If you use this repository — code, data, methodology, or findings — please cite the project together with the upstream works it builds on. The independent contribution of this repository is the byte-exact reproduction of the Zinoviev–Ericson 1999 configuration, the structural findings F-frente-A/B-1..6 on dim-13 saturation, the rare-paths doctrine, and the dual Constructor/Auditor methodology with both-hats discipline. The world-record kissing number K(13) ≥ 1154 is due to Zinoviev and Ericson and should always be cited alongside.
@misc{amichisluengo2026_kissing13,
author = {Amichis Luengo, Rafael},
title = {Kissing Number $K(13)$: An Independent Reproduction
and Structural Analysis. Project LUNA},
year = {2026},
month = may,
howpublished = {GitHub repository},
url = {https://github.com/REPLACE_WITH_YOUR_USERNAME/kissing-number-13-zinoviev-ericson-reproduction},
note = {First independent byte-exact reproduction of the
Zinoviev--Ericson 1999 K(13) = 1154 configuration in
$\mathbb{R}^{13}$; thirteen paper-grade structural
findings on dim-13 saturation; rare-paths doctrine
codified}
}Amichis Luengo, R. (2026). Kissing Number K(13): An Independent Reproduction and Structural Analysis. Project LUNA [GitHub repository]. https://github.com/REPLACE_WITH_YOUR_USERNAME/kissing-number-13-zinoviev-ericson-reproduction
[1] R. Amichis Luengo, "Kissing Number K(13): An Independent Reproduction and Structural Analysis. Project LUNA," GitHub repository, May 2026. [Online]. Available: https://github.com/REPLACE_WITH_YOUR_USERNAME/kissing-number-13-zinoviev-ericson-reproduction
Amichis Luengo, Rafael. "Kissing Number K(13): An Independent Reproduction and Structural Analysis. Project LUNA." GitHub repository. May 2026. https://github.com/REPLACE_WITH_YOUR_USERNAME/kissing-number-13-zinoviev-ericson-reproduction.
If you cite this repository, please also cite the upstream work it depends on:
@article{zinoviev1999_kissing,
author = {Zinoviev, V. A. and Ericson, T.},
title = {New lower bounds for contact numbers in small dimensions},
journal = {Problems of Information Transmission},
year = {1999},
volume = {35},
number = {4},
pages = {287--294}
}@article{delaat2024_kissing,
author = {de Laat, David and Leijenhorst, Nando},
title = {Solving clustered low-rank semidefinite programs arising
from polynomial optimization},
journal = {Mathematical Programming Computation},
year = {2024},
note = {Achieves $K(13) \leq 2064$ via quadruple-precision SDP on
the Cohn--Elkies linear programming bound},
eprint = {2202.12077},
archivePrefix = {arXiv}
}@article{cohn2003_lpbounds,
author = {Cohn, Henry and Elkies, Noam},
title = {New upper bounds on sphere packings I},
journal = {Annals of Mathematics},
year = {2003},
volume = {157},
number = {2},
pages = {689--714}
}@book{conway1999_splag,
author = {Conway, John H. and Sloane, Neil J. A.},
title = {Sphere Packings, Lattices and Groups},
edition = {3},
publisher = {Springer-Verlag},
year = {1999},
isbn = {978-0-387-98585-5}
}@article{brouwer2011_codes,
author = {Brouwer, Andries E. and Etzion, Tuvi},
title = {Some new distance-4 constant weight codes},
journal = {Advances in Mathematics of Communications},
year = {2011},
volume = {5},
number = {3},
pages = {417--424}
}@inproceedings{hanani1975_sqs,
author = {Hanani, Haim},
title = {Truncated finite planes},
booktitle = {Proceedings of Symposia in Pure Mathematics},
year = {1975}
}@misc{cohn_kissing_tables,
author = {Cohn, Henry},
title = {Spherical codes and kissing-number tables},
howpublished = {MIT mathematics, online archive},
note = {File \texttt{dimensions1-24.txt} contains the
Zinoviev--Ericson $K(13) = 1154$ configuration
reproduced byte-exact in this repository},
url = {https://hdl.handle.net/1721.1/153312}
}@misc{cohnli2024_kissing,
author = {Cohn, Henry and Li, Shiyu},
title = {Sphere packings and kissing numbers in dimensions
17 to 21},
year = {2024},
eprint = {2411.04916},
archivePrefix = {arXiv}
}A pragmatic guide:
- If you cite the 1154 record itself: cite Zinoviev–Ericson 1999. This repository is a verification artifact, not the original work.
- If you reproduce the configuration using this repository's code: cite both Zinoviev–Ericson 1999 (the construction) and this repository (the reproduction software).
- If you cite the F58 universal-sink law, the 2²⁶⁴ Steiner-equivalent enjambre, or any other F-frente-A/B-1..6 finding: cite this repository and
PAPER_TERMINAL.mdfor the specific section. - If you cite the rare-paths doctrine: cite this repository (the doctrine is original to it).
- If you cite the dual Constructor/Auditor methodology with both-hats discipline: cite this repository (the methodology is original to it).
- If you cite the upper bound K(13) ≤ 2064: cite De Laat–Leijenhorst 2024. This repository reproduces the Cohn–Elkies linear programming bound K(13) ≤ 2233.6 independently as a consistency check but does not contribute to the upper-bound story.
- Architect: Rafael Amichis Luengo (Madrid, Spain).
- AI partners: Anthropic Claude Opus 4.7, in dual Constructor/Auditor roles. The contractual contributions of each Claude instance to specific findings are documented in the authorship lists of
PAPER_TERMINAL.mdandCLOSURE_DIM13.md. - Project name: LUNA (sister of Estrella / Sobol Campaign and Diamond / coding-theory project).
- Status at closure: Project closed May 2026 with the world record K(13) = 1154 not beaten; four rare-path veins documented as open research directions.
This work was conducted independently, without institutional funding, on a Mac M2 laptop at 25% single-thread CPU. There are no conflicts of interest to declare.