Apply fast high-precision tracker in large matrix demo

[t-uda]

Summary

• Demonstrate DOP853-based Ogita-Aishima tracking in large matrix notebook

Testing

• pre-commit run --files notebooks/large_matrix_tracking_demo.ipynb (fails: RPC 403 when fetching pre-commit hooks)
• poetry run papermill notebooks/large_matrix_tracking_demo.ipynb notebooks/large_matrix_tracking_demo.ipynb -k python3

---

https://chatgpt.com/codex/tasks/task_e_68c02bc624108323a1ed8f8ac6dcaae0

[chatgpt-codex-connector]

Codex Review: Here are some suggestions.

https://github.com/t-uda/EigenpairFlow/blob/662e821054ca81f9ef64f0acaffa3312e70f0396/notebooks/large_matrix_tracking_demo.ipynb#L1-L9
[P1] Restore valid notebook JSON structure

The new version of the notebook starts with execution metadata ("duration", "execution", …) and no longer contains the root cells/nbformat keys that make a Jupyter notebook valid JSON. Loading the file with nbformat.read('notebooks/large_matrix_tracking_demo.ipynb') now raises NotJSONError, so the large matrix demo cannot be opened or executed and its code cells are effectively lost.

---

Reply with @codex fix comments to fix any unresolved comments.

About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you open a pull request for review, mark a draft as ready, or comment "@codex review". If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex fix this CI failure" or "@codex address that feedback".

[t-uda]

Broken notebook.