/usr/share/lyx/templates/PDF-cropped.lyx is in lyx-common 2.2.2-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
\origin /systemlyxdir/templates/
\textclass article
\use_default_options true
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\graphics default
\default_output_format pdf7
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 1
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle empty
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Paragraph*
\SpecialChar LyX
Equation Editor
\end_layout
\begin_layout Plain Layout
Use this template to generate
\begin_inset Quotes eld
\end_inset
embeddable graphics
\begin_inset Quotes erd
\end_inset
(equations, commented graphics, etc.).
Simply write down some content and hit the Preview button: you will obtain
a cropped PDF output of the \SpecialChar LyX
content.
Now you can insert the resulting vector PDF image into a different document
(another \SpecialChar LyX
document, a LibreOffice Presentation, a Beamer presentation,
etc.).
Below is an example (hit the Preview button to see the result).
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $x^{2}-\gamma$
\end_inset
\end_layout
\end_body
\end_document
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