1 A Shared Starting Point, Not a Uniform Voice

A good PhysicsLibrary article should be understandable on its own, easy to navigate, and useful in both HTML and pdf. These recommendations are a proposed author convention, not a requirement to rewrite every existing article. The examples use ordinary LaTeX packages; no new PhysicsLibrary style package is required or assumed.

Authors should choose the depth, notation, examples, and organization that best serve their readers. A short definition may need only a few paragraphs. A tutorial may need worked examples; a mathematical treatment may need hypotheses, lemmas, and proofs. Keep the parts that help and omit the rest.

Recommended defaults: an opening explanation, a clear heading hierarchy, automatic numbering, explicit assumptions, defined symbols, and sources readers can follow.

Reasonable alternatives: unnumbered headings in a short entry, section-based numbering in a long treatment, specialist notation with an explanation, and additional packages that render successfully. Consistency within an article matters more than forcing every article into the same outline.

2 Titles and Heading Structure

Use a descriptive title in PL’s title field, preserving proper names, acronyms, and mathematical notation. Do not type section numbers into the title. In an encyclopedia entry, begin the content with an explanation rather than repeating the title as a numbered section.

Use \section{...} for the first level of organization and \subsection{...} only inside a section. This gives sections 1, 2, 3 and subsections 1.1, 1.2, 2.1. Starting with a subsection before a numbered section can produce 0.1.

For a compact entry, paragraphs alone or \section*{...} headings are fine. Starred headings do not advance the section counter. Avoid mixing numbered and unnumbered headings without a clear purpose. Use meaningful headings such as Assumptions or Physical Interpretation; not every entry needs an introduction heading.

3 Definitions, Theorems, and Numbering

For most standalone articles, use one article-wide sequence for definitions, theorems, lemmas, propositions, corollaries, and examples. For example, Definition 1 may be followed by Proposition 2 and Example 3. Keep equations in a separate sequence: (1), (2), and so on.

This convention works even when there are no numbered sections. A short entry with one definition can also use an unnumbered definition environment. Number statements when readers will benefit from referring to them.

3.1 Why Definition 0.1 Appears

A declaration such as

\newtheorem{definition}{Definition}[section]

makes the definition counter depend on the section counter. Before Section 1, the first definition can therefore be numbered 0.1. An article title or a starred heading does not supply a numbered section.

For a fresh article-wide sequence, the declaration is instead

\newtheorem{definition}{Definition}

The template later in this guide shows a shared sequence for several statement types. Choose one setup; do not paste competing declarations for the same environment into an existing preamble.

Do not set the section counter to 1 merely to hide a leading zero: that changes the numbering without fixing the article structure.

3.2 Long Articles May Use Section-Based Numbers

For a long article with numbered sections, Definition 2.1 and Theorem 2.2 can be useful. In the template, replace the theorem declaration with the following, keeping the other environments attached to it:

\newtheorem{theorem}{Theorem}[section]

Begin a numbered section before the first numbered statement. Section-based equation numbering is also available:

\numberwithin{equation}{section}

Use this only when the extra level helps navigation. Avoid changing numbering schemes midway through an article.

4 References That Survive Editing

Use \label with \ref for sections and statements, and \eqref for equations. Put an equation label inside its environment, a section label after the heading, and a statement label just after the environment begins.

Prefer Equation~\eqref{shm:eq:motion} to a literal Equation (1). Use meaningful, article-specific prefixes such as shm:eq:motion, not just eq1. Labels resolve within a document; a label in another PL article is not automatically a cross-article link.

5 Readable Mathematics and Figures

Define symbols and state assumptions near their first use. Explain coordinate frames, units, signs, and conventions when they affect interpretation. Distinguish an exact result from an approximation.

Use \(...\) or dollar signs for inline mathematics, \[...\] for an unnumbered display, equation for a numbered equation, and align for related lines:

\begin{align}
E &= T+V, \label{energy:eq:total}\\
T &= \frac{1}{2}m\dot{x}^{2}.
\end{align}

Use \nonumber on a line that needs no number. Reserve \tag for a deliberate external numbering convention. For a squared derivative, write (y’)^2 or {y’}^2, rather than attaching a second superscript to a prime.

Use blank lines for paragraphs. Avoid repeated \\, manual spaces, and negative vertical spacing to position prose or equations. Those adjustments can behave differently in HTML and PDF.

Figures should have readable labels, an explanatory caption, and a source or credit where appropriate. Use uploaded article assets with simple filenames. With \usepackage{graphicx} in the preamble, an optional figure can look like this:

\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\linewidth]{oscillator.png}
\caption{Displacement measured from equilibrium.}
\label{shm:fig:oscillator}
\end{figure}

Upload the named file before enabling the example. HTML may position a figure differently from PDF. Explain the figure in the text and do not rely on color alone to communicate a distinction.

6 Using the Template in PhysicsLibrary

The following pages contain a complete, small worked example: Simple Harmonic Motion. It demonstrates the structure rather than prescribing a minimum article length.

For a new encyclopedia article, enter the title in its title field, use the preamble in the preamble field, and use the content in the content field. Do not place \documentclass, \begin{document}, or \end{document} in an encyclopedia content field.

When adapting an existing entry, merge only the needed packages and definitions. An existing theorem environment may already have a counter. Keep a single hyperref package load and adjust link options with \hypersetup; repeated loads with different options can fail.

The accompanying PL-Article-Template.tex is a local compilation wrapper. This guide itself is a complete document suitable for a collaboration that accepts full LaTeX source.

7 Template: Article Preamble

This setup uses an article-wide statement counter. Theorem-like results use the usual italic body; definitions and examples use upright text. An unnumbered remark is available for a brief observation.

\usepackage{amsmath,amssymb,amsthm}
\usepackage{hyperref}
\hypersetup{colorlinks=true,linkcolor=blue,citecolor=blue,
urlcolor=blue}
\providecommand{\PMlinkexternal}[2]{\href{#2}{#1}}

\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\theoremstyle{remark}
\newtheorem*{remark}{Remark}

If your article has no theorem-like statements, omit their declarations and the amsthm package. Add packages when the content needs them, and check both HTML and PDF after doing so.

The two external-link commands take their arguments in different orders:

\href{URL}{link text}
\href{URL}{link text}

A complete bibliographic reference remains useful even when a link is unavailable.

8 Template: Article Content

Title field: Simple Harmonic Motion. Adapt the subject, assumptions, label prefix, and references together.

Simple harmonic motion describes oscillation about an equilibrium
with acceleration proportional to the negative displacement.
Here we consider one-dimensional, undamped motion with constant
mass $m>0$ and spring constant $k>0$.
\section{Model and Assumptions}
\label{shm:sec:model}
Let $x(t)$ be the displacement from equilibrium at time $t$.
Hooke’s law and Newton’s second law give
\begin{equation}
m\frac{d^2x}{dt^2}+kx=0.
\label{shm:eq:motion}
\end{equation}
\begin{definition}[Angular frequency]
\label{shm:def:frequency}
The natural angular frequency is
$\omega_0=\sqrt{k/m}$, measured in radians per second.
\end{definition}
\section{Solution}
\label{shm:sec:solution}
\begin{proposition}
\label{shm:prop:solution}
For $x(0)=x_0$ and $\dot{x}(0)=v_0$, the solution is
\begin{equation}
x(t)=x_0\cos(\omega_0t)
+\frac{v_0}{\omega_0}\sin(\omega_0t).
\label{shm:eq:solution}
\end{equation}
\end{proposition}
\begin{proof}
Differentiating twice verifies Equation~\eqref{shm:eq:motion}.
Evaluation at $t=0$ gives the prescribed displacement and velocity.
Uniqueness follows from the linear initial-value problem.
\end{proof}
\subsection{Release from Rest}
\label{shm:sec:rest}
\begin{example}
If $v_0=0$, Equation~\eqref{shm:eq:solution} reduces to
$x(t)=x_0\cos(\omega_0t)$.
\end{example}
\section{Interpretation and Limits}
The period is $T=2\pi/\omega_0$. This ideal model neglects
damping, external driving, and departures from Hooke’s law.
For further background, see \cite{openstax-shm}.
\begin{thebibliography}{9}
\bibitem{openstax-shm}
OpenStax, \emph{University Physics, Volume 1},
Section 15.1, \emph{Simple Harmonic Motion}.
\url{https://openstax.org/books/university-physics-volume-1}
\end{thebibliography}

9 Preparing for Future Compilations

These are design recommendations for future collections, not a description of an implemented PL compilation feature.

An article should make sense independently: explain its subject, define its notation, and identify prerequisites. Link to background material without making the reader guess which definition or convention applies.

For a collection that treats each article as a chapter, a useful scheme is:

The collection should supply chapter numbers, page layout, and shared style. Authors should not hard-code a prospective chapter number in their article source. Other collection formats may use a different hierarchy.

Article-specific label and citation keys reduce collisions, but a compilation builder will still need to resolve duplicate keys, macro names, theorem declarations, and package options. Simply concatenating complete LaTeX documents is not sufficient.

Use descriptive names for custom commands and define them in the preamble. Avoid redefining standard commands solely for a local shortcut. Keep the source editable: screenshots of equations and page-sized images of text are poor substitutes for mathematical source.

10 A Short Review Before Publishing

1. Does the opening explain the subject and intended scope?
2. Are assumptions, symbols, units, and conventions clear?
3. Does the heading hierarchy fit the length of the article?
4. Are statement and equation numbers useful and free of accidental leading zeros? Do all references resolve?
5. Do figures and tables remain readable at the displayed width?
6. Are sources and asset credits included where needed?
7. Have both HTML and PDF been previewed, including the last page?

For an existing article, check literal references such as Theorem 2.1 before changing counters. A different numbering scheme is acceptable when it helps the reader and is applied consistently.

Further Reading

The AMS guide documents theorem environments and shared counters: Using the amsthm Package.

The LaTeX Project maintains official LaTeX documentation. Check that any newer features are available in the site’s installed TeX version.

For the worked example’s physics, see OpenStax, University Physics, Volume 1, Section 15.1. For reuse terms, consult the PhysicsLibrary license notice.