@article{ASW1951,
  author  = {Aissen, Michael and Schoenberg, I. J. and Whitney, A. M.},
  title   = {On the generating functions of totally positive sequences},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  volume  = {37},
  number  = {5},
  pages   = {303--307},
  year    = {1951},
  doi     = {10.1073/pnas.37.5.303}
}

@article{deBruijn1950,
  author  = {de Bruijn, N. G.},
  title   = {The roots of trigonometric integrals},
  journal = {Duke Mathematical Journal},
  volume  = {17},
  number  = {3},
  pages   = {197--226},
  year    = {1950},
  doi     = {10.1215/S0012-7094-50-01720-0}
}

@article{Edrei1953,
  author  = {Edrei, Albert},
  title   = {Proof of a conjecture of {Schoenberg} on the generating function of a totally positive sequence},
  journal = {Canadian Journal of Mathematics},
  volume  = {5},
  pages   = {86--94},
  year    = {1953},
  doi     = {10.4153/CJM-1953-010-3}
}

@article{Schoenberg1951,
  author  = {Schoenberg, I. J.},
  title   = {On {P{\'o}lya} frequency functions. {I}. The totally positive functions and their Laplace transforms},
  journal = {Journal d'Analyse Math{\'e}matique},
  volume  = {1},
  pages   = {331--374},
  year    = {1951}
}

@article{Schoenberg1955,
  author  = {Schoenberg, I. J.},
  title   = {On the zeros of the generating functions of multiply positive sequences and functions},
  journal = {Annals of Mathematics},
  volume  = {62},
  number  = {3},
  pages   = {447--471},
  year    = {1955}
}

@article{KatkovaOstrovskii1990,
  author  = {Katkova, Olga M. and Ostrovskii, I. V.},
  title   = {Zero sets of entire generating functions of {P{\'o}lya} frequency sequences of finite order},
  journal = {Mathematics of the USSR-Izvestiya},
  volume  = {35},
  number  = {1},
  pages   = {101--112},
  year    = {1990}
}

@article{RodgersTao2020,
  author  = {Rodgers, Brad and Tao, Terence},
  title   = {The {de Bruijn--Newman} constant is non-negative},
  journal = {Forum of Mathematics, Pi},
  volume  = {8},
  pages   = {e6},
  year    = {2020},
  doi     = {10.1017/fmp.2020.6}
}

@article{Polymath2019,
  author  = {{D. H. J. Polymath}},
  title   = {Effective approximation of heat flow evolution of the {Riemann} $\xi$-function, and a new upper bound for the {de Bruijn--Newman} constant},
  journal = {Research in the Mathematical Sciences},
  volume  = {6},
  number  = {3},
  pages   = {Article 31},
  year    = {2019},
  doi     = {10.1007/s40687-019-0193-1}
}

@article{PlattTrudgian2021,
  author  = {Platt, David J. and Trudgian, Timothy S.},
  title   = {The {Riemann} hypothesis is true up to $3\cdot 10^{12}$},
  journal = {Bulletin of the London Mathematical Society},
  volume  = {53},
  number  = {3},
  pages   = {792--797},
  year    = {2021},
  doi     = {10.1112/blms.12460}
}

@book{Macdonald1995,
  author    = {Macdonald, I. G.},
  title     = {{Symmetric Functions and Hall Polynomials}},
  edition   = {2},
  publisher = {Oxford University Press},
  address   = {Oxford},
  year      = {1995}
}

@book{Pinkus2010,
  author    = {Pinkus, Allan},
  title     = {{Totally Positive Matrices}},
  series    = {Cambridge Tracts in Mathematics},
  volume    = {181},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2010},
  doi       = {10.1017/CBO9780511760319}
}

@article{Katkova2007,
  author  = {Katkova, Olga M.},
  title   = {Multiple positivity and the {Riemann} zeta-function},
  journal = {Computational Methods and Function Theory},
  volume  = {7},
  number  = {1},
  pages   = {13--31},
  year    = {2007},
  note    = {Preprint available as arXiv:math/0505174}
}

@misc{Michalowski2026,
  author       = {Michalowski, Wojciech},
  title        = {An explicit uniform cubic wedge for consecutive {Toeplitz} minors of the {Riemann} $\xi$ coefficients},
  year         = {2026},
  month        = jul,
  howpublished = {Preprint, arXiv:2607.16795},
  url          = {https://arxiv.org/abs/2607.16795},
  note         = {Posted 18 July 2026}
}

@misc{Sra2026xi,
  author       = {Sra, Suvrit},
  title        = {On some positivity properties of the {Riemann} {Xi} function},
  year         = {2026},
  month        = oct,
  howpublished = {Preprint, version v1},
  url          = {https://suvrit.github.io/papers/riem-xi/},
  note         = {Version released 20 October 2026}
}

@misc{Sra2026theta,
  author       = {Sra, Suvrit},
  title        = {Sharp order-four sign regularity of a {Jacobi} theta kernel},
  year         = {2026},
  month        = oct,
  howpublished = {Preprint, version v1},
  url          = {https://suvrit.github.io/papers/csordas/},
  note         = {Version released 10 October 2026}
}

@misc{Gordon2026,
  author       = {Gordon, Stefan},
  title        = {A computer-assisted upper bound for the {de Bruijn--Newman} constant},
  year         = {2026},
  month        = oct,
  howpublished = {Preprint posted to SSRN},
  url          = {https://ssrn.com/abstract=7608638},
  note         = {Posted 14 October 2026, revised 15 October 2026; reports Lambda < 0.158 and gives a Lean companion conditional on stated analytic inputs}
}

@misc{Mosaic2026,
  author       = {{Mosaic Intelligence}},
  title        = {A certified unconditional upper bound $\Lambda\leq0.1875$ for the {de Bruijn--Newman} constant},
  year         = {2026},
  month        = jul,
  howpublished = {Public certificate package},
  doi          = {10.5281/zenodo.21175533},
  url          = {https://doi.org/10.5281/zenodo.21175533},
  note         = {Self-archived computational manuscript; status should be checked against the live certificate repository}
}

@misc{Gomila2026,
  author       = {Gomila, Jude},
  title        = {A computer-assisted proof of the bound $\Lambda\leq0.1787854$},
  year         = {2026},
  month        = aug,
  howpublished = {Public certificate repository},
  url          = {https://github.com/judegomila/dbn-lambda-01787854-candidate-audit},
  note         = {Released 20 August 2026; not yet peer reviewed according to the repository status statement}
}

@misc{Kornaus2026,
  author       = {Kornaus, Daniel Martin},
  title        = {A computer-assisted unconditional upper bound $\Lambda<0.172422$ for the {de Bruijn--Newman} constant},
  year         = {2026},
  month        = sep,
  howpublished = {Public certificate package},
  url          = {https://zenodo.org/records/22658444},
  note         = {Version 2 reported as released 8 September 2026; peer-review and certificate status should be checked directly}
}

@misc{HakimogluBrown2026,
  author       = {Hakimoglu-Brown, Cetin},
  title        = {A conditional bound $\Lambda\leq0.13963$ for the {de Bruijn--Newman} constant},
  year         = {2026},
  month        = oct,
  howpublished = {Preprint, arXiv:2610.12803},
  url          = {https://arxiv.org/abs/2610.12803},
  note         = {Conditional on a zero-free hypothesis for zeta in Re(s)>7/8}
}


@misc{Mosaic2026latest,
  author       = {{Mosaic Intelligence}},
  title        = {A certified unconditional upper bound $\Lambda<0.1595$ for the {de Bruijn--Newman} constant},
  year         = {2026},
  howpublished = {Public certificate package and current index entry},
  url          = {https://teorth.github.io/optimizationproblems/constants/21a.html},
  note         = {The index labels post-2021 packages as self-archived, non-refereed, and not independently replayed; this package is listed as descended from the 0.1875 package}
}