{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IPTTOT2CZ5E6F5RY6L7GHN2NAS","short_pith_number":"pith:IPTTOT2C","schema_version":"1.0","canonical_sha256":"43e7374f42cf49e2f638f2fe63b74d0485ec18e648b56621ff079f51d715b1c3","source":{"kind":"arxiv","id":"1702.03990","version":1},"attestation_state":"computed","paper":{"title":"Symmetries and choreographies in families bifurcating from the polygonal relative equilibrium of the $n$-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Garc\\'ia-Azpeitia, Eusebius Doedel, Renato Calleja","submitted_at":"2017-02-13T21:24:50Z","abstract_excerpt":"We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits. These arise from the polygonal system of $n$ bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship then the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along t"},"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":"1702.03990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-13T21:24:50Z","cross_cats_sorted":[],"title_canon_sha256":"c1778dcd85f3fb180b1bcf4cc361a4298d0e3f65841214b338ba5269fad1b9e4","abstract_canon_sha256":"4d4eff48e9312a4f18bdec1589ec7d7e4165f9ccc5030c7c7fcc9554c51eb8d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:04.352802Z","signature_b64":"rCIo9otohI5d9dGKCSKUGOntDOQIHy+551Qdey6j5ZE4HyvJfz+yul7H5ynJULP3fnqrTSl0yNE2AadwMFGaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43e7374f42cf49e2f638f2fe63b74d0485ec18e648b56621ff079f51d715b1c3","last_reissued_at":"2026-05-18T00:10:04.352073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:04.352073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries and choreographies in families bifurcating from the polygonal relative equilibrium of the $n$-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Garc\\'ia-Azpeitia, Eusebius Doedel, Renato Calleja","submitted_at":"2017-02-13T21:24:50Z","abstract_excerpt":"We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits. These arise from the polygonal system of $n$ bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship then the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03990","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.03990","created_at":"2026-05-18T00:10:04.352184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03990v1","created_at":"2026-05-18T00:10:04.352184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03990","created_at":"2026-05-18T00:10:04.352184+00:00"},{"alias_kind":"pith_short_12","alias_value":"IPTTOT2CZ5E6","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IPTTOT2CZ5E6F5RY","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IPTTOT2C","created_at":"2026-05-18T12:31:21.493067+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/IPTTOT2CZ5E6F5RY6L7GHN2NAS","json":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS.json","graph_json":"https://pith.science/api/pith-number/IPTTOT2CZ5E6F5RY6L7GHN2NAS/graph.json","events_json":"https://pith.science/api/pith-number/IPTTOT2CZ5E6F5RY6L7GHN2NAS/events.json","paper":"https://pith.science/paper/IPTTOT2C"},"agent_actions":{"view_html":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS","download_json":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS.json","view_paper":"https://pith.science/paper/IPTTOT2C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03990&json=true","fetch_graph":"https://pith.science/api/pith-number/IPTTOT2CZ5E6F5RY6L7GHN2NAS/graph.json","fetch_events":"https://pith.science/api/pith-number/IPTTOT2CZ5E6F5RY6L7GHN2NAS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS/action/storage_attestation","attest_author":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS/action/author_attestation","sign_citation":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS/action/citation_signature","submit_replication":"https://pith.science/pith/IPTTOT2CZ5E6F5RY6L7GHN2NAS/action/replication_record"}},"created_at":"2026-05-18T00:10:04.352184+00:00","updated_at":"2026-05-18T00:10:04.352184+00:00"}