{"paper":{"title":"The Gregory-Newton Problem for Kissing Sticky Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"physics.atm-clus","authors_text":"Lukas Trombach, Peter Schwerdtfeger","submitted_at":"2018-08-09T00:58:26Z","abstract_excerpt":"All possible non-isomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model, and subsequently projected by geometry optimization onto a set of structures derived from an attractive Lennard-Jones (LJ) type of potential. It is shown that all 737 derived SHS contact graphs corresponding to the 12 outer spheres are (edge-induced) subgraphs of the icosahedral graph. The most widely used LJ(6,12) potential has only one minimum structure corresponding to the ideal icosahedron where the 12 outer spheres do not touch e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02982","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":""},"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"}