@article{Blackwell1956,
  author = {Blackwell, David},
  title = {An analog of the minimax theorem for vector payoffs},
  journal = {Pacific Journal of Mathematics},
  volume = {6},
  number = {1},
  pages = {1--8},
  year = {1956},
  note = {\url{https://msp.org/pjm/1956/6-1/pjm-v6-n1-p01-s.pdf}},
  url = {https://msp.org/pjm/1956/6-1/pjm-v6-n1-p01-s.pdf}
}

@inproceedings{AbernethyBartlettHazan2011,
  author = {Abernethy, Jacob and Bartlett, Peter L. and Hazan, Elad},
  title = {{Blackwell} Approachability and No-Regret Learning are Equivalent},
  booktitle = {Proceedings of the 24th Annual Conference on Learning Theory},
  series = {Proceedings of Machine Learning Research},
  volume = {19},
  pages = {27--46},
  publisher = {PMLR},
  year = {2011},
  note = {\url{https://proceedings.mlr.press/v19/abernethy11b.html}},
  url = {https://proceedings.mlr.press/v19/abernethy11b.html}
}

@inproceedings{DannEtAl2025,
  author = {Dann, Christoph and Mansour, Yishay and Mohri, Mehryar and
            Schneider, Jon and Sivan, Balasubramanian},
  title = {Rate-Preserving Reductions for {Blackwell} Approachability},
  booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
  series = {Proceedings of Machine Learning Research},
  volume = {291},
  pages = {1380--1414},
  publisher = {PMLR},
  year = {2025},
  note = {Theorem 4 and Appendix G.5; fixed-point convention in Section 2.2.
          \url{https://proceedings.mlr.press/v291/dann25a.html}},
  url = {https://proceedings.mlr.press/v291/dann25a.html}
}

@misc{ReductionArtifact,
  author = {Ramos, Arthur Freitas and de Queiroz, Ruy Jose Guerra Barretto
            and Hulak, David Barros},
  title = {Finite tight approachability-to-improper-regret reduction},
  year = {2026},
  howpublished = {Lean 4 source artifact in the nested project
                  rate-preserving-reduction},
  note = {Registered commit 42b9d7c77e77fc158d44cb31ef320798c3c73492;
          manuscript source inspection on October 1, 2026.
          \url{https://github.com/Arthur742Ramos/blackwell-approachability-lean/tree/42b9d7c77e77fc158d44cb31ef320798c3c73492/rate-preserving-reduction}},
  url = {https://github.com/Arthur742Ramos/blackwell-approachability-lean/tree/42b9d7c77e77fc158d44cb31ef320798c3c73492/rate-preserving-reduction}
}

@misc{PalomarReduction,
  author = {{Palomar Registry}},
  title = {Finite tight {Blackwell} approachability-to-improper phi-regret
           reduction in {Lean}},
  year = {2026},
  note = {PALOMAR-2026-09-20-000001, version 1; registered September 20, 2026.
          Immutable record inspected October 1, 2026.
          \url{https://palomar-registry.org/entry?id=PALOMAR-2026-09-20-000001&version=1}},
  url = {https://palomar-registry.org/entry?id=PALOMAR-2026-09-20-000001&version=1}
}

@misc{OfficialVerification,
  author = {{Palomar Registry}},
  title = {Verify submission geavw0mtiip5},
  year = {2026},
  howpublished = {PalomarSubmission GitHub Actions run 35480464336, attempt 1},
  note = {Historical successful verification workflow of September 20, 2026.
          \url{https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/35480464336}},
  url = {https://github.com/PalomarRegistry/PalomarSubmission/actions/runs/35480464336}
}