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I am writing a paper in which one part of the proof uses a certified computation (for example, interval arithmetic, exact arithmetic checks, or machine-checkable certificates), and I would like to present it in a way that is clear to referees and future readers.

What are current best practices for documenting and citing such computations in a mathematics paper?

For example:

  • What should go in the main text vs. an appendix vs. supplementary material?
  • Is it better to cite a repository, or to archive a specific version (e.g. with a DOI)?
  • What level of implementation/environment detail is usually expected?
  • If certificates/checker output are used, how are they typically presented and cited?

Examples of papers or references with especially good practice would also be appreciated!

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My comment above mentions related MO questions, but one important issue that is not very well addressed (except perhaps in a comment) is how to ensure that your certified computation can be reproduced many years from now by another researcher. Probably the best one can do nowadays is:

  • Perform the computation using open-source software only, to avoid intellectual property problems.
  • Create a Docker container (or some similar alternative such as Podman) so that people can still run your code in the future when operating systems and programming language versions have changed.
  • Upload to Zenodo for long-term archival stability. (GitHub is more convenient and there's no reason not to use it, but Zenodo is probably more stable in the long term.)

This doesn't address some of your other important questions about how to present your work in a user-friendly manner, but the answers to the other MO questions say quite a bit about that.

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