@article{CourtadeKumar2014,
  author = {Courtade, Thomas A. and Kumar, Gowtham R.},
  title = {Which {Boolean} Functions Maximize Mutual Information on Noisy Inputs?},
  journal = {IEEE Transactions on Information Theory},
  year = {2014},
  volume = {60},
  number = {8},
  pages = {4515--4525},
  doi = {10.1109/TIT.2014.2326877},
  url = {https://people.eecs.berkeley.edu/~courtade/pdfs/CourtadeKumar_TransITAug2014.pdf},
  note = {\href{https://doi.org/10.1109/TIT.2014.2326877}{doi:10.1109/TIT.2014.2326877}}
}

@misc{ChenGohariNair2025,
  author = {Chen, Zijie and Gohari, Amin and Nair, Chandra},
  title = {A Differential Equation Approach to the {Most-Informative Boolean Function Conjecture}},
  year = {2025},
  howpublished = {\url{https://arxiv.org/abs/2502.10019v2}},
  note = {Version 2, revised 5 August 2026}
}

@inproceedings{KumarCourtade2013,
  author = {Kumar, Gowtham R. and Courtade, Thomas A.},
  title = {Which {Boolean} Functions are Most Informative?},
  booktitle = {2013 IEEE International Symposium on Information Theory (ISIT)},
  year = {2013},
  pages = {226--230},
  doi = {10.1109/ISIT.2013.6620221},
  note = {\href{https://doi.org/10.1109/ISIT.2013.6620221}{doi:10.1109/ISIT.2013.6620221}}
}

@inproceedings{OrdentlichShayevitzWeinstein2016,
  author = {Ordentlich, Or and Shayevitz, Ofer and Weinstein, Omri},
  title = {An Improved Upper Bound for the Most Informative {Boolean} Function Conjecture},
  booktitle = {2016 IEEE International Symposium on Information Theory (ISIT)},
  year = {2016},
  pages = {500--504},
  doi = {10.1109/ISIT.2016.7541349},
  note = {\href{https://doi.org/10.1109/ISIT.2016.7541349}{doi:10.1109/ISIT.2016.7541349}}
}

@article{Samorodnitsky2016,
  author = {Samorodnitsky, Alex},
  title = {On the Entropy of a Noisy Function},
  journal = {IEEE Transactions on Information Theory},
  year = {2016},
  volume = {62},
  number = {10},
  pages = {5446--5464},
  doi = {10.1109/TIT.2016.2584625},
  note = {\href{https://doi.org/10.1109/TIT.2016.2584625}{doi:10.1109/TIT.2016.2584625}}
}

@article{Yu2023,
  author = {Yu, Lei},
  title = {On the {$\Phi$}-Stability and Related Conjectures},
  journal = {Probability Theory and Related Fields},
  year = {2023},
  volume = {186},
  number = {3--4},
  pages = {1045--1080},
  doi = {10.1007/s00440-023-01209-5},
  note = {\href{https://doi.org/10.1007/s00440-023-01209-5}{doi:10.1007/s00440-023-01209-5}}
}

@article{Yu2026,
  author = {Yu, Lei},
  title = {Local Optimality of Dictator Functions with Applications to {Courtade--Kumar} and {Li--M{\'e}dard} Conjectures},
  journal = {The Annals of Applied Probability},
  year = {2026},
  note = {Accepted for publication. \url{https://arxiv.org/abs/2410.10147v5}}
}

@article{PichlerPiantanidaMatz2018,
  author = {Pichler, Georg and Piantanida, Pablo and Matz, Gerald},
  title = {Dictator Functions Maximize Mutual Information},
  journal = {The Annals of Applied Probability},
  year = {2018},
  volume = {28},
  number = {5},
  pages = {3094--3101},
  doi = {10.1214/18-AAP1384},
  note = {\href{https://doi.org/10.1214/18-AAP1384}{doi:10.1214/18-AAP1384}}
}

@misc{KindlerODonnellWitmer2016,
  author = {Kindler, Guy and O'Donnell, Ryan and Witmer, David},
  title = {Continuous Analogues of the {Most Informative Function} Problem},
  year = {2016},
  howpublished = {\url{https://arxiv.org/abs/1506.03167v3}},
  note = {Version 3, revised 25 January 2016}
}

@article{LiMedard2021,
  author = {Li, Jiange and M{\'e}dard, Muriel},
  title = {{Boolean} Functions: Noise Stability, Non-Interactive Correlation Distillation, and Mutual Information},
  journal = {IEEE Transactions on Information Theory},
  year = {2021},
  volume = {67},
  number = {2},
  pages = {778--789},
  doi = {10.1109/TIT.2020.3041028},
  note = {\href{https://doi.org/10.1109/TIT.2020.3041028}{doi:10.1109/TIT.2020.3041028}}
}

@inproceedings{BarnesOzgur2020,
  author = {Barnes, Leighton Pate and {\"O}zg{\"u}r, Ayfer},
  title = {The {Courtade--Kumar Most Informative Boolean Function} Conjecture and a Symmetrized {Li--M{\'e}dard} Conjecture are Equivalent},
  booktitle = {2020 IEEE International Symposium on Information Theory (ISIT)},
  year = {2020},
  pages = {2205--2209},
  doi = {10.1109/ISIT44484.2020.9174063},
  note = {\href{https://doi.org/10.1109/ISIT44484.2020.9174063}{doi:10.1109/ISIT44484.2020.9174063}}
}

@misc{JavanmardWoodruff2026,
  author = {Javanmard, Adel and Woodruff, David P.},
  title = {Progress on the {Courtade--Kumar} Conjecture: Optimal High-Noise Entropy Bounds and Generalized Coordinate-wise Mutual Information},
  year = {2026},
  howpublished = {\url{https://arxiv.org/abs/2601.09679v1}},
  note = {Version 1, 14 January 2026}
}

@article{GohariNair2022,
  author = {Gohari, Amin and Nair, Chandra},
  title = {Outer Bounds for Multiuser Settings: The Auxiliary Receiver Approach},
  journal = {IEEE Transactions on Information Theory},
  year = {2022},
  volume = {68},
  number = {2},
  pages = {701--736},
  doi = {10.1109/TIT.2021.3128136},
  url = {https://chandra.ie.cuhk.edu.hk/pub/papers/NIT/Auxiliary-Receiver.pdf}
}

@misc{ChenWatanabeYu2026,
  author = {Chen, Jun and Watanabe, Shun and Yu, Lei},
  title = {On the Most Discriminative {Boolean} Functions for Correlated Sources},
  year = {2026},
  howpublished = {\url{https://arxiv.org/abs/2607.28162v1}},
  note = {Version 1, 30 July 2026}
}

@misc{ChenEtAl2026CK,
  author = {Chen, Zijie and Gohari, Amin and Javanmard, Adel and Lin, Honghao and Mirrokni, Vahab and Nair, Chandra and Woodruff, David P.},
  title = {A Proof of the Most Informative {Boolean} Function Conjecture},
  year = {2026},
  eprint = {2609.24931},
  howpublished = {\url{https://arxiv.org/abs/2609.24931v1}},
  archivePrefix = {arXiv},
  primaryClass = {cs.DS},
  doi = {10.48550/arXiv.2609.24931},
  url = {https://arxiv.org/abs/2609.24931},
  note = {Version 1, September 21, 2026}
}

@misc{KyTran2026CK,
  author = {Ky, Vu Khac and Tran, Tuan},
  title = {Dictators Are Most Informative},
  year = {2026},
  eprint = {2609.24184},
  howpublished = {\url{https://arxiv.org/abs/2609.24184v1}},
  archivePrefix = {arXiv},
  primaryClass = {cs.IT},
  doi = {10.48550/arXiv.2609.24184},
  url = {https://arxiv.org/abs/2609.24184},
  note = {Version 1, September 21, 2026}
}

@misc{MahdavifarBeirami2026CK,
  author = {Mahdavifar, Hessam and Beirami, Ahmad},
  title = {The Most Informative Bit and Beyond: A Proof of the {Courtade--Kumar} Conjecture and Multibit Extensions},
  year = {2026},
  eprint = {2609.26444},
  howpublished = {\url{https://arxiv.org/abs/2609.26444v1}},
  archivePrefix = {arXiv},
  primaryClass = {cs.IT},
  doi = {10.48550/arXiv.2609.26444},
  url = {https://arxiv.org/abs/2609.26444},
  note = {Version 1, September 22, 2026}
}

@misc{KramerSaglam2026,
  author = {Kramer, Dimiter and Saglam, Mert},
  title = {On the Most Informative {Boolean} Function under Noise},
  year = {2026},
  month = {September},
  howpublished = {Preprint},
  note = {\href{https://github.com/deepinfra/courtade-kumar/blob/93074b31e9d280e532e4b96e89f5fb199b3b5f6a/courtade-kumar.pdf}{Fixed source version}}
}

@article{WynerZiv1973,
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