{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZYN2UDPRAOVFKRSKVKCNCYRHQR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"77208110d07e35fe2f1fd4293e9ff182eb7045da5a97da5070db9c7a34657d4c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-27T14:19:52Z","title_canon_sha256":"48e29f54a2e15fa940bc8611149765e29febb7b9bffa5a082ce98957a5a3abcc"},"schema_version":"1.0","source":{"id":"1606.08760","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08760","created_at":"2026-05-17T23:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08760v3","created_at":"2026-05-17T23:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08760","created_at":"2026-05-17T23:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZYN2UDPRAOVF","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZYN2UDPRAOVFKRSK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZYN2UDPR","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:848a9a94a48d0161cdd5c49e23b42d5dd62d7879cd112b38ae17987c9396b540","target":"graph","created_at":"2026-05-17T23:57:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We report on figure-eight choreographic solutions to a system of three identical particles interacting through a potential of Lennard-Jones type, $1/r^{12}-1/r^6$ where $r$ is a distance between the particles. By numerical search, we found there are a multitude of such solutions. A series of them are close to a figure-eight solutions to a homogeneous system with no $1/r^{12}$ term in the potential. The rest are very different from them and have several points with large curvatures in their figure-eight orbits, at which particles are repelled. Here figure-eight choreographies are the periodic m","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Toshiaki Fujiwara","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-27T14:19:52Z","title":"Figure-eight choreographies of the equal mass three-body problem with Lennard-Jones-type potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08760","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1cb162ef57a899953c660844b543e911b3fae4526408ae9a9c56dafeda95d0f0","target":"record","created_at":"2026-05-17T23:57:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"77208110d07e35fe2f1fd4293e9ff182eb7045da5a97da5070db9c7a34657d4c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-27T14:19:52Z","title_canon_sha256":"48e29f54a2e15fa940bc8611149765e29febb7b9bffa5a082ce98957a5a3abcc"},"schema_version":"1.0","source":{"id":"1606.08760","kind":"arxiv","version":3}},"canonical_sha256":"ce1baa0df103aa55464aaa84d16227847e8606d171a6967107f427221a142e2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce1baa0df103aa55464aaa84d16227847e8606d171a6967107f427221a142e2f","first_computed_at":"2026-05-17T23:57:00.942715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:00.942715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9RP4rvRE4a6EOaEuvJOeecqcRyyx0xnwFvDoRQ9CrR+QI7/9Kui50noDHYEhkIC2O98hPy6TU4tAlOUrQKwgBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:00.943345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08760","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cb162ef57a899953c660844b543e911b3fae4526408ae9a9c56dafeda95d0f0","sha256:848a9a94a48d0161cdd5c49e23b42d5dd62d7879cd112b38ae17987c9396b540"],"state_sha256":"0fda8d09be7a070dd18ebaaa30688a7ff56192a741f8c5484cd7c674194d48b9"}