Add example LaTeX document for bot demonstration

[mchenco]

LaTeX Bot Demonstration

This PR demonstrates the LaTeX Bot in action!

What this shows

• Automatic compilation of .tex files
• PDF generation in .latex-bot-output/
• Comment updates with compilation status
• Package auto-installation

What to expect

1. Bot detects the .tex file change
2. Compiles with pdflatex
3. Commits PDF to .latex-bot-output/example.pdf
4. Posts comment with results and download links

[mchenco]

✅ Compiled successfully!

File: example.tex
Output: Download PDF | View on GitHub

View compilation logs

] [21] [22] [23] [24] [25] [26] [28] [31] [32] [36] [39] [44]
[45] [46] [42] [47] [60] [61] [62] [77] [79] [87] [110] [91] [93] [94] [95]
[96] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137]
[138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149]
[150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161]
[162] [163] [164] [165] [166] [167] [168] [169] [171] [172] [173] [174]
[175] [177] [176] [180] [181] [182] [183] [184] [187] [191] [214] [246])
(/usr/share/texlive/texmf-dist/fonts/source/jknappen/ec/txromod.mf
 Ok [48] [49] [50] [51] [52] [53] [54] [55] [56] [57])
(/usr/share/texlive/texmf-dist/fonts/source/jknappen/ec/txrsuper.mf
 Ok [185] [178] [179] [170] [186])
(/usr/share/texlive/texmf-dist/fonts/source/jknappen/ec/txrfract.mf
 Ok [188] [189] [190]) ) ) )
(some charht values had to be adjusted by as much as 0.06943pt)
Font metrics written on tcrm1000.tfm.
Output written on tcrm1000.600gf (128 characters, 23548 bytes).
Transcript written on tcrm1000.log.
mktexpk: /root/.texlive2021/texmf-var/fonts/pk/ljfour/jknappen/ec/tcrm1000.600pk: successfully generated.

=== Second pass ===
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2022/dev/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./example.tex
LaTeX2e <2021-11-15> patch level 1
L3 programming layer <2022-01-21>
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2021/10/04 v1.4n Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo))
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def)
(./example.aux) [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2]
(./example.aux) ) </root/.texlive2021/texmf-var/fonts/pk/ljfour/jknappen/ec/tcr
m1000.600pk></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx1
0.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb>
</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/t
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texlive/
texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/font
s/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type
1/public/amsfonts/cm/cmtt10.pfb>
Output written on example.pdf (2 pages, 109215 bytes).
Transcript written on example.log.