The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
A FORMAL PROOF OF THE KEPLER CONJECTURE
Open accessAbstract
This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.
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Cites
Introduction to Interval Analysis
Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898717716 · Cited by 2,591
Klein, G., Elphinstone, K., Heiser, G., Andronick, J., Cock, D., Derrin, P., Elkaduwe, D., Engelhardt, K., Kolanski, R., Norrish, M., et al. (2009) · Proceedings of the ACM SIGOPS 22nd symposium on Operating systems principles · doi:10.1145/1629575.1629596 · Cited by 1,633
(2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-45949-9 · Cited by 1,629
Introduction to HOL: a theorem proving environment for higher order logic
Gordon, M., & Melham, T. (1993) · Cambridge University Press eBooks · Cited by 1,299
A proof of the Kepler conjecture
Hales, T. (2005) · Annals of Mathematics · doi:10.4007/annals.2005.162.1065 · Cited by 992
Self-citationGNU Parallel: The Command-Line Power Tool.
Tange, O. (2011) · ;login:: the magazine of USENIX & SAGE · Cited by 905
Formal certification of a compiler back-end or: programming a compiler with a proof assistant
Leroy, X. (2006) · Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages · doi:10.1145/1111037.1111042 · Cited by 661
Gordon, M. J., Milner, A. J., & Wadsworth, C. P. (1979) · Lecture Notes in Computer Science · doi:10.1007/3-540-09724-4 · Cited by 628
Edinburgh LCF: A mechanised logic of computation
Gordon, M. J. C. (1979) · Medical Entomology and Zoology · Cited by 580
Lagerungen in der Ebene auf der Kugel und im Raum
Tóth, L. F. (1972) · Springer eBooks · doi:10.1007/978-3-642-65234-9 · Cited by 578
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HyperTree Proof Search for Neural Theorem Proving
Lample, G., Lacroix, T., Lachaux, M.-A., Rodriguez, A., Hayat, A., Lavril, T., Ebner, G., & Martinet, X. (2022) · Advances in Neural Information Processing Systems 35 · doi:10.52202/068431-1910 · Cited by 45
HyperTree Proof Search for Neural Theorem Proving
Lample, G., Lachaux, M.-A., Lavril, T., Martinet, X., Hayat, A., Ebner, G., Rodriguez, A., & Lacroix, T. (2022) · arXiv · doi:10.48550/arxiv.2205.11491 · Cited by 45
INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving
Wu, Y., Jiang, A. Q., Ba, J., & Grosse, R. (2020) · arXiv · doi:10.48550/arxiv.2007.02924 · Cited by 30
A Promising Path Towards Autoformalization and General Artificial Intelligence
Szegedy, C. (2020) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-53518-6_1 · Cited by 29
Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofs
Cunningham, G., Bunescu, R. C., & Juedes, D. (2023) · arXiv · doi:10.48550/arxiv.2301.02195 · Cited by 10
Metadata
- Authors
- HALES, T., ADAMS, M., BAUER, G., DANG, T. D., HARRISON, J., HOANG, L. T., KALISZYK, C., MAGRON, V., MCLAUGHLIN, S., NGUYEN, T. T., NGUYEN, Q. T., NIPKOW, T., OBUA, S., PLESO, J., RUTE, J., SOLOVYEV, A., TA, T. H. A., TRAN, N. T., TRIEU, T. D., URBAN, J., VU, K., & ZUMKELLER, R.
- Venue
- Forum of Mathematics, Pi
- Publisher
- Cambridge University Press (CUP)
- Published
- 2017
- Volume
- 5
- ISSN
- 2050-5086 (ISSN-L)
- OpenAlex
- W1825294361
- Cited by
- 342
- References
- 23
- FWCI
- 19.68
- Type
- journal article
- Language
- en
- Open access
- gold
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- The paper
- HALES, T., ADAMS, M., BAUER, G., DANG, T. D., HARRISON, J., HOANG, L. T., KALISZYK, C., MAGRON, V., MCLAUGHLIN, S., NGUYEN, T. T., NGUYEN, Q. T., NIPKOW, T., OBUA, S., PLESO, J., RUTE, J., SOLOVYEV, A., TA, T. H. A., TRAN, N. T., TRIEU, T. D., . . . ZUMKELLER, R. (2017). A FORMAL PROOF OF THE KEPLER CONJECTURE. Forum of Mathematics, Pi. https://doi.org/10.1017/fmp.2017.1
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
