docs(PauliMatrices): cite the published source for the three-Pauli identities

[zhikaip]

The docstrings of the two three-Pauli identities in Relations.lean referred to "Equation (2.26)" and "Equation (2.27)" without naming a source. Those numbers come from the 2004 draft linked in #341, where the two equations differ from the statements proved here (as noted in #1568).

This removes the bare equation numbers from the docstrings and adds a References section to the module docstring citing equations (2.54) and (2.55) of the published paper, arXiv:0812.1594, which agree with the Lean statements and conventions. It also puts each formula in those docstrings on a single line, so the inline code is not broken across lines, and removes a stale "not currently cited" note from the bibliography entry.

No lemmas or definitions are added, removed or changed.

Disclaimer: I instructed Claude to find the proper reference; I have checked the cited equations myself.

🤖 Generated with Claude Code

[github-actions]

Thank you for this pull-request (PR). If this is your first PR, welcome to the community!

Below is what will happen next. Please read carefully if you are not familiar with the process. You may open other PRs while this one is being reviewed, and can stack PRs on top of each other, so don't let these steps slow you down.

1. Some automated checks will be run on your PR. You can see the results of these checks at the buttom of your PR page. If any of these checks fail, you will need to fix the issues before your PR can be merged. You can learn more about these here, including how to run them locally, which is sometimes quicker than relying on the GitHub Actions. If you have never had a PR merged before, you may have to wait for a reviewer to manually start these checks (this is for security).

2. A reviewer will look at your PR and may ask you to make changes. This may happen a couple of days after you submit your PR, so you may need to be patient. But it should not be longer than that - if it is please bring it to the attention of the community on the Zulip. The level of review will depend on where your PR is submitted. If it is submitted to ./Physlib or ./QuantumInfo, the review will be more thorough than if it is submitted to ./PhyslibAlpha. You can find out more about what the review process is looking for in our review guidelines. If a reviewer adds an awaiting-author label to your PR, address the review comments, then please remove that label by adding a comment with -awaiting-author. This helps us keep track of reviews.

3. The reviewer will either approve your PR, or request more changes (in which case we return to step 2). Once your PR is approved, it will be merged by a maintainer, this should happen shortly after approval, though you may get more comments at this stage.

Tip: The easiest way to get have a fast review is to submit a PR that is small and self-contained, and has clear documentation explaining why things are the way they are in your chages.

If you have any problems or questions, please reach out to the community on the Zulip.

[jstoobysmith]

Approved