@article{Friedgut1999,
  author = {Friedgut, Ehud},
  title = {Sharp thresholds of graph properties, and the {$k$-SAT} problem},
  journal = {Journal of the American Mathematical Society},
  volume = {12},
  number = {4},
  year = {1999},
  pages = {1017--1054},
  note = {With an appendix by Jean Bourgain},
  doi = {10.1090/S0894-0347-99-00305-7},
  url = {https://doi.org/10.1090/S0894-0347-99-00305-7}
}

@article{BGT2013,
  author = {Bayati, Mohsen and Gamarnik, David and Tetali, Prasad},
  title = {Combinatorial approach to the interpolation method and scaling limits in sparse random graphs},
  journal = {The Annals of Probability},
  volume = {41},
  number = {6},
  year = {2013},
  pages = {4080--4115},
  doi = {10.1214/12-AOP816},
  eprint = {0912.2444},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0912.2444v3}
}

@article{DSS2022,
  author = {Ding, Jian and Sly, Allan and Sun, Nike},
  title = {Proof of the satisfiability conjecture for large {$k$}},
  journal = {Annals of Mathematics},
  volume = {196},
  number = {1},
  year = {2022},
  pages = {1--388},
  doi = {10.4007/annals.2022.196.1.1},
  url = {https://annals.math.princeton.edu/2022/196-1/p01}
}

@article{Panchenko2013UM,
  author = {Panchenko, Dmitry},
  title = {The {Parisi} ultrametricity conjecture},
  journal = {Annals of Mathematics},
  volume = {177},
  number = {1},
  year = {2013},
  pages = {383--393},
  doi = {10.4007/annals.2013.177.1.8},
  eprint = {1112.1003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1112.1003v2}
}

@article{AustinPanchenko2014,
  author = {Austin, Tim and Panchenko, Dmitry},
  title = {A hierarchical version of the {de Finetti} and {Aldous--Hoover} representations},
  journal = {Probability Theory and Related Fields},
  volume = {159},
  number = {3--4},
  year = {2014},
  pages = {809--823},
  doi = {10.1007/s00440-013-0521-0},
  eprint = {1301.1259},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1301.1259v4}
}

@article{Panchenko2015HE,
  author = {Panchenko, Dmitry},
  title = {Hierarchical exchangeability of pure states in mean field spin glass models},
  journal = {Probability Theory and Related Fields},
  volume = {161},
  number = {3--4},
  year = {2015},
  pages = {619--650},
  doi = {10.1007/s00440-014-0555-y},
  eprint = {1307.2207},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1307.2207v1}
}

@article{Panchenko2015FRSB,
  author = {Panchenko, Dmitry},
  title = {Structure of finite-{RSB} asymptotic {Gibbs} measures in the diluted spin glass models},
  journal = {Journal of Statistical Physics},
  volume = {162},
  number = {1},
  year = {2016},
  pages = {1--42},
  doi = {10.1007/s10955-015-1385-8},
  eprint = {1406.4702},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1406.4702v2},
  note = {\href{https://arxiv.org/abs/1406.4702v2}{arXiv:1406.4702v2}}
}

@article{Panchenko2013SD,
  author = {Panchenko, Dmitry},
  title = {Spin glass models from the point of view of spin distributions},
  journal = {The Annals of Probability},
  volume = {41},
  number = {3A},
  year = {2013},
  pages = {1315--1361},
  doi = {10.1214/11-AOP696},
  eprint = {1005.2720},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1005.2720v2},
  note = {\href{https://arxiv.org/abs/1005.2720v2}{arXiv:1005.2720v2}}
}

@article{Panchenko2010DS,
  author = {Panchenko, Dmitry},
  title = {On the {Dovbysh--Sudakov} representation result},
  journal = {Electronic Communications in Probability},
  volume = {15},
  year = {2010},
  pages = {330--338},
  doi = {10.1214/ECP.v15-1562},
  eprint = {0905.1524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0905.1524v1}
}

@article{Panchenko2010GG,
  author = {Panchenko, Dmitry},
  title = {A connection between the {Ghirlanda--Guerra} identities and ultrametricity},
  journal = {The Annals of Probability},
  volume = {38},
  number = {1},
  year = {2010},
  pages = {327--347},
  doi = {10.1214/09-AOP484},
  eprint = {0810.0743},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0810.0743v3}
}

@article{Ruelle1987,
  author = {Ruelle, David},
  title = {A mathematical reformulation of {Derrida}'s {REM} and {GREM}},
  journal = {Communications in Mathematical Physics},
  volume = {108},
  number = {2},
  year = {1987},
  pages = {225--239},
  doi = {10.1007/BF01210613},
  url = {https://www.ihes.fr/~ruelle/PUBLICATIONS/87derrida_rem.pdf}
}

@article{PanchenkoTalagrand2007,
  author = {Panchenko, Dmitry and Talagrand, Michel},
  title = {On one property of {Derrida--Ruelle} cascades},
  journal = {Comptes Rendus Mathematique},
  volume = {345},
  year = {2007},
  pages = {653--656},
  doi = {10.1016/j.crma.2007.10.035},
  url = {https://comptes-rendus.academie-sciences.fr/mathematique/item/10.1016/j.crma.2007.10.035.pdf}
}

@book{DominguezMourrat2024,
  author = {Dominguez, Tomas and Mourrat, Jean-Christophe},
  title = {Statistical Mechanics of Mean-Field Disordered Systems: A {Hamilton--Jacobi} Approach},
  series = {Zurich Lectures in Advanced Mathematics},
  publisher = {EMS Press},
  year = {2024},
  doi = {10.4171/ZLAM/32},
  eprint = {2311.08976},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2311.08976v2}
}

@article{FranzLeone2003,
  author = {Franz, Silvio and Leone, Michele},
  title = {Replica bounds for optimization problems and diluted spin systems},
  journal = {Journal of Statistical Physics},
  volume = {111}, year = {2003}, pages = {535--564},
  doi = {10.1023/A:1022885828956},
  url = {https://arxiv.org/abs/cond-mat/0208280v1}
}
@article{PanchenkoTalagrand2004,
  author = {Panchenko, Dmitry and Talagrand, Michel},
  title = {Bounds for diluted mean-fields spin glass models},
  journal = {Probability Theory and Related Fields},
  volume = {130}, number = {3}, year = {2004}, pages = {319--336},
  doi = {10.1007/s00440-004-0342-2},
  url = {https://arxiv.org/abs/math/0405357v1}
}
@article{AizenmanSimsStarr2003,
  author = {Aizenman, Michael and Sims, Robert and Starr, Shannon L.},
  title = {Extended variational principle for the {Sherrington--Kirkpatrick} spin-glass model},
  journal = {Physical Review B}, volume = {68}, year = {2003}, pages = {214403},
  doi = {10.1103/PhysRevB.68.214403},
  url = {https://arxiv.org/abs/cond-mat/0306386v1},
  note = {\href{https://arxiv.org/abs/cond-mat/0306386v1}{arXiv:cond-mat/0306386v1}}
}

@misc{FixedClauseThreshold,
  author = {{OpenAI}},
  title = {{A Limiting Satisfiability Threshold for Every Fixed Clause Size}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026/article.pdf}{OAI:A-Limiting-Satisfiability-Threshold-for-Every-Fixed-Clause-Size-September-25-2026}},
  year = {2026},
  note = {Theorem~1.1}
}
@techreport{Carenini2026Polynomial,
  author = {Carenini, Gaia},
  title = {{A polynomial scaling window for random $k$-SAT and a proof of the satisfiability conjecture}},
  institution = {Electronic Colloquium on Computational Complexity},
  number = {TR26-229},
  year = {2026},
  url = {https://eccc.weizmann.ac.il/report/2026/229/},
  note = {Published 5 October 2026. \url{https://eccc.weizmann.ac.il/report/2026/229/}}
}

@techreport{Carenini,
  author = {Carenini, Gaia},
  title = {The Scaling Window of Random {$k$}-{SAT}},
  institution = {Electronic Colloquium on Computational Complexity},
  number = {TR26-145},
  year = {2026},
  eprint = {2609.26222},
  archivePrefix = {arXiv},
  url = {https://eccc.weizmann.ac.il/report/2026/145/},
  note = {Also arXiv:2609.26222v1}
}

@article{Specker1949,
  author = {Specker, Ernst},
  title = {Nicht konstruktiv beweisbare {S{\"a}tze} der {Analysis}},
  journal = {The Journal of Symbolic Logic},
  volume = {14},
  number = {3},
  pages = {145--158},
  year = {1949},
  doi = {10.2307/2267043},
  url = {https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/nicht-konstruktiv-beweisbare-satze-der-analysis/7DF80F87A63EAA248758D8C27416CED1}
}
@article{Hall1935,
  author = {Hall, Philip},
  title = {On Representatives of Subsets},
  journal = {Journal of the London Mathematical Society},
  volume = {s1-10},
  number = {1},
  pages = {26--30},
  year = {1935},
  doi = {10.1112/jlms/s1-10.37.26},
  url = {https://doi.org/10.1112/jlms/s1-10.37.26}
}

@article{GhirlandaGuerra1998,
  author = {Ghirlanda, Stefano and Guerra, Francesco},
  title = {General properties of overlap probability distributions in disordered spin systems. {Towards} {Parisi} ultrametricity},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {31},
  number = {46},
  year = {1998},
  pages = {9149--9155},
  doi = {10.1088/0305-4470/31/46/006},
  eprint = {cond-mat/9807333},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9807333v1},
  note = {\href{https://arxiv.org/abs/cond-mat/9807333v1}{arXiv:cond-mat/9807333v1}}
}

@article{Guerra2003,
  author = {Guerra, Francesco},
  title = {Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model},
  journal = {Communications in Mathematical Physics},
  volume = {233},
  number = {1},
  year = {2003},
  pages = {1--12},
  doi = {10.1007/s00220-002-0773-5},
  eprint = {cond-mat/0205123},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/0205123v1},
  note = {\href{https://arxiv.org/abs/cond-mat/0205123v1}{arXiv:cond-mat/0205123v1}}
}

@book{Talagrand2011MF1,
  author = {Talagrand, Michel},
  title = {Mean Field Models for Spin Glasses. Volume I: Basic Examples},
  series = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge},
  volume = {54},
  publisher = {Springer Berlin Heidelberg},
  year = {2011},
  doi = {10.1007/978-3-642-15202-3},
  url = {https://michel.talagrand.net/challenge/volume1.pdf},
  note = {Author manuscript dated September 14, 2010; \url{https://michel.talagrand.net/challenge/volume1.pdf}}
}

@misc{OpenAIDilutedPressure2026,
  author = {{OpenAI}},
  title = {{The M{\'e}zard--Parisi formula for diluted spin glasses}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf}{OAI:The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026}},
  year = {2026},
  note = {Theorem~2.1 and Corollary~10.2}
}

@inproceedings{MSL1992,
  author = {Mitchell, David and Selman, Bart and Levesque, Hector},
  title = {Hard and Easy Distributions of {SAT} Problems},
  booktitle = {Proceedings of the Tenth National Conference on Artificial Intelligence},
  year = {1992},
  pages = {459--465},
  publisher = {AAAI Press},
  url = {https://cdn.aaai.org/AAAI/1992/AAAI92-071.pdf}
}

@article{MPZ2002,
  author = {M{\'e}zard, Marc and Parisi, Giorgio and Zecchina, Riccardo},
  title = {Analytic and Algorithmic Solution of Random Satisfiability Problems},
  journal = {Science},
  volume = {297},
  number = {5582},
  pages = {812--815},
  year = {2002},
  doi = {10.1126/science.1073287}
}

@article{MZ2002,
  author = {M{\'e}zard, Marc and Zecchina, Riccardo},
  title = {Random {$K$}-satisfiability problem: From an analytic solution to an efficient algorithm},
  journal = {Physical Review E},
  volume = {66},
  number = {5},
  pages = {056126},
  year = {2002},
  doi = {10.1103/PhysRevE.66.056126}
}

@article{MMZ2006,
  author = {Mertens, Stephan and M{\'e}zard, Marc and Zecchina, Riccardo},
  title = {Threshold values of random {$K$}-{SAT} from the cavity method},
  journal = {Random Structures \& Algorithms},
  volume = {28},
  number = {3},
  pages = {340--373},
  year = {2006},
  doi = {10.1002/rsa.20090}
}

@article{KaporisKirousisLalas2006,
  author = {Kaporis, Alexis C. and Kirousis, Lefteris M. and Lalas, Efthimios G.},
  title = {The probabilistic analysis of a greedy satisfiability algorithm},
  journal = {Random Structures \& Algorithms},
  volume = {28},
  number = {4},
  pages = {444--480},
  year = {2006},
  doi = {10.1002/rsa.20104}
}

@article{DiazKirousisMitschePerezGimenez2009,
  author = {D{\'i}az, Josep and Kirousis, Lefteris M. and Mitsche, Dieter and P{\'e}rez-Gim{\'e}nez, Xavier},
  title = {On the satisfiability threshold of formulas with three literals per clause},
  journal = {Theoretical Computer Science},
  volume = {410},
  number = {30--32},
  pages = {2920--2934},
  year = {2009},
  doi = {10.1016/j.tcs.2009.02.020}
}

@misc{HajiaghayiSorkin2003,
  author = {Hajiaghayi, MohammadTaghi and Sorkin, Gregory B.},
  title = {The Satisfiability Threshold of Random {3-SAT} Is at Least 3.52},
  year = {2003},
  eprint = {math/0310193},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0310193v2},
  note = {arXiv:math/0310193v2}
}
