@article{kauffman1986autocatalytic,
  author  = {Kauffman, Stuart A.},
  title   = {Autocatalytic sets of proteins},
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  volume  = {119},
  number  = {1},
  pages   = {1--24},
  year    = {1986},
  doi     = {10.1016/S0022-5193(86)80047-9}
}


@book{kauffman1993origins,
  author    = {Kauffman, Stuart A.},
  title     = {The Origins of Order: Self-Organization and Selection in Evolution},
  publisher = {Oxford University Press},
  address   = {New York},
  year      = {1993}
}


@article{eigen1971selforganization,
  author  = {Eigen, Manfred},
  title   = {Selforganization of matter and the evolution of biological macromolecules},
  journal = {Naturwissenschaften},
  volume  = {58},
  number  = {10},
  pages   = {465--523},
  year    = {1971},
  doi     = {10.1007/BF00623322}
}


@article{steel2000emergence,
  author  = {Steel, Mike},
  title   = {The emergence of a self-catalysing structure in abstract origin-of-life studies},
  journal = {Applied Mathematics Letters},
  volume  = {13},
  number  = {3},
  pages   = {91--95},
  year    = {2000},
  doi     = {10.1016/S0893-9659(99)00191-3}
}


@article{hordijk2004detecting,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Detecting autocatalytic, self-sustaining sets in chemical reaction systems},
  journal = {Journal of Theoretical Biology},
  volume  = {227},
  number  = {4},
  pages   = {451--461},
  year    = {2004},
  doi     = {10.1016/j.jtbi.2003.11.020}
}


@article{mossel2005random,
  author  = {Mossel, Elchanan and Steel, Mike},
  title   = {Random biochemical networks: the probability of self-sustaining autocatalysis},
  journal = {Journal of Theoretical Biology},
  volume  = {233},
  number  = {3},
  pages   = {327--336},
  year    = {2005},
  doi     = {10.1016/j.jtbi.2004.10.011}
}


@article{hordijk2010autocatalytic,
  author  = {Hordijk, Wim and Hein, Jotun and Steel, Mike},
  title   = {Autocatalytic sets and the origin of life},
  journal = {Entropy},
  volume  = {12},
  number  = {7},
  pages   = {1733--1742},
  year    = {2010},
  doi     = {10.3390/e12071733}
}


@article{hordijk2011required,
  author  = {Hordijk, Wim and Kauffman, Stuart A. and Steel, Mike},
  title   = {Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems},
  journal = {International Journal of Molecular Sciences},
  volume  = {12},
  number  = {5},
  pages   = {3085--3101},
  year    = {2011},
  doi     = {10.3390/ijms12053085}
}


@article{hordijk2012extended,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Autocatalytic sets extended: Dynamics, inhibition, and a generalization},
  journal = {Journal of Systems Chemistry},
  volume  = {3},
  pages   = {5},
  year    = {2012},
  doi     = {10.1186/1759-2208-3-5}
}


@article{hordijk2012structure,
  author  = {Hordijk, Wim and Steel, Mike and Kauffman, Stuart},
  title   = {The structure of autocatalytic sets: Evolvability, enablement, and emergence},
  journal = {Acta Biotheoretica},
  volume  = {60},
  number  = {4},
  pages   = {379--392},
  year    = {2012},
  doi     = {10.1007/s10441-012-9165-1}
}


@article{hordijk2014specificity,
  author  = {Hordijk, Wim and Wills, Peter R. and Steel, Mike},
  title   = {Autocatalytic sets and biological specificity},
  journal = {Bulletin of Mathematical Biology},
  volume  = {76},
  number  = {1},
  pages   = {201--224},
  year    = {2014},
  doi     = {10.1007/s11538-013-9916-4}
}


@article{smith2014partitioned,
  author  = {Smith, Joshua I. and Steel, Mike and Hordijk, Wim},
  title   = {Autocatalytic sets in a partitioned biochemical network},
  journal = {Journal of Systems Chemistry},
  volume  = {5},
  pages   = {2},
  year    = {2014},
  doi     = {10.1186/1759-2208-5-2}
}


@article{hordijk2015algorithms,
  author  = {Hordijk, Wim and Smith, Joshua I. and Steel, Mike},
  title   = {Algorithms for detecting and analysing autocatalytic sets},
  journal = {Algorithms for Molecular Biology},
  volume  = {10},
  pages   = {15},
  year    = {2015},
  doi     = {10.1186/s13015-015-0042-8}
}


@article{hordijk2016variable,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Autocatalytic sets in polymer networks with variable catalysis distributions},
  journal = {Journal of Mathematical Chemistry},
  volume  = {54},
  number  = {10},
  pages   = {1997--2021},
  year    = {2016},
  doi     = {10.1007/s10910-016-0666-z}
}


@article{hordijk2017chasing,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Chasing the tail: The emergence of autocatalytic networks},
  journal = {Biosystems},
  volume  = {152},
  pages   = {1--10},
  year    = {2017},
  doi     = {10.1016/j.biosystems.2016.12.002}
}


@article{hordijk2018life,
  author  = {Hordijk, Wim and Steel, Mike},
  title   = {Autocatalytic networks at the basis of life's origin and organization},
  journal = {Life},
  volume  = {8},
  number  = {4},
  pages   = {62},
  year    = {2018},
  doi     = {10.3390/life8040062}
}


@article{steel2019autocatalytic,
  author  = {Steel, Mike and Hordijk, Wim and Xavier, Joana C.},
  title   = {Autocatalytic networks in biology: structural theory and algorithms},
  journal = {Journal of the Royal Society Interface},
  volume  = {16},
  number  = {151},
  pages   = {20180808},
  year    = {2019},
  doi     = {10.1098/rsif.2018.0808}
}


@article{vaidya2012spontaneous,
  author  = {Vaidya, Nilesh and Manapat, Michael L. and Chen, Irene A. and Xulvi-Brunet, Ramon and Hayden, Eric J. and Lehman, Niles},
  title   = {Spontaneous network formation among cooperative {RNA} replicators},
  journal = {Nature},
  volume  = {491},
  number  = {7422},
  pages   = {72--77},
  year    = {2012},
  doi     = {10.1038/nature11549}
}


@article{varanasi2026emergence,
  author  = {Varanasi, Varun and Korenaga, Jun},
  title   = {Emergence of autocatalysis in prebiotic reaction networks},
  journal = {Physical Review E},
  volume  = {113},
  pages   = {044304},
  year    = {2026},
  doi     = {10.1103/nmt5-qsym}
}


@misc{varanasi2026repository,
  author       = {Varanasi, Varun},
  title        = {{Emergence-of-Autocatalysis-in-Prebiotic-Reaction-Networks}: public source and data repository},
  howpublished = {\url{https://github.com/VJ-Varanasi/Emergence-of-Autocatalysis-in-Prebiotic-Reaction-Networks/tree/314f1e664cd7a8ccc97eed950f28d33311d0b5ef}},
  year         = {2026},
  note         = {Reaction catalogue and shared-direction catalytic sampler; immutable commit 314f1e664cd7a8ccc97eed950f28d33311d0b5ef, inspected 15 October 2026. RAF detection is a separate implementation question}
}


@article{lyndon1962equation,
  author  = {Lyndon, Roger C. and Sch{\"u}tzenberger, Marcel-Paul},
  title   = {The equation $a^M=b^Nc^P$ in a free group},
  journal = {Michigan Mathematical Journal},
  volume  = {9},
  number  = {4},
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  year    = {1962},
  doi     = {10.1307/mmj/1028998766}
}


@book{lothaire1997combinatorics,
  author    = {Lothaire, M.},
  title     = {Combinatorics on Words},
  series    = {Cambridge Mathematical Library},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1997},
  doi       = {10.1017/CBO9780511566097}
}


@book{grimmett1999percolation,
  author    = {Grimmett, Geoffrey},
  title     = {Percolation},
  edition   = {2nd},
  series    = {Grundlehren der mathematischen Wissenschaften},
  volume    = {321},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1999},
  doi       = {10.1007/978-3-662-03981-6}
}


@article{peierls1936ising,
  author  = {Peierls, Rudolf},
  title   = {On {I}sing's model of ferromagnetism},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume  = {32},
  number  = {3},
  pages   = {477--481},
  year    = {1936},
  doi     = {10.1017/S0305004100019174}
}


@inproceedings{demoura2021lean4,
  author    = {de Moura, Leonardo and Ullrich, Sebastian},
  title     = {The {L}ean 4 theorem prover and programming language},
  booktitle = {Automated Deduction -- CADE 28},
  series    = {Lecture Notes in Computer Science},
  volume    = {12699},
  publisher = {Springer},
  pages     = {625--635},
  year      = {2021},
  doi       = {10.1007/978-3-030-79876-5_37}
}


@inproceedings{mathlib2020,
  author    = {{The mathlib Community}},
  title     = {The {L}ean mathematical library},
  booktitle = {Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020)},
  publisher = {ACM},
  pages     = {367--381},
  year      = {2020},
  doi       = {10.1145/3372885.3373824}
}