% OpenAI Math release. Pinned snapshot adc7f1241b42e322a6451854ab7e4b4c146bf78a
% Original citation keys retained. Historical entries follow when available.

@misc{OAI:The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026,
  author = {{OpenAI}},
  title = {{The spacetime Penrose inequality with charge and original-data rigidity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf}{OAI:The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf}
}

@misc{OAI:A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026,
  author = {{OpenAI}},
  title = {{A Charged Reduction of the Spacetime Penrose Inequality in Spatial Dimensions at Least Four}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026/paper.pdf}{OAI:A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-October-5-2026/paper.pdf}
}

@misc{OAI:Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026,
  author = {{OpenAI}},
  title = {{Spacetime Penrose inequalities: enclosing area, charge, and rigidity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026/paper.pdf}{OAI:Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026/paper.pdf}
}

@misc{OAI:The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026,
  author = {{OpenAI}},
  title = {{The Kerr--Newman Penrose Inequality for Axisymmetric Electrovacuum Exteriors}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026/paper.pdf}{OAI:The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Kerr-Newman-Penrose-Inequality-for-Axisymmetric-Electrovacuum-Exteriors-October-5-2026/paper.pdf}
}

@misc{OAI:Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026,
  author = {{OpenAI}},
  title = {{Electromagnetic tails and the Kerr--Newman Penrose inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026/paper.pdf}{OAI:Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Electromagnetic-tails-and-the-Kerr-Newman-Penrose-inequality-October-5-2026/paper.pdf}
}

@misc{OAI:The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026,
  author = {{OpenAI}},
  title = {{The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026/paper.pdf}{OAI:The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026/paper.pdf}
}

@misc{OAI:The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026,
  author = {{OpenAI}},
  title = {{The Penrose inequality for maximal asymptotically hyperbolic initial data}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026/paper.pdf}{OAI:The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026/paper.pdf}
}

@misc{OAI:A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026,
  author = {{OpenAI}},
  title = {{A local Penrose inequality for conformal perturbations of Schwarzschild--anti-de Sitter data}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026/paper.pdf}{OAI:A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-local-Penrose-inequality-for-conformal-perturbations-of-Schwarzschild-anti-de-Sitter-data-October-5-2026/paper.pdf}
}

@misc{OAI:The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026,
  author = {{OpenAI}},
  title = {{The spacetime Penrose inequality and enclosing area}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026/paper.pdf}{OAI:The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spacetime-Penrose-inequality-and-enclosing-area-September-27-2026/paper.pdf}
}

@misc{OAI:Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026,
  author = {{OpenAI}},
  title = {{Conformal flow and the Riemannian Penrose inequality with minimizing frontiers}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026/paper.pdf}{OAI:Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Conformal-flow-and-the-Riemannian-Penrose-inequality-with-minimizing-frontiers-September-27-2026/paper.pdf}
}

@misc{OAI:Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026,
  author = {{OpenAI}},
  title = {{Equality and rigidity in the spacetime Penrose inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf}{OAI:Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Equality-and-rigidity-in-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf}
}

@misc{OAI:Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026,
  author = {{OpenAI}},
  title = {{Boundary graph deformations for the spacetime Penrose inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf}{OAI:Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf}
}

@misc{OAI:Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026,
  author = {{OpenAI}},
  title = {{Area-controlled end replacement and the Bondi--Penrose inequality in the CKS class}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026/paper.pdf}{OAI:Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Area-controlled-end-replacement-and-the-Bondi-Penrose-inequality-in-the-CKS-class-September-27-2026/paper.pdf}
}

@misc{OAI:Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026,
  author = {{OpenAI}},
  title = {{Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026/paper.pdf}{OAI:Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Absolutely-Continuous-Spectrum-for-Weak-Disorder-Anderson-Models-in-Dimensions-at-Least-Three-September-23-2026/paper.pdf}
}

@misc{OAI:Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026,
  author = {{OpenAI}},
  title = {{Pure-Point Spectrum for the Two-Dimensional Anderson Model at Every Positive Disorder}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026/paper.pdf}{OAI:Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Pure-Point-Spectrum-for-the-Two-Dimensional-Anderson-Model-at-Every-Positive-Disorder-September-23-2026/paper.pdf}
}

@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/adc7f1241b42e322a6451854ab7e4b4c146bf78a/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},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026/sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf}
}

@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/adc7f1241b42e322a6451854ab7e4b4c146bf78a/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},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf}
}

@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/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf}{OAI:Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026/paper.pdf}
}

@misc{OAI:Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026,
  author = {{OpenAI}},
  title = {{Uniform excess charge for Coulomb molecules and the outer radius of neutral atoms}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf}{OAI:Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-excess-charge-for-Coulomb-molecules-and-the-outer-radius-of-neutral-atoms-September-24-2026/paper.pdf}
}

@misc{OAI:Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026,
  author = {{OpenAI}},
  title = {{Generalized ionization energies for full Coulomb atoms}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026/paper.pdf}{OAI:Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generalized-ionization-energies-for-full-Coulomb-atoms-September-24-2026/paper.pdf}
}

@misc{OAI:Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026,
  author = {{OpenAI}},
  title = {{Generalized outer-electron radii of neutral Coulomb atoms}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026/paper.pdf}{OAI:Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generalized-outer-electron-radii-of-neutral-Coulomb-atoms-September-24-2026/paper.pdf}
}

@misc{OAI:Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026,
  author = {{OpenAI}},
  title = {{Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf}{OAI:Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf}
}

@misc{OAI:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026,
  author = {{OpenAI}},
  title = {{Generic $C^1$ Future Inextendibility Near Rotating Subextremal Kerr Spacetimes}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf}{OAI:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf}
}

@misc{OAI:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026,
  author = {{OpenAI}},
  title = {{Quantitative Near-Kerr Evolution and Generic $C^2$ Future Inextendibility}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf}{OAI:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf}
}

@misc{OAI:A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026,
  author = {{OpenAI}},
  title = {{A two-dimensional area law from a global spectral gap}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf}{OAI:A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf}
}

@misc{OAI:Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026,
  author = {{OpenAI}},
  title = {{Polynomial PEPS approximation of gapped square-grid ground states}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf}{OAI:Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf}
}

@misc{OAI:The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026,
  author = {{OpenAI}},
  title = {{The maximum number of mutually unbiased bases in dimension six}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026.pdf}{OAI:The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026.pdf}
}

@misc{OAI:Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026,
  author = {{OpenAI}},
  title = {{Exact Fourier certificates for complex Hadamard matrices of order six}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026.pdf}{OAI:Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026.pdf}
}

@misc{OAI:Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026,
  author = {{OpenAI}},
  title = {{Bose--Einstein condensation at positive temperature in the dilute hard-sphere gas}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026/positive-temperature-hard-spheres.pdf}{OAI:Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026/positive-temperature-hard-spheres.pdf}
}

@misc{OAI:Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026,
  author = {{OpenAI}},
  title = {{Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf}{OAI:Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf}
}

@misc{OAI:Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026,
  author = {{OpenAI}},
  title = {{Quantum Depletion for Fixed Bounded Repulsive Potentials}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf}{OAI:Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf}
}

@misc{OAI:A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026,
  author = {{OpenAI}},
  title = {{A density-uniform condensate bound for dilute Bose gases}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026/paper.pdf}{OAI:A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026/paper.pdf}
}

@misc{OAI:Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026,
  author = {{OpenAI}},
  title = {{Ground-state condensation in the dilute hard-sphere gas}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf}{OAI:Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf}
}

@misc{OAI:The-periodic-spin-one-Haldane-gap-September-24-2026,
  author = {{OpenAI}},
  title = {{The periodic spin-one Haldane gap}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf}{OAI:The-periodic-spin-one-Haldane-gap-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf}
}

@misc{OAI:A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026,
  author = {{OpenAI}},
  title = {{A boundary-field gap for the spin-one Heisenberg chain}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026/paper.pdf}{OAI:A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-boundary-field-gap-for-the-spin-one-Heisenberg-chain-September-24-2026/paper.pdf}
}

@misc{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026,
  author = {{OpenAI}},
  title = {{Uniform Stability of the Spherical Laughlin Gap}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf}{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf}
}

@misc{OAI:A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026,
  author = {{OpenAI}},
  title = {{A Fock-space inequality and the Laughlin spectral gap}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf}{OAI:A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026/A-Fock-space-inequality-and-the-Laughlin-spectral-gap-September-24-2026.pdf}
}

@misc{OAI:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026,
  author = {{OpenAI}},
  title = {{The unique threshold bound state of the $\mathrm{SU}(N)$ BFSS model}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026/paper.pdf}{OAI:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026/paper.pdf}
}

@misc{OAI:Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026,
  author = {{OpenAI}},
  title = {{Positive eigenvalues of the relative $\mathrm{SU}(2)$ BFSS Hamiltonian}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026/positive-eigenvalues-relative-su2-bfss.pdf}{OAI:Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026/positive-eigenvalues-relative-su2-bfss.pdf}
}

@misc{OAI:Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026,
  author = {{OpenAI}},
  title = {{Bloch's Law for Finite-Range Heisenberg Ferromagnets in Three Dimensions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026/bloch-law-heisenberg.pdf}{OAI:Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Blochs-Law-for-Finite-Range-Heisenberg-Ferromagnets-in-Three-Dimensions-October-5-2026/bloch-law-heisenberg.pdf}
}

@misc{OAI:The-first-lattice-correction-to-Blochs-law-October-5-2026,
  author = {{OpenAI}},
  title = {{The first lattice correction to Bloch's law}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026/first-lattice-correction-bloch-law.pdf}{OAI:The-first-lattice-correction-to-Blochs-law-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-first-lattice-correction-to-Blochs-law-October-5-2026/first-lattice-correction-bloch-law.pdf}
}

@misc{OAI:The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026,
  author = {{OpenAI}},
  title = {{The spherical magnetization law for the three-dimensional quantum Heisenberg ferromagnet}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026/spherical-magnetization.pdf}{OAI:The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-spherical-magnetization-law-for-the-three-dimensional-quantum-Heisenberg-ferromagnet-October-5-2026/spherical-magnetization.pdf}
}

@misc{OAI:Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026,
  author = {{OpenAI}},
  title = {{Spontaneous magnetization in the quantum Heisenberg ferromagnet}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf}{OAI:Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Spontaneous-magnetization-in-the-quantum-Heisenberg-ferromagnet-September-24-2026/paper.pdf}
}

@misc{OAI:Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026,
  author = {{OpenAI}},
  title = {{Entanglement with zero distillable secret key in local dimension ten}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf}{OAI:Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf}
}

@misc{OAI:The-entropy-photon-number-inequality-September-24-2026,
  author = {{OpenAI}},
  title = {{The entropy photon-number inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf}{OAI:The-entropy-photon-number-inequality-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf}
}

@misc{OAI:Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026,
  author = {{OpenAI}},
  title = {{Product-projection localization and the $\mathrm{QAC}^0$ parity lower bound}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf}{OAI:Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf}
}

@misc{OAI:Regular-trajectories-pruning-and-quantum-parity-September-24-2026,
  author = {{OpenAI}},
  title = {{Regular trajectories, pruning and quantum parity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf}{OAI:Regular-trajectories-pruning-and-quantum-parity-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf}
}

@misc{OAI:Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026,
  author = {{OpenAI}},
  title = {{Continuum Coulomb hardness with binary nuclear charges}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026.pdf}{OAI:Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026/Continuum-Coulomb-hardness-with-binary-nuclear-charges-September-24-2026.pdf}
}

@misc{OAI:QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026,
  author = {{OpenAI}},
  title = {{QMA-hardness of continuum Coulomb energy with unit nuclear charges}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026.pdf}{OAI:QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026/QMA-hardness-of-continuum-Coulomb-energy-with-unit-nuclear-charges-September-24-2026.pdf}
}

@misc{OAI:Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026,
  author = {{OpenAI}},
  title = {{Classical capacity and entropy inequalities for generalized amplitude damping}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/paper.pdf}{OAI:Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/paper.pdf}
}

@misc{OAI:Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026,
  author = {{OpenAI}},
  title = {{Threshold parallel repetition for finite-dimensional entangled games}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf}{OAI:Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf}
}

@misc{OAI:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026,
  author = {{OpenAI}},
  title = {{A Coulomb ground-state density without Kohn--Sham ensemble representation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf}{OAI:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf}
}

@misc{OAI:Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026,
  author = {{OpenAI}},
  title = {{Exact quantum factoring over a fixed finite gate set}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/main.pdf}{OAI:Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/main.pdf}
}

@misc{OAI:Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026,
  author = {{OpenAI}},
  title = {{Strongly rational unitary vertex operator algebras and conformal nets}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026/paper.pdf}{OAI:Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026/paper.pdf}
}

@misc{OAI:QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026,
  author = {{OpenAI}},
  title = {{QAOA attains the SK ground-state energy in the thermodynamic-first limit}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026.pdf}{OAI:QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026.pdf}
}

@misc{OAI:Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026,
  author = {{OpenAI}},
  title = {{Full support of the zero-temperature Sherrington--Kirkpatrick order parameter}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026/main.pdf}{OAI:Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026/main.pdf}
}

@misc{OAI:Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026,
  author = {{OpenAI}},
  title = {{Scale and conformal symmetry in four-dimensional operational quantum field theory}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026/main.pdf}{OAI:Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Scale-and-conformal-symmetry-in-four-dimensional-operational-quantum-field-theory-September-26-2026/main.pdf}
}

@misc{OAI:Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026,
  author = {{OpenAI}},
  title = {{Polynomial-Time Unitary Synthesis from a Boolean Oracle}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026/paper.pdf}{OAI:Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026/paper.pdf}
}

@misc{OAI:A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026,
  author = {{OpenAI}},
  title = {{A Nearly Quartic Separation Between Randomized and Quantum Query Complexity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026/quartic-query-separation.pdf}{OAI:A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026}},
  year = {2026},
  url = {https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-Nearly-Quartic-Separation-Between-Randomized-and-Quantum-Query-Complexity-October-5-2026/quartic-query-separation.pdf}
}

% Historical sources: original arXiv record dates or verified journal years.

@misc{Background:0705-2024,
  title = {{An Area Law for One Dimensional Quantum Systems}},
  author = {Hastings, M. B.},
  year = {2007},
  url = {https://arxiv.org/abs/0705.2024},
  eprint = {0705.2024},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:0710-5666,
  title = {{The Entropy Photon-Number Inequality and its Consequences}},
  author = {Guha, Saikat and Erkmen, Baris I. and Shapiro, Jeffrey H.},
  year = {2007},
  url = {https://arxiv.org/abs/0710.5666},
  eprint = {0710.5666},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:0712-0483,
  title = {{Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory}},
  author = {Schuch, Norbert and Verstraete, Frank},
  year = {2007},
  url = {https://arxiv.org/abs/0712.0483},
  eprint = {0712.0483},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:0906-5566,
  title = {{Present status of the Penrose inequality}},
  author = {Mars, Marc},
  year = {2009},
  url = {https://arxiv.org/abs/0906.5566},
  eprint = {0906.5566},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1103-1025,
  title = {{Mutually unbiased bases in dimension six: The four most distant bases}},
  author = {Raynal, Philippe and Lü, Xin and Englert, Berthold-Georg},
  year = {2011},
  url = {https://arxiv.org/abs/1103.1025},
  eprint = {1103.1025},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1201-0640,
  title = {{The problem of mutually unbiased bases in dimension 6}},
  author = {Jaming, Philippe and Matolcsi, Mate and Mora, Peter},
  year = {2012},
  url = {https://arxiv.org/abs/1201.0640},
  eprint = {1201.0640},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1309-2921,
  title = {{On Scale and Conformal Invariance in Four Dimensions}},
  author = {Dymarsky, Anatoly and Komargodski, Zohar and Schwimmer, Adam and Theisen, Stefan},
  year = {2013},
  url = {https://arxiv.org/abs/1309.2921},
  eprint = {1309.2921},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1402-6322,
  title = {{Scale Invariance, Conformality, and Generalized Free Fields}},
  author = {Dymarsky, Anatoly and Farnsworth, Kara and Komargodski, Zohar and Luty, Markus A. and Prilepina, Valentina},
  year = {2014},
  url = {https://arxiv.org/abs/1402.6322},
  eprint = {1402.6322},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1404-4717,
  title = {{Validity of spin wave theory for the quantum Heisenberg model}},
  author = {Correggi, Michele and Giuliani, Alessandro and Seiringer, Robert},
  year = {2014},
  url = {https://arxiv.org/abs/1404.4717},
  eprint = {1404.4717},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1503-01260,
  title = {{From vertex operator algebras to conformal nets and back}},
  author = {Carpi, Sebastiano and Kawahigashi, Yasuyuki and Longo, Roberto and Weiner, Mihály},
  year = {2015},
  url = {https://arxiv.org/abs/1503.01260},
  eprint = {1503.01260},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1604-04340,
  title = {{A parallel repetition theorem for all entangled games}},
  author = {Yuen, Henry},
  year = {2016},
  url = {https://arxiv.org/abs/1604.04340},
  eprint = {1604.04340},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1710-01722,
  title = {{The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon}},
  author = {Dafermos, Mihalis and Luk, Jonathan},
  year = {2017},
  url = {https://arxiv.org/abs/1710.01722},
  eprint = {1710.01722},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1903-07747,
  title = {{Information-theoretic aspects of the generalized amplitude damping channel}},
  author = {Khatri, Sumeet and Sharma, Kunal and Wilde, Mark M.},
  year = {2019},
  url = {https://arxiv.org/abs/1903.07747},
  eprint = {1903.07747},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:1910-08187,
  title = {{The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size}},
  author = {Farhi, Edward and Goldstone, Jeffrey and Gutmann, Sam and Zhou, Leo},
  year = {2019},
  url = {https://arxiv.org/abs/1910.08187},
  eprint = {1910.08187},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2007-09326,
  title = {{The Lieb-Thirring inequalities: Recent results and open problems}},
  author = {Frank, Rupert L.},
  year = {2020},
  url = {https://arxiv.org/abs/2007.09326},
  eprint = {2007.09326},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2010-12629,
  title = {{Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem}},
  author = {Aaronson, Scott and Ben-David, Shalev and Kothari, Robin and Rao, Shravas and Tal, Avishay},
  year = {2020},
  url = {https://arxiv.org/abs/2010.12629},
  eprint = {2010.12629},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2110-14206,
  title = {{The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model}},
  author = {Basso, Joao and Farhi, Edward and Marwaha, Kunal and Villalonga, Benjamin and Zhou, Leo},
  year = {2021},
  url = {https://arxiv.org/abs/2110.14206},
  eprint = {2110.14206},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2310-08870,
  title = {{A one-query lower bound for unitary synthesis and breaking quantum cryptography}},
  author = {Lombardi, Alex and Ma, Fermi and Wright, John},
  year = {2023},
  url = {https://arxiv.org/abs/2310.08870},
  eprint = {2310.08870},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2410-06499,
  title = {{On the Computational Power of QAC0 with Barely Superlinear Ancillae}},
  author = {Anshu, Anurag and Dong, Yangjing and Ou, Fengning and Yao, Penghui},
  year = {2024},
  url = {https://arxiv.org/abs/2410.06499},
  eprint = {2410.06499},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:2411-00976,
  title = {{Low-degree approximation of QAC$^0$ circuits}},
  author = {Montanaro, Ashley and Shao, Changpeng and Verdon, Dominic},
  year = {2024},
  url = {https://arxiv.org/abs/2411.00976},
  eprint = {2411.00976},
  archivePrefix = {arXiv},
  note = {Withdrawn; used only to document withdrawal, not as proof.}
}

@misc{Background:gr-qc-0312047,
  title = {{The Penrose Inequality}},
  author = {Bray, Hubert L. and Chrusciel, Piotr T.},
  year = {2003},
  url = {https://arxiv.org/abs/gr-qc/0312047},
  eprint = {gr-qc/0312047},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:hep-th-9610043,
  title = {{M Theory As A Matrix Model: A Conjecture}},
  author = {Banks, T. and Fischler, W. and Shenker, S. H. and Susskind, L.},
  year = {1996},
  url = {https://arxiv.org/abs/hep-th/9610043},
  eprint = {hep-th/9610043},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:math-ph-0012026,
  title = {{The Ionization Conjecture in Hartree-Fock Theory}},
  author = {Solovej, Jan Philip},
  year = {2000},
  url = {https://arxiv.org/abs/math-ph/0012026},
  eprint = {math-ph/0012026},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:math-ph-0112032,
  title = {{Proof of Bose-Einstein Condensation for Dilute Trapped Gases}},
  author = {Lieb, Elliott H. and Seiringer, Robert},
  year = {2001},
  url = {https://arxiv.org/abs/math-ph/0112032},
  eprint = {math-ph/0112032},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:quant-ph-0309110,
  title = {{Secure key from bound entanglement}},
  author = {Horodecki, Karol and Horodecki, Michal and Horodecki, Pawel and Oppenheim, Jonathan},
  year = {2003},
  url = {https://arxiv.org/abs/quant-ph/0309110},
  eprint = {quant-ph/0309110},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:quant-ph-9508027,
  title = {{Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer}},
  author = {Shor, Peter W.},
  year = {1995},
  url = {https://arxiv.org/abs/quant-ph/9508027},
  eprint = {quant-ph/9508027},
  archivePrefix = {arXiv},
  note = {Historical background; bibliographic record and abstract checked.}
}

@misc{Background:10-1103-PhysRev-109-1492,
  title = {{Absence of Diffusion in Certain Random Lattices}},
  author = {P. W. Anderson},
  year = {1958},
  url = {https://doi.org/10.1103/PhysRev.109.1492},
  doi = {10.1103/PhysRev.109.1492}
}

@misc{Background:10-1103-PhysRev-140-A1133,
  title = {{Self-Consistent Equations Including Exchange and Correlation Effects}},
  author = {W. Kohn and L. J. Sham},
  year = {1965},
  url = {https://doi.org/10.1103/PhysRev.140.A1133},
  doi = {10.1103/PhysRev.140.A1133}
}

@misc{Background:10-1103-PhysRevLett-42-673,
  title = {{Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions}},
  author = {E. Abrahams and P. W. Anderson and D. C. Licciardello and T. V. Ramakrishnan},
  year = {1979},
  url = {https://doi.org/10.1103/PhysRevLett.42.673},
  doi = {10.1103/PhysRevLett.42.673}
}

@misc{Background:10-1103-PhysRevLett-50-1153,
  title = {{Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State}},
  author = {F. D. M. Haldane},
  year = {1983},
  url = {https://doi.org/10.1103/PhysRevLett.50.1153},
  doi = {10.1103/PhysRevLett.50.1153}
}

@misc{Background:10-1103-PhysRevLett-50-1395,
  title = {{Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations}},
  author = {R. B. Laughlin},
  year = {1983},
  url = {https://doi.org/10.1103/PhysRevLett.50.1395},
  doi = {10.1103/PhysRevLett.50.1395}
}

@misc{Background:10-1103-PhysRevLett-51-605,
  title = {{Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States}},
  author = {F. D. M. Haldane},
  year = {1983},
  url = {https://doi.org/10.1103/PhysRevLett.51.605},
  doi = {10.1103/PhysRevLett.51.605}
}