Explicit near-D5 local results for the five-dimensional kissing number (computer-assisted, unreviewed)
Abstract
Computer-assisted, exact-arithmetic local results for the kissing problem in dimension 5. If 36 (resp. 35, 34) points of a 5-dimensional kissing configuration lie within distance 1/18 (resp. 1/35, 1/44) of distinct D5 root directions, after one common rotation, then the configuration has at most 40 points. The bundle also contains moving-33 at radius 1/174, a D4-core result at radius 1/24, and a conditional bridge from pairwise angles to a common D5 frame. It includes two papers (PDF), exact certificates, and independent checkers (cddlib and lrs). The known bounds 40 <= tau_5 <= 44 are unchanged.
The project was initiated and directed by Uchral Nyam-Osor. The mathematics and computation were carried out by the AI systems Claude (Anthropic) and ChatGPT (OpenAI), each checking the other with independent code. No mathematician has reviewed this work yet.
Contact: [email protected]
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BibTeX
@misc{nyamosor2026explicit,
title = {{Explicit near-D5 local results for the five-dimensional kissing number (computer-assisted, unreviewed)}},
author = {Uchral Nyam-Osor},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23478579},
url = {https://zenodo.org/records/23478579},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit near-D5 local results for the five-dimensional kissing number (computer-assisted, unreviewed)
AU - Uchral Nyam-Osor
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23478579
UR - https://zenodo.org/records/23478579
AB - Computer-assisted, exact-arithmetic local results for the kissing problem in dimension 5. If 36 (resp. 35, 34) points of a 5-dimensional kissing configuration lie within distance 1/18 (resp. 1/35, 1/44) of distinct D5 root directions, after one common rotation, then the configuration has at most 40 points. The bundle also contains moving-33 at radius 1/174, a D4-core result at radius 1/24, and a conditional bridge from pairwise angles to a common D5 frame. It includes two papers (PDF), exact certificates, and independent checkers (cddlib and lrs). The known bounds 40 <= tau_5 <= 44 are unchanged. The project was initiated and directed by Uchral Nyam-Osor. The mathematics and computation were carried out by the AI systems Claude (Anthropic) and ChatGPT (OpenAI), each checking the other with independent code. No mathematician has reviewed this work yet. Contact: [email protected]
ER -