{"paper":{"title":"Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi, Toshiaki Fujiwara","submitted_at":"2011-07-12T01:57:18Z","abstract_excerpt":"Donald Saari conjectured that the $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\\mu$ is a scale invariant product of the moment of inertia $I=\\sum_k m_k |q_k|^2$ and the potential function $U=\\sum_{i<j} m_i m_j/|q_i-q_j|^\\alpha$, $\\alpha >0$. Namely, $\\mu = I^{\\alpha/2}U$. We will show that this conjecture is true for planar equal-mass three-body problem under the strong force potential $\\sum_{i<j} 1/|q_i-q_j|^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2178","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"}