{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ISM2SGPCEZIXVJNECARCHYBB4X","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":"101c59032696eff0350d49b10b1c8616ae09b2d46db2691c9c9eb50536c35a40","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-05-29T10:41:03Z","title_canon_sha256":"8827c34e7c02dfb07d66037b6517918e56aafa6d58c251e1246fdf3346c9d42c"},"schema_version":"1.0","source":{"id":"1405.7517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7517","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7517v2","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7517","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"ISM2SGPCEZIX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ISM2SGPCEZIXVJNE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ISM2SGPC","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:4aeb3de4b3e8d993979332522993ca60293256ca9a934baafa3718aa428dfc8a","target":"graph","created_at":"2026-05-18T02:48:35Z","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 investigate the natural families of periodic orbits associated with the equilibrium configurations of the the planar restricted $1+n$ body problem for the case $2\\leq n \\leq 4$ equal mass satellites. Such periodic orbits can be used to model both trojan exoplanetary systems and parking orbits for captured asteroids within the solar system. For $n=2$ there are two families of periodic orbits associated with the equilibria of the system: the well known horseshoe and tadpole orbits. For $n=3$ there are three families that emanate from the equilibrium configurations of the satellites, while for","authors_text":"Colin McInnes, Patricia Verrier","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-05-29T10:41:03Z","title":"Periodic orbits for 3 and 4 co-orbital bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7517","kind":"arxiv","version":2},"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":"sha256:8f1161e990bee3c0b201e1b4c6dcd49ea191750a6a3ae0cef78bc0a140874442","target":"record","created_at":"2026-05-18T02:48:35Z","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":"101c59032696eff0350d49b10b1c8616ae09b2d46db2691c9c9eb50536c35a40","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-05-29T10:41:03Z","title_canon_sha256":"8827c34e7c02dfb07d66037b6517918e56aafa6d58c251e1246fdf3346c9d42c"},"schema_version":"1.0","source":{"id":"1405.7517","kind":"arxiv","version":2}},"canonical_sha256":"4499a919e226517aa5a4102223e021e5d1154a22240a7ed9bb53ad8373c6f856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4499a919e226517aa5a4102223e021e5d1154a22240a7ed9bb53ad8373c6f856","first_computed_at":"2026-05-18T02:48:35.676224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:35.676224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6USM6munB+SBvS5YPBokIJNB8/kOypzjOcSEuW73mqOxK4HTajDTA2+Ctj+/zIwPewSfw04QUXDFrDU6ldmpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:35.676894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f1161e990bee3c0b201e1b4c6dcd49ea191750a6a3ae0cef78bc0a140874442","sha256:4aeb3de4b3e8d993979332522993ca60293256ca9a934baafa3718aa428dfc8a"],"state_sha256":"c46d340f8dbfbace7f39b7e9f99bda5fa15b8f39b992f85ceaca3c9f4c40298e"}