{"paper":{"title":"Structure of kissing arrangements in ${\\mathbb R}^{12}$ and a place for the $841$st sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rustem Takhanov, Stanislav Yun, Zhenisbek Assylbekov","submitted_at":"2026-06-17T12:05:28Z","abstract_excerpt":"Most currently known kissing arrangements of size $840$ in $\\mathbb R^{12}$ share a common structure. They consist of $60$ vectors supported on $\\mathbb R^6\\times\\{\\mathbf 0\\}$, another $60$ vectors supported on $\\{\\mathbf 0\\}\\times\\mathbb R^6$, and $720$ additional \\emph{bridge vectors}. The bridge vectors encode the interaction between the two six-dimensional factors and are constructed from the unique $1$-factorization of the complete graph $K_6$.\n  In this paper we investigate kissing arrangements of this type while keeping the bridge vectors fixed. We show that each $60$-point block admit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18984","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18984/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}