@article{Strassen1969,
  author  = {Strassen, Volker},
  title   = {Gaussian elimination is not optimal},
  journal = {Numerische Mathematik},
  volume  = {13},
  number  = {4},
  pages   = {354--356},
  year    = {1969},
  doi     = {10.1007/BF02165411}
}

@article{FawziEtAl2022,
  author  = {Fawzi, Alhussein and Balog, Matej and Huang, Aja and Hubert, Thomas and Romera-Paredes, Bernardino and Barekatain, Mohammadamin and Novikov, Alexander and Ruiz, Francisco J. R. and Schrittwieser, Julian and Swirszcz, Grzegorz and Silver, David and Hassabis, Demis and Kohli, Pushmeet},
  title   = {Discovering faster matrix multiplication algorithms with reinforcement learning},
  journal = {Nature},
  volume  = {610},
  number  = {7930},
  pages   = {47--53},
  year    = {2022},
  doi     = {10.1038/s41586-022-05172-4}
}

@misc{NovikovEtAl2025AlphaEvolve,
  author        = {Novikov, Alexander and V{\~u}, Ng{\^a}n and Eisenberger, Marvin and Dupont, Emilien and Huang, Po-Sen and Wagner, Adam Zsolt and Shirobokov, Sergey and Kozlovskii, Borislav and Ruiz, Francisco J. R. and Mehrabian, Abbas and Kumar, M. Pawan and See, Abigail and Chaudhuri, Swarat and Holland, George and Davies, Alex and Nowozin, Sebastian and Kohli, Pushmeet and Balog, Matej},
  title         = {{AlphaEvolve}: A coding agent for scientific and algorithmic discovery},
  year          = {2025},
  eprint        = {2506.13131},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2506.13131}
}

@misc{DumasPernetSedoglavic2025,
  author        = {Dumas, Jean-Guillaume and Pernet, Cl{\'e}ment and Sedoglavic, Alexandre},
  title         = {A non-commutative algorithm for multiplying $4\times 4$ matrices using 48 non-complex multiplications},
  year          = {2025},
  eprint        = {2506.13242},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2506.13242}
}

@misc{DumasEtAl2026practice,
  author        = {Dumas, Jean-Guillaume and Pernet, Cl{\'e}ment and Sedoglavic, Alexandre and Stapleton, Joshua and Tichavsk{\'y}, Petr},
  title         = {Fast matrix multiplication via recursive $\langle 4\times 4\times 4{:}48\rangle$ algorithms into practice},
  year          = {2026},
  eprint        = {2609.12027},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2609.12027}
}

@inproceedings{KauersMoosbauer2023flip,
  author        = {Kauers, Manuel and Moosbauer, Jakob},
  title         = {Flip Graphs for Matrix Multiplication},
  booktitle     = {Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (ISSAC '23)},
  pages         = {381--388},
  publisher     = {ACM},
  year          = {2023},
  doi           = {10.1145/3597066.3597120},
  eprint        = {2212.01175},
  archivePrefix = {arXiv}
}

@misc{KauersMoosbauer2022Z2,
  author        = {Kauers, Manuel and Moosbauer, Jakob},
  title         = {The {FBHHRBNRSSSHK}-Algorithm for Multiplication in $\mathbb{Z}_2^{5\times5}$ is still not the end of the story},
  year          = {2022},
  eprint        = {2210.04045},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2210.04045}
}

@article{KauersMoosbauer2024nm6,
  author        = {Kauers, Manuel and Moosbauer, Jakob},
  title         = {Some New Non-Commutative Matrix Multiplication Algorithms of Size $(n,m,6)$},
  journal       = {ACM Communications in Computer Algebra},
  volume        = {58},
  number        = {1},
  pages         = {1--11},
  year          = {2024},
  doi           = {10.1145/3712020.3712021},
  eprint        = {2306.00882},
  archivePrefix = {arXiv}
}


@inproceedings{KauersMoosbauer2022normal,
  author        = {Kauers, Manuel and Moosbauer, Jakob},
  title         = {A Normal Form for Matrix Multiplication Schemes},
  booktitle     = {Algebraic Informatics (CAI 2022)},
  editor        = {Poulakis, Dimitrios and Rahonis, George},
  series        = {Lecture Notes in Computer Science},
  pages         = {149--160},
  publisher     = {Springer},
  year          = {2022},
  doi           = {10.1007/978-3-031-19685-0_11},
  eprint        = {2206.00550},
  archivePrefix = {arXiv}
}

@inproceedings{HeuleKauersSeidl2019,
  author        = {Heule, Marijn J. H. and Kauers, Manuel and Seidl, Martina},
  title         = {Local Search for Fast Matrix Multiplication},
  booktitle     = {Theory and Applications of Satisfiability Testing -- SAT 2019},
  editor        = {Janota, Mikol{\'a}{\v{s}} and Lynce, In{\^e}s},
  series        = {Lecture Notes in Computer Science},
  pages         = {155--163},
  publisher     = {Springer},
  year          = {2019},
  doi           = {10.1007/978-3-030-24258-9_10},
  eprint        = {1903.11391},
  archivePrefix = {arXiv}
}

@article{HeuleKauersSeidl2021,
  author        = {Heule, Marijn J. H. and Kauers, Manuel and Seidl, Martina},
  title         = {New ways to multiply $3\times 3$-matrices},
  journal       = {Journal of Symbolic Computation},
  volume        = {104},
  pages         = {899--916},
  year          = {2021},
  doi           = {10.1016/j.jsc.2020.10.003},
  eprint        = {1905.10192},
  archivePrefix = {arXiv}
}

@inproceedings{AraiIchikawaHukushima2024,
  author        = {Arai, Yamato and Ichikawa, Yuma and Hukushima, Koji},
  title         = {Adaptive Flip Graph Algorithm for Matrix Multiplication},
  booktitle     = {Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation (ISSAC '24)},
  pages         = {292--298},
  publisher     = {ACM},
  year          = {2024},
  doi           = {10.1145/3666000.3669701},
  eprint        = {2312.16960},
  archivePrefix = {arXiv}
}

@inproceedings{MoosbauerPoole2025,
  author        = {Moosbauer, Jakob and Poole, Michael},
  title         = {Flip Graphs with Symmetry and New Matrix Multiplication Schemes},
  booktitle     = {Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation (ISSAC '25)},
  pages         = {233--239},
  publisher     = {ACM},
  year          = {2025},
  doi           = {10.1145/3747199.3747566},
  eprint        = {2502.04514},
  archivePrefix = {arXiv}
}

@article{KauersWood2025consequences,
  author        = {Kauers, Manuel and Wood, Isaac},
  title         = {Consequences of the {Moosbauer}--{Poole} Algorithms},
  journal       = {ACM Communications in Computer Algebra},
  volume        = {59},
  number        = {4},
  pages         = {74--76},
  year          = {2025},
  doi           = {10.1145/3832046.3832048},
  eprint        = {2505.05896},
  archivePrefix = {arXiv}
}

@misc{KauersWood2025meta,
  author        = {Kauers, Manuel and Wood, Isaac},
  title         = {Exploring the Meta Flip Graph for Matrix Multiplication},
  year          = {2025},
  eprint        = {2510.19787},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2510.19787}
}


@phdthesis{Moosbauer2023thesis,
  author = {Moosbauer, Jakob},
  title  = {Search Techniques for Matrix Algorithms},
  school = {Johannes Kepler University Linz},
  year   = {2023},
  url    = {https://epub.jku.at/obvulihs/content/titleinfo/9217131}
}

@article{Pan1980,
  author  = {Pan, V. Ya.},
  title   = {New Fast Algorithms for Matrix Operations},
  journal = {SIAM Journal on Computing},
  volume  = {9},
  number  = {2},
  pages   = {321--342},
  year    = {1980},
  doi     = {10.1137/0209027}
}

@misc{MedleyEtAl2026,
  author        = {Medley, Zeke and Gokul, Anagha and Luu, Quan and Manolios, Panagiotis},
  title         = {{GPU}-Accelerated Search for Fast Matrix Multiplication over $\mathbb{F}_2$},
  year          = {2026},
  eprint        = {2609.17533},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2609.17533}
}


@article{Pan1966,
  author  = {Pan, V. Ya.},
  title   = {Methods of computing values of polynomials},
  journal = {Russian Mathematical Surveys},
  volume  = {21},
  number  = {1},
  pages   = {105--136},
  year    = {1966},
  doi     = {10.1070/RM1966v021n01ABEH004147}
}


@article{HopcroftKerr1971,
  author  = {Hopcroft, J. E. and Kerr, L. R.},
  title   = {On Minimizing the Number of Multiplications Necessary for Matrix Multiplication},
  journal = {SIAM Journal on Applied Mathematics},
  volume  = {20},
  number  = {1},
  pages   = {30--36},
  year    = {1971},
  doi     = {10.1137/0120004}
}

@article{JaJa1979,
  author  = {Ja'Ja', Joseph},
  title   = {Optimal Evaluation of Pairs of Bilinear Forms},
  journal = {SIAM Journal on Computing},
  volume  = {8},
  number  = {3},
  pages   = {443--462},
  year    = {1979},
  doi     = {10.1137/0208037}
}

@article{JaJaTakche1986,
  author  = {Ja'Ja', Joseph and Takche, Jean},
  title   = {On the Validity of the Direct Sum Conjecture},
  journal = {SIAM Journal on Computing},
  volume  = {15},
  number  = {4},
  pages   = {1004--1020},
  year    = {1986},
  doi     = {10.1137/0215071}
}

@article{Hastad1990,
  author  = {H{\aa}stad, Johan},
  title   = {Tensor rank is {NP}-complete},
  journal = {Journal of Algorithms},
  volume  = {11},
  number  = {4},
  pages   = {644--654},
  year    = {1990},
  doi     = {10.1016/0196-6774(90)90014-6}
}

@article{Strassen1983,
  author  = {Strassen, Volker},
  title   = {Rank and optimal computation of generic tensors},
  journal = {Linear Algebra and its Applications},
  volume  = {52/53},
  pages   = {645--685},
  year    = {1983},
  doi     = {10.1016/0024-3795(83)90041-1}
}

@article{Bshouty1989,
  author  = {Bshouty, Nader H.},
  title   = {A Lower Bound for Matrix Multiplication},
  journal = {SIAM Journal on Computing},
  volume  = {18},
  number  = {4},
  pages   = {759--765},
  year    = {1989},
  doi     = {10.1137/0218052}
}

@inproceedings{Blaser1999FOCS,
  author    = {Bl{\"a}ser, Markus},
  title     = {A $\frac{5}{2}n^2$-lower bound for the rank of $n\times n$-matrix multiplication over arbitrary fields},
  booktitle = {40th Annual Symposium on Foundations of Computer Science (FOCS '99)},
  pages     = {45--50},
  publisher = {IEEE Computer Society},
  year      = {1999},
  doi       = {10.1109/SFFCS.1999.814576}
}

@article{Blaser1999CC,
  author  = {Bl{\"a}ser, Markus},
  title   = {Lower bounds for the multiplicative complexity of matrix multiplication},
  journal = {Computational Complexity},
  volume  = {8},
  number  = {3},
  pages   = {203--226},
  year    = {1999},
  doi     = {10.1007/s000370050028}
}

@article{Blaser2003,
  author  = {Bl{\"a}ser, Markus},
  title   = {On the complexity of the multiplication of matrices of small formats},
  journal = {Journal of Complexity},
  volume  = {19},
  number  = {1},
  pages   = {43--60},
  year    = {2003},
  doi     = {10.1016/S0885-064X(02)00007-9}
}

@article{Blaser2013survey,
  author  = {Bl{\"a}ser, Markus},
  title   = {Fast Matrix Multiplication},
  journal = {Theory of Computing Graduate Surveys},
  volume  = {5},
  pages   = {1--60},
  year    = {2013},
  doi     = {10.4086/toc.gs.2013.005}
}

@incollection{Blaser2014explicit,
  author    = {Bl{\"a}ser, Markus},
  title     = {Explicit Tensors},
  booktitle = {Perspectives in Computational Complexity: The Somenath Biswas Anniversary Volume},
  editor    = {Agrawal, Manindra and Arvind, Vikraman},
  pages     = {117--130},
  publisher = {Springer International Publishing},
  address   = {Cham},
  year      = {2014},
  doi       = {10.1007/978-3-319-05446-9_6}
}

@article{Shpilka2003,
  author  = {Shpilka, Amir},
  title   = {Lower Bounds for Matrix Product},
  journal = {SIAM Journal on Computing},
  volume  = {32},
  number  = {5},
  pages   = {1185--1200},
  year    = {2003},
  doi     = {10.1137/S0097539702405954}
}

@inproceedings{AFT2011,
  author        = {Alexeev, Boris and Forbes, Michael A. and Tsimerman, Jacob},
  title         = {Tensor Rank: Some Lower and Upper Bounds},
  booktitle     = {2011 IEEE 26th Annual Conference on Computational Complexity (CCC)},
  pages         = {283--291},
  publisher     = {IEEE},
  year          = {2011},
  doi           = {10.1109/CCC.2011.28},
  eprint        = {1102.0072},
  archivePrefix = {arXiv}
}

@article{Landsberg2014rank,
  author        = {Landsberg, J. M.},
  title         = {New Lower Bounds for the Rank of Matrix Multiplication},
  journal       = {SIAM Journal on Computing},
  volume        = {43},
  number        = {1},
  pages         = {144--149},
  year          = {2014},
  doi           = {10.1137/120880276},
  eprint        = {1206.1530},
  archivePrefix = {arXiv}
}

@article{MassarentiRaviolo2013,
  author  = {Massarenti, Alex and Raviolo, Emanuele},
  title   = {The rank of $n\times n$ matrix multiplication is at least $3n^2-2\sqrt{2}n^{3/2}-3n$},
  journal = {Linear Algebra and its Applications},
  volume  = {438},
  number  = {11},
  pages   = {4500--4509},
  year    = {2013},
  doi     = {10.1016/j.laa.2013.01.031}
}

@article{MassarentiRaviolo2014corr,
  author  = {Massarenti, Alex and Raviolo, Emanuele},
  title   = {Corrigendum to ``{T}he rank of $n\times n$ matrix multiplication is at least $3n^2-2\sqrt{2}n^{3/2}-3n$''},
  journal = {Linear Algebra and its Applications},
  volume  = {445},
  pages   = {369--371},
  year    = {2014},
  doi     = {10.1016/j.laa.2013.12.009}
}

@article{LandsbergOttaviani2013,
  author        = {Landsberg, J. M. and Ottaviani, Giorgio},
  title         = {Equations for secant varieties of {V}eronese and other varieties},
  journal       = {Annali di Matematica Pura ed Applicata},
  volume        = {192},
  number        = {4},
  pages         = {569--606},
  year          = {2013},
  doi           = {10.1007/s10231-011-0238-6},
  eprint        = {1111.4567},
  archivePrefix = {arXiv}
}

@article{LandsbergOttaviani2015,
  author        = {Landsberg, J. M. and Ottaviani, Giorgio},
  title         = {New lower bounds for the border rank of matrix multiplication},
  journal       = {Theory of Computing},
  volume        = {11},
  pages         = {285--298},
  year          = {2015},
  doi           = {10.4086/toc.2015.v011a011},
  eprint        = {1112.6007},
  archivePrefix = {arXiv}
}

@article{LandsbergMichalek2017SIAGA,
  author        = {Landsberg, J. M. and Micha{\l}ek, Mateusz},
  title         = {On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry},
  journal       = {SIAM Journal on Applied Algebra and Geometry},
  volume        = {1},
  number        = {1},
  pages         = {2--19},
  year          = {2017},
  doi           = {10.1137/16M1067457},
  eprint        = {1601.08229},
  archivePrefix = {arXiv}
}

@article{LandsbergMichalek2018IMRN,
  author        = {Landsberg, J. M. and Micha{\l}ek, Mateusz},
  title         = {A $2n^2-\log_2(n)-1$ lower bound for the border rank of matrix multiplication},
  journal       = {International Mathematics Research Notices},
  volume        = {2018},
  number        = {15},
  pages         = {4722--4733},
  year          = {2018},
  doi           = {10.1093/imrn/rnx025},
  eprint        = {1608.07486},
  archivePrefix = {arXiv}
}

@article{LandsbergMichalek2017abelian,
  author        = {Landsberg, J. M. and Micha{\l}ek, Mateusz},
  title         = {Abelian tensors},
  journal       = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  volume        = {108},
  number        = {3},
  pages         = {333--371},
  year          = {2017},
  doi           = {10.1016/j.matpur.2016.11.004},
  eprint        = {1504.03732},
  archivePrefix = {arXiv}
}

@article{Farnsworth2016,
  author  = {Farnsworth, Cameron},
  title   = {{Koszul--Young} flattenings and symmetric border rank of the determinant},
  journal = {Journal of Algebra},
  volume  = {447},
  pages   = {664--676},
  year    = {2016},
  doi     = {10.1016/j.jalgebra.2015.11.011}
}

@article{BPR2020,
  author        = {Buczy{\'n}ski, Jaros{\l}aw and Postinghel, Elisa and Rupniewski, Filip},
  title         = {On {S}trassen's Rank Additivity for Small Three-way Tensors},
  journal       = {SIAM Journal on Matrix Analysis and Applications},
  volume        = {41},
  number        = {1},
  pages         = {106--133},
  year          = {2020},
  doi           = {10.1137/19M1243099},
  eprint        = {1902.06582},
  archivePrefix = {arXiv}
}

@article{GharahiLysikov2024,
  author        = {Gharahi, Masoud and Lysikov, Vladimir},
  title         = {Persistent Tensors and Multiqudit Entanglement Transformation},
  journal       = {Quantum},
  volume        = {8},
  pages         = {1238},
  year          = {2024},
  doi           = {10.22331/q-2024-01-31-1238},
  eprint        = {2211.00652},
  archivePrefix = {arXiv}
}

@misc{Shitov2016,
  author        = {Shitov, Yaroslav},
  title         = {How hard is the tensor rank?},
  year          = {2016},
  eprint        = {1611.01559},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:1611.01559}
}

@misc{Wang2026automated,
  author        = {Wang, Chengu},
  title         = {Automated Lower Bounds for Bilinear Complexity over Finite Fields},
  year          = {2026},
  eprint        = {2603.07280},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2603.07280}
}

@misc{Wang2026rank21,
  author        = {Wang, Chengu},
  title         = {A Lower Bound of 21 for $3\times 3$ Matrix Multiplication over $\mathbb{F}_2$},
  year          = {2026},
  eprint        = {2609.06725},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2609.06725}
}



@book{Landsberg2012TGA,
  author    = {Landsberg, J. M.},
  title     = {Tensors: Geometry and Applications},
  series    = {Graduate Studies in Mathematics},
  volume    = {128},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {2012},
  doi       = {10.1090/gsm/128}
}


@book{Landsberg2017GCT,
  author    = {Landsberg, J. M.},
  title     = {Geometry and Complexity Theory},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2017},
  doi       = {10.1017/9781108183192}
}

@book{BCS1997,
  author    = {B{\"u}rgisser, Peter and Clausen, Michael and Shokrollahi, M. Amin},
  title     = {Algebraic Complexity Theory},
  series    = {Grundlehren der mathematischen Wissenschaften},
  volume    = {315},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1997},
  doi       = {10.1007/978-3-662-03338-8}
}


@inproceedings{deMouraUllrich2021,
  author    = {de Moura, Leonardo and Ullrich, Sebastian},
  title     = {The {Lean} 4 Theorem Prover and Programming Language},
  booktitle = {Automated Deduction -- CADE 28},
  editor    = {Platzer, Andr{\'e} and Sutcliffe, Geoff},
  series    = {Lecture Notes in Computer Science},
  pages     = {625--635},
  publisher = {Springer},
  year      = {2021},
  doi       = {10.1007/978-3-030-79876-5_37}
}

@inproceedings{mathlib2020,
  author        = {{The mathlib Community}},
  title         = {The {Lean} Mathematical Library},
  booktitle     = {Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020)},
  pages         = {367--381},
  publisher     = {ACM},
  year          = {2020},
  doi           = {10.1145/3372885.3373824},
  eprint        = {1910.09336},
  archivePrefix = {arXiv}
}

@inproceedings{BiereEtAl2024CaDiCaL,
  author    = {Biere, Armin and Faller, Tobias and Fazekas, Katalin and Fleury, Mathias and Froleyks, Nils and Pollitt, Florian},
  title     = {{CaDiCaL} 2.0},
  booktitle = {Computer Aided Verification (CAV 2024)},
  editor    = {Gurfinkel, Arie and Ganesh, Vijay},
  series    = {Lecture Notes in Computer Science},
  pages     = {133--152},
  publisher = {Springer},
  year      = {2024},
  doi       = {10.1007/978-3-031-65627-9_7}
}


@inproceedings{BiereEtAl2020SATComp,
  author    = {Biere, Armin and Fazekas, Katalin and Fleury, Mathias and Heisinger, Maximilian},
  title     = {{CaDiCaL}, {Kissat}, {Paracooba}, {Plingeling} and {Treengeling} Entering the {SAT} {Competition} 2020},
  booktitle = {Proceedings of SAT Competition 2020 -- Solver and Benchmark Descriptions},
  editor    = {Balyo, Tomas and Froleyks, Nils and Heule, Marijn and Iser, Markus and J{\"a}rvisalo, Matti and Suda, Martin},
  series    = {Department of Computer Science Report Series B},
  volume    = {B-2020-1},
  pages     = {50--53},
  publisher = {University of Helsinki},
  year      = {2020}
}

@inproceedings{CruzFilipeEtAl2017LRAT,
  author    = {Cruz-Filipe, Lu{\'i}s and Heule, Marijn J. H. and Hunt, Warren A. and Kaufmann, Matt and Schneider-Kamp, Peter},
  title     = {Efficient Certified {RAT} Verification},
  booktitle = {Automated Deduction -- CADE 26},
  editor    = {de Moura, Leonardo},
  series    = {Lecture Notes in Computer Science},
  pages     = {220--236},
  publisher = {Springer},
  year      = {2017},
  doi       = {10.1007/978-3-319-63046-5_14}
}

@inproceedings{WetzlerHeuleHunt2014DRATtrim,
  author    = {Wetzler, Nathan and Heule, Marijn J. H. and Hunt, Warren A.},
  title     = {{DRAT-trim}: Efficient Checking and Trimming Using Expressive Clausal Proofs},
  booktitle = {Theory and Applications of Satisfiability Testing -- SAT 2014},
  editor    = {Sinz, Carsten and Egly, Uwe},
  series    = {Lecture Notes in Computer Science},
  pages     = {422--429},
  publisher = {Springer},
  year      = {2014},
  doi       = {10.1007/978-3-319-09284-3_31}
}


@misc{KauersSchemes444x47,
  author       = {Kauers, Manuel},
  title        = {Rank-47 multiplication schemes for $4\times 4$ matrices over $\mathbb{Z}_2$},
  howpublished = {Web directory, \url{http://www.algebra.uni-linz.ac.at/people/mkauers/matrix-mult/solutions/444/x47/}},
  note         = {99{,}101 scheme files dated 4 November 2022; accessed 23 October 2026},
  year         = {2022}
}

@misc{KauersSchemes444r47,
  author       = {Kauers, Manuel},
  title        = {Rank-47 multiplication schemes for $4\times 4$ matrices over $\mathbb{Z}_2$, directory \texttt{47}},
  howpublished = {Web directory, \url{http://www.algebra.uni-linz.ac.at/people/mkauers/matrix-mult/solutions/444/47/}},
  note         = {19 scheme files dated 6 to 29 October 2022; accessed 24 October 2026},
  year         = {2022}
}

@misc{KauersMoosbauerFlipsRepo,
  author       = {Moosbauer, Jakob},
  title        = {\texttt{flips} ({GitHub} repository)},
  howpublished = {\url{https://github.com/jakobmoosbauer/flips}},
  note         = {Repository cited in \cite{KauersMoosbauer2023flip}; contains \texttt{solutions/444-47-mod2.exp}},
  year         = {2022}
}

@misc{Tomar2026rank23,
  author        = {Tomar, Tejasvi Singh},
  title         = {The rank of $3\times 3$ matrix multiplication over $\mathbb{F}_2$ is $23$},
  year          = {2026},
  eprint        = {2610.11823},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2610.11823}
}


@misc{DAmbrosio2026,
  author       = {D'Ambrosio, Ian},
  title        = {The Exact {$\mathbb{F}_2$}-Rank of $2\times 3$ by $3\times 4$ Matrix Multiplication},
  howpublished = {Preprint, Zenodo},
  year         = {2026},
  doi          = {10.5281/zenodo.21895176}
}

@misc{YangEtAl2026,
  author        = {Yang, Shuxing and others},
  title         = {A Structural Proof of the Lower Bound 21 for $3\times 3$ Matrix Multiplication over {$\mathbb{F}_2$}},
  year          = {2026},
  eprint        = {2609.18722},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2609.18722}
}

@article{LempelWinograd1977,
  author  = {Lempel, Abraham and Winograd, Shmuel},
  title   = {A New Approach to Error-Correcting Codes},
  journal = {IEEE Transactions on Information Theory},
  volume  = {23},
  number  = {4},
  pages   = {503--508},
  year    = {1977},
  doi     = {10.1109/TIT.1977.1055735}
}

@article{BrockettDobkin1978,
  author  = {Brockett, Roger W. and Dobkin, David},
  title   = {On the Optimal Evaluation of a Set of Bilinear Forms},
  journal = {Linear Algebra and its Applications},
  volume  = {19},
  number  = {3},
  pages   = {207--235},
  year    = {1978},
  doi     = {10.1016/0024-3795(78)90012-5}
}

@article{Wei1991,
  author  = {Wei, Victor K.},
  title   = {Generalized {H}amming Weights for Linear Codes},
  journal = {IEEE Transactions on Information Theory},
  volume  = {37},
  number  = {5},
  pages   = {1412--1418},
  year    = {1991},
  doi     = {10.1109/18.133259}
}

@misc{Zaru2026,
  author       = {Zaru, Nadim F.},
  title        = {Exact Symmetry-Stratified Search for Fast Matrix Multiplication over {$\mathbb{F}_2$}: A Second Inequivalent Rank-47 Scheme for $4\times4$, Rigidity Theorems, and Large Same-Rank Families at $5\times5$ and $6\times6$},
  howpublished = {Zenodo, version 1.0.1},
  year         = {2026},
  doi          = {10.5281/zenodo.22823142}
}

@misc{Agarwal2026,
  author        = {Agarwal, Abhinav},
  title         = {Certified local rank and uniqueness barriers for a 48-term matrix-multiplication decomposition},
  year          = {2026},
  eprint        = {2609.13596},
  archivePrefix = {arXiv},
  howpublished  = {arXiv:2609.13596}
}