Improve how references are used throughout Physlib

[Alex-Zughaid]

• References section at the top of the file
• Each reference must appear in the BibTex file
• The bib ID should appear next to the reference within the Lean files, however we still keep name/author etc. to ensure human readability
• Added check_references.py which uses regex to check these rules are followed (Similar to lint_bib.sh in mathlib)
• if you have no references but have a ##References section add * None to make prevent the regex from breaking.

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[Alex-Zughaid]

Very big PR - important files are references.bib and check_references.py

[jstoobysmith]

Could you make a comment on the relevant Zulip channel about this?

[jstoobysmith]

Delete this file and all .axiomatic

[jstoobysmith]

These should be filled out correctly.

[morrison-daniel]

Can't attest to the linter files but I checked the references and they look good, with a few suggestions.

[morrison-daniel]

The style is much more uniform but we should probably discuss what should/shouldn't be in the reference section of the module. As it is now, the style guide is:

1. References section in the module doc-string, either as ##References (old doc-strings) or iv. References (new table of contents style)
2. If no references simply write * None.
3. References are of the style `* , <title> (arXiv:XXXX.XXXX [if applicable, else empty]), <specific sections, equations, problems of note, usually for textbooks>. [ref: <bib_reference>]

The variations on point 3 are

• Authors may not be present
• Titles are sometimes italicized
• Sometimes a link is included when available

I could go either way on author inclusion, it would probably nice to include them but they are in the full bib file so I think we could remove them and rely on the link to the full reference. Removing would help keep it shorter and I think the doc-strings are already too long.

Again, italics is probably more correct but this isn't an actual citation. No italics is much more common, but we just need to pick one. I would say no formatting just to keep it simple.

Link is another one I'm not sure about since they're very convenient but take up space. Many are arXiv links, but many arXiv refs just use the arXiv:XXXX.XXXX label which is perhaps sufficient since arXiv is well-known and easy to find. Maybe one proposal could be to only use the axXiv ID for arXiv papers and include a full link to harder to find refs like lecture notes hosted on a personal website.

I think what we have here is already an improvement and I don't want to hold this up with more discussion so I'd be happy to merge this and make edits when we hash out some details.

[morrison-daniel]

I'm happy at this point so I'll leave the approval and mark this as ready-to-merge. @jstoobysmith if you're happy go ahead and merge.