{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W3LKEBR3UPT7AMB2RDDMQT2KGZ","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":"1333a8458ea076cbda090c987fe6fde4cb44204861469328e1a569a90efae216","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-17T19:57:47Z","title_canon_sha256":"92718f948d8b1334830b672a6c89304c94f8329148d60b1e15bfdbd51f10822c"},"schema_version":"1.0","source":{"id":"1311.4209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4209","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4209v1","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4209","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"W3LKEBR3UPT7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W3LKEBR3UPT7AMB2","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W3LKEBR3","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:240d32e934a0259f63fd9b88fc4a809204bbf2f7ec27c3dada4fde189a32a843","target":"graph","created_at":"2026-05-18T03:06:53Z","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 study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of symmetric periodic orbits, including ``Schubart-like\" orbits and brake orbits, by using topological shooting arguments.","authors_text":"Nai-Chia Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-17T19:57:47Z","title":"Symmetric Periodic Orbits in Three Sub-Problems of the N-body Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4209","kind":"arxiv","version":1},"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":"sha256:172038ba039403c2f6156338006ea9b0a35998130d6c763acc4a4141455fb270","target":"record","created_at":"2026-05-18T03:06:53Z","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":"1333a8458ea076cbda090c987fe6fde4cb44204861469328e1a569a90efae216","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-17T19:57:47Z","title_canon_sha256":"92718f948d8b1334830b672a6c89304c94f8329148d60b1e15bfdbd51f10822c"},"schema_version":"1.0","source":{"id":"1311.4209","kind":"arxiv","version":1}},"canonical_sha256":"b6d6a2063ba3e7f0303a88c6c84f4a364a7b0191ea5b561dfc9c8beec2992b32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6d6a2063ba3e7f0303a88c6c84f4a364a7b0191ea5b561dfc9c8beec2992b32","first_computed_at":"2026-05-18T03:06:53.307132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:53.307132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M10mW2ITh5oYlUD302B/iirpqgIp4n4zHClhf6REk0q6ikPRSzneBY9MOdcZSzK3x8JMl7mxBk1l6febNNRiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:53.307806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:172038ba039403c2f6156338006ea9b0a35998130d6c763acc4a4141455fb270","sha256:240d32e934a0259f63fd9b88fc4a809204bbf2f7ec27c3dada4fde189a32a843"],"state_sha256":"36ec784ee5e4f640d80d0427261b797eb2f823132d850522319c6bb51cca6eec"}