{"paper":{"title":"Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.AG"],"primary_cat":"cond-mat.soft","authors_text":"Danny Z. Chen, David J. Wales, Dhagash Mehta, Halim Kusumaatmaja, Jianxu Chen","submitted_at":"2016-05-26T21:57:11Z","abstract_excerpt":"The Thomson Problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here we show that the energy landscape of the Thomson Problem for $N$ particles with $N=132, 135, 138, 141, 144, 147$ and $150$ is single funnelled, characteristic of a structure-seeking organisation where the global minimum is easily accessible. Algorithmically constructing starting points close to the global minimum of such a potential with spherical constraints is one of Smale's 18 unsolved problems in mathematics for the 21st century because it is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08459","kind":"arxiv","version":2},"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"}