@misc{FKCompanion,
  author = {{OpenAI}},
  title = {{Square-lattice FK interfaces and nested loops for $1\le q<4$}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026/paper.pdf}{OAI:Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026}},
  year = {2026}
}

@misc{GFFCompanion,
  author = {{OpenAI}},
  title = {{The Gaussian free field limit of the balanced six-vertex model with variance multiplier $1/\arcsin(c/2)$}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf}{OAI:The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026}},
  year = {2026}
}

@article{DMT,
  author = {Duminil-Copin, Hugo and Manolescu, Ioan and Tassion, Vincent},
  title = {Planar random-cluster model: fractal properties of the critical phase},
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  volume = {181},
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  year = {2021},
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  eprint = {2007.14707},
  archivePrefix = {arXiv},
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}

@article{CDCH,
  author = {Chelkak, Dmitry and Duminil-Copin, Hugo and Hongler, Cl{\'e}ment},
  title = {Crossing probabilities in topological rectangles for the critical
    planar {FK-Ising} model},
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  number = {5},
  pages = {1--28},
  year = {2016},
  doi = {10.1214/16-EJP3452},
  eprint = {1312.7785},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1312.7785}
}

@article{DCLM,
  author = {Duminil-Copin, Hugo and Li, Jhih-Huang and Manolescu, Ioan},
  title = {Universality for the random-cluster model on isoradial graphs},
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  volume = {23},
  pages = {1--70},
  year = {2018},
  doi = {10.1214/18-EJP223},
  eprint = {1711.02338},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1711.02338}
}

@misc{DKLM,
  author = {Duminil-Copin, Hugo and Kozlowski, Karol Kajetan and
    Lammers, Piet and Manolescu, Ioan},
  title = {{Gaussian} free field convergence of the six-vertex model with
    $-1\le\Delta\le-\tfrac12$},
  year = {2026},
  month = mar,
  note = {Preprint, arXiv:2603.06268v1, March 6, 2026},
  doi = {10.48550/arXiv.2603.06268},
  eprint = {2603.06268},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2603.06268v1}
}

@article{Schramm,
  author = {Schramm, Oded},
  title = {Scaling limits of loop-erased random walks and uniform spanning trees},
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  eprint = {math/9904022},
  archivePrefix = {arXiv},
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}

@article{Beffara,
  author = {Beffara, Vincent},
  title = {The dimension of the {SLE} curves},
  journal = {The Annals of Probability},
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  number = {4},
  pages = {1421--1452},
  year = {2008},
  doi = {10.1214/07-AOP364},
  eprint = {math/0211322},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0211322}
}

@article{LawlerSheffield,
  author = {Lawler, Gregory F. and Sheffield, Scott},
  title = {A natural parametrization for the {Schramm--Loewner} evolution},
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  number = {5},
  pages = {1896--1937},
  year = {2011},
  doi = {10.1214/10-AOP560},
  eprint = {0906.3804},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0906.3804}
}

@article{LawlerZhou,
  author = {Lawler, Gregory F. and Zhou, Wang},
  title = {{SLE} curves and natural parametrization},
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  number = {3A},
  pages = {1556--1584},
  year = {2013},
  doi = {10.1214/12-AOP742},
  eprint = {1006.4936},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1006.4936}
}

@misc{LawlerRezaeiBasic,
  author = {Lawler, Gregory F. and Rezaei, Mohammad A.},
  title = {Basic properties of the natural parametrization for the
    {Schramm--Loewner} evolution},
  year = {2012},
  note = {Preprint, arXiv:1203.3259},
  eprint = {1203.3259},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1203.3259}
}

@article{LawlerRezaeiContent,
  author = {Lawler, Gregory F. and Rezaei, Mohammad A.},
  title = {Minkowski content and natural parameterization for the
    {Schramm--Loewner} evolution},
  journal = {The Annals of Probability},
  volume = {43},
  number = {3},
  pages = {1082--1120},
  year = {2015},
  doi = {10.1214/13-AOP874},
  eprint = {1211.4146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1211.4146}
}

@article{LawlerRezaeiTwoPoint,
  author = {Lawler, Gregory F. and Rezaei, Mohammad A.},
  title = {Up-to-constants bounds on the two-point {Green}'s function for {SLE} curves},
  journal = {Electronic Communications in Probability},
  volume = {20},
  number = {45},
  pages = {1--13},
  year = {2015},
  doi = {10.1214/ECP.v20-4246},
  eprint = {1503.06689},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1503.06689}
}

@article{GPS,
  author = {Garban, Christophe and Pete, G{\'a}bor and Schramm, Oded},
  title = {Pivotal, cluster, and interface measures for critical planar percolation},
  journal = {Journal of the American Mathematical Society},
  volume = {26},
  number = {4},
  pages = {939--1024},
  year = {2013},
  doi = {10.1090/S0894-0347-2013-00772-9},
  eprint = {1008.1378},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1008.1378}
}

@article{HLS,
  author = {Holden, Nina and Li, Xinyi and Sun, Xin},
  title = {Natural parametrization of percolation interface and pivotal points},
  journal = {Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume = {58},
  number = {1},
  pages = {7--25},
  year = {2022},
  doi = {10.1214/21-AIHP1160},
  eprint = {1804.07286},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1804.07286}
}

@article{DGLZ,
  author = {Du, Hang and Gao, Yifan and Li, Xinyi and Zhuang, Zijie},
  title = {Sharp asymptotics for arm probabilities in critical planar percolation},
  journal = {Communications in Mathematical Physics},
  volume = {405},
  year = {2024},
  note = {Article 182},
  doi = {10.1007/s00220-024-05028-0},
  eprint = {2205.15901},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2205.15901}
}

@article{LawlerViklund,
  author = {Lawler, Gregory F. and Viklund, Fredrik},
  title = {Convergence of loop-erased random walk in the natural parameterization},
  journal = {Duke Mathematical Journal},
  volume = {170},
  number = {10},
  pages = {2289--2370},
  year = {2021},
  doi = {10.1215/00127094-2020-0075},
  eprint = {1603.05203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1603.05203}
}

@article{IsingInterfaces,
  author = {Chelkak, Dmitry and Duminil-Copin, Hugo and Hongler, Cl{\'e}ment
    and Kemppainen, Antti and Smirnov, Stanislav},
  title = {Convergence of {Ising} interfaces to {Schramm}'s {SLE} curves},
  journal = {Comptes Rendus Math{\'e}matique},
  volume = {352},
  number = {2},
  pages = {157--161},
  year = {2014},
  doi = {10.1016/j.crma.2013.12.002},
  eprint = {1312.0533},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1312.0533}
}

@book{LawlerLimic2010,
  author = {Lawler, Gregory F. and Limic, Vlada},
  title = {Random Walk: A Modern Introduction},
  publisher = {Cambridge University Press},
  year = {2010},
  doi = {10.1017/CBO9780511750854},
  url = {https://www.math.uchicago.edu/~lawler/srwbook.pdf},
  note = {Theorem numbering follows the author-hosted text}
}