{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4EKZO56BWP62VLJWQ3SFBCCWS2","short_pith_number":"pith:4EKZO56B","schema_version":"1.0","canonical_sha256":"e1159777c1b3fdaaad3686e4508856968c5eb3a9224c17e307e7b26f6e058cbe","source":{"kind":"arxiv","id":"1107.2178","version":2},"attestation_state":"computed","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 $\\sum_{i<j} 1/|q_i-q_j|^2$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.2178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-12T01:57:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8dd5d0ae636318db313aa18a15c8969b1fb66677dc95a8c15387c705e67ede2d","abstract_canon_sha256":"d439cf9f5afac6701b4d3203204ddda1f69622de5b45f2e0bec1c0b1dec2c569"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:42.917081Z","signature_b64":"ArU0LUm8EgLc8OsLcotmet/M0+MnZteUmC8Aw7szUhTRzuHs/SH3eWNMINSHb7tEIw2iFOe0TtMo9N9L/ctoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1159777c1b3fdaaad3686e4508856968c5eb3a9224c17e307e7b26f6e058cbe","last_reissued_at":"2026-05-18T02:21:42.916691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:42.916691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1107.2178","created_at":"2026-05-18T02:21:42.916748+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.2178v2","created_at":"2026-05-18T02:21:42.916748+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2178","created_at":"2026-05-18T02:21:42.916748+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EKZO56BWP62","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EKZO56BWP62VLJW","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EKZO56B","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2","json":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2.json","graph_json":"https://pith.science/api/pith-number/4EKZO56BWP62VLJWQ3SFBCCWS2/graph.json","events_json":"https://pith.science/api/pith-number/4EKZO56BWP62VLJWQ3SFBCCWS2/events.json","paper":"https://pith.science/paper/4EKZO56B"},"agent_actions":{"view_html":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2","download_json":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2.json","view_paper":"https://pith.science/paper/4EKZO56B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.2178&json=true","fetch_graph":"https://pith.science/api/pith-number/4EKZO56BWP62VLJWQ3SFBCCWS2/graph.json","fetch_events":"https://pith.science/api/pith-number/4EKZO56BWP62VLJWQ3SFBCCWS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2/action/storage_attestation","attest_author":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2/action/author_attestation","sign_citation":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2/action/citation_signature","submit_replication":"https://pith.science/pith/4EKZO56BWP62VLJWQ3SFBCCWS2/action/replication_record"}},"created_at":"2026-05-18T02:21:42.916748+00:00","updated_at":"2026-05-18T02:21:42.916748+00:00"}