{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IXQHGJ77NXCF62BNSJZVH6HDGF","short_pith_number":"pith:IXQHGJ77","canonical_record":{"source":{"id":"1905.03451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T06:23:28Z","cross_cats_sorted":[],"title_canon_sha256":"ed31b801c8ad15875ae3b71472774b23d97805d7f62ea210721963e9ead39d67","abstract_canon_sha256":"9d64ec7f355a383831597af9f1bae04495bde4536242e30bc790c44f7d8cdc6b"},"schema_version":"1.0"},"canonical_sha256":"45e07327ff6dc45f682d927353f8e33145af6ffbc2941b591058753051297fc4","source":{"kind":"arxiv","id":"1905.03451","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03451","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03451v1","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03451","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"IXQHGJ77NXCF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IXQHGJ77NXCF62BN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IXQHGJ77","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IXQHGJ77NXCF62BNSJZVH6HDGF","target":"record","payload":{"canonical_record":{"source":{"id":"1905.03451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T06:23:28Z","cross_cats_sorted":[],"title_canon_sha256":"ed31b801c8ad15875ae3b71472774b23d97805d7f62ea210721963e9ead39d67","abstract_canon_sha256":"9d64ec7f355a383831597af9f1bae04495bde4536242e30bc790c44f7d8cdc6b"},"schema_version":"1.0"},"canonical_sha256":"45e07327ff6dc45f682d927353f8e33145af6ffbc2941b591058753051297fc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:39.850427Z","signature_b64":"k+k8100PMCT7fO8wHN4R/qPEOKUgqpiXX7yXGg1DdMlDhNhppT2dAErra8uQw4mojurjvdxLwPwrCPCtRtszAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45e07327ff6dc45f682d927353f8e33145af6ffbc2941b591058753051297fc4","last_reissued_at":"2026-05-17T23:46:39.849650Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:39.849650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.03451","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahAdNPHvWrNkEJZx7BVVwC3f5j+sz407bUpCv82XgmiLuk8YbcIs4mouQM5lmfMIRbpXQb00at+D0Jo0VLjaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:22.758070Z"},"content_sha256":"1154c702c939cb108d42e395e9089b80488cce8e0e091ec04e74776f5ad32e81","schema_version":"1.0","event_id":"sha256:1154c702c939cb108d42e395e9089b80488cce8e0e091ec04e74776f5ad32e81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IXQHGJ77NXCF62BNSJZVH6HDGF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Meirong Zhang, Xiuli Cen, Xuhua Cheng, Zaitang Huang","submitted_at":"2019-05-09T06:23:28Z","abstract_excerpt":"Motivated by the recent works on the stability of symmetric periodic orbits of the elliptic Sitnikov problem, for time-periodic Newtonian equations with symmetries, we will study symmetric periodic solutions which are emanated from nonconstant periodic solutions of autonomous equations. By using the theory of Hill's equations, we will first deduce in this paper a criterion for the linearized stability and instability of periodic solutions which are odd in time. Such a criterion is complementary to that for periodic solutions which are even in time, obtained recently by the present authors. App"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03451","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJa2Ejhs7WGLqWyNIhORfhs+I2jptOfmpfd3BZSaWtQ30khqV+IlOnd87WUqr8HX4cYtRewdWFrIZ6B/YJpwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:22.758746Z"},"content_sha256":"f1cdec3d7b392c7203a87f66b0a31cd76ee028189dbab34703b4451de54a8187","schema_version":"1.0","event_id":"sha256:f1cdec3d7b392c7203a87f66b0a31cd76ee028189dbab34703b4451de54a8187"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/bundle.json","state_url":"https://pith.science/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T01:36:22Z","links":{"resolver":"https://pith.science/pith/IXQHGJ77NXCF62BNSJZVH6HDGF","bundle":"https://pith.science/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/bundle.json","state":"https://pith.science/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXQHGJ77NXCF62BNSJZVH6HDGF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IXQHGJ77NXCF62BNSJZVH6HDGF","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":"9d64ec7f355a383831597af9f1bae04495bde4536242e30bc790c44f7d8cdc6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T06:23:28Z","title_canon_sha256":"ed31b801c8ad15875ae3b71472774b23d97805d7f62ea210721963e9ead39d67"},"schema_version":"1.0","source":{"id":"1905.03451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03451","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03451v1","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03451","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"IXQHGJ77NXCF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IXQHGJ77NXCF62BN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IXQHGJ77","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:f1cdec3d7b392c7203a87f66b0a31cd76ee028189dbab34703b4451de54a8187","target":"graph","created_at":"2026-05-17T23:46:39Z","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":"Motivated by the recent works on the stability of symmetric periodic orbits of the elliptic Sitnikov problem, for time-periodic Newtonian equations with symmetries, we will study symmetric periodic solutions which are emanated from nonconstant periodic solutions of autonomous equations. By using the theory of Hill's equations, we will first deduce in this paper a criterion for the linearized stability and instability of periodic solutions which are odd in time. Such a criterion is complementary to that for periodic solutions which are even in time, obtained recently by the present authors. App","authors_text":"Meirong Zhang, Xiuli Cen, Xuhua Cheng, Zaitang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T06:23:28Z","title":"On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03451","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":"sha256:1154c702c939cb108d42e395e9089b80488cce8e0e091ec04e74776f5ad32e81","target":"record","created_at":"2026-05-17T23:46:39Z","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":"9d64ec7f355a383831597af9f1bae04495bde4536242e30bc790c44f7d8cdc6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T06:23:28Z","title_canon_sha256":"ed31b801c8ad15875ae3b71472774b23d97805d7f62ea210721963e9ead39d67"},"schema_version":"1.0","source":{"id":"1905.03451","kind":"arxiv","version":1}},"canonical_sha256":"45e07327ff6dc45f682d927353f8e33145af6ffbc2941b591058753051297fc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45e07327ff6dc45f682d927353f8e33145af6ffbc2941b591058753051297fc4","first_computed_at":"2026-05-17T23:46:39.849650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:39.849650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+k8100PMCT7fO8wHN4R/qPEOKUgqpiXX7yXGg1DdMlDhNhppT2dAErra8uQw4mojurjvdxLwPwrCPCtRtszAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:39.850427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1154c702c939cb108d42e395e9089b80488cce8e0e091ec04e74776f5ad32e81","sha256:f1cdec3d7b392c7203a87f66b0a31cd76ee028189dbab34703b4451de54a8187"],"state_sha256":"b51a389d8603b1c7cd153d9e021744acf244075de7d25fbdf7f68f02b40e460b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iI9SeAj7Fz7+AE+dpj+tftk7INDc1kMrlf7bb5ddBF88PyNonAw5pZ09BjO3ftmKY5jNSVAmWtgIM3jD7U8hCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:36:22.762232Z","bundle_sha256":"16590c4b771ddd7bf221a0d4d2905d588db3890321071b9a8a31b289e89db731"}}