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@misc{OAI:Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026,
  author = {{OpenAI}},
  title = {{Equality cases in the sharp one-dimensional matrix Lieb--Thirring inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026/sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf}{OAI:Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026}},
  year = {2026}
}

@misc{OAI:Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026,
  author = {{OpenAI}},
  title = {{Sharp one-dimensional Lieb--Thirring inequalities for matrix potentials}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf}{OAI:Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026}},
  year = {2026}
}

@misc{OAI:Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026,
  author = {{OpenAI}},
  title = {{Sharp one-dimensional Lieb--Thirring constants}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf}{OAI:Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026}},
  year = {2026}
}