item When in doubt, follow the best practice that will result in zero warnings when checked by chktex.
    \item \textbf{IMPORTANT}: Use the math commands defined in the auxiliary files command.tex, commands.tex, or preamble.tex if provided. Do not redefine commands that are already defined there.
    \item \textbf{IMPORTANT}: The output document must be self-contained. Write as if the reader is a third party who has never read and will never read our conversations --- they should be able to understand and follow the document on its own. Define all notations, abbreviations, and terminology before first use.
\end{itemize}