{"paper":{"title":"Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Tetsuya Taniguchi, Toshiaki Fujiwara","submitted_at":"2015-03-02T03:52:30Z","abstract_excerpt":"Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, $U=\\alpha^{-1}\\sum m_i m_j/r_{ij}^\\alpha$ for $\\alpha\\ne 0$, a motion having constant configurational measure $\\mu=I^{\\alpha/2}U$ is homographic, where $I$ represents the moment of inertia defined by $I=\\sum m_i m_j r_{ij}^2/\\sum m_k$, $m_i$ the mass, and $r_{ij}$ the distance between particles.\n  We prove this conjecture for general masses $m_k>0$ in the planar three-body problem under Newton potential ($\\alpha=1$) and a strong force potential ($\\alpha=2$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00407","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"}