{"paper":{"title":"On a $K_4$-UH self-dual 1-configuration $(102_4)_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Italo J. Dejter","submitted_at":"2010-02-02T21:02:30Z","abstract_excerpt":"Self-dual 1-configurations $(n_d)_1$ possess their Menger graph $\\mathcal Y$ most $K_4$-separated among connected self-dual configurations $(n_d)$. Such $\\mathcal Y$ is most symmetric if $K_d$-ultrahomogeneous. In this work, such a $\\mathcal Y$ is presented for $(n,d)=(102,4)$ and shown to relate $n$ copies of the cuboctahedral graph $L(Q_3)$ to the $n$ copies of $K_d$; these are shown to share each copy of $K_3$ exactly with two copies of $L(Q_3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0588","kind":"arxiv","version":28},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}