{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZOX3TIC4B265V46MCVU4K3BDEJ","short_pith_number":"pith:ZOX3TIC4","canonical_record":{"source":{"id":"1807.06095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T20:26:53Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"0ef2f47f0d44443292219f00ec540cb375dfbb0c64721a52cf21ef01b0c29f4f","abstract_canon_sha256":"64a0831a3a5c3c7e87d972c8890b994bc24ac9b5e4bed1fafc7738e8853e9a6e"},"schema_version":"1.0"},"canonical_sha256":"cbafb9a05c0ebddaf3cc1569c56c23226b36f8e2ecb4ba9d47dcf8af16b3c660","source":{"kind":"arxiv","id":"1807.06095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06095","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06095v1","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06095","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZOX3TIC4B265","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZOX3TIC4B265V46M","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZOX3TIC4","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZOX3TIC4B265V46MCVU4K3BDEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T20:26:53Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"0ef2f47f0d44443292219f00ec540cb375dfbb0c64721a52cf21ef01b0c29f4f","abstract_canon_sha256":"64a0831a3a5c3c7e87d972c8890b994bc24ac9b5e4bed1fafc7738e8853e9a6e"},"schema_version":"1.0"},"canonical_sha256":"cbafb9a05c0ebddaf3cc1569c56c23226b36f8e2ecb4ba9d47dcf8af16b3c660","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:34.069775Z","signature_b64":"b4JvzZB5DZfHGiSl/TwP8RTgsdkhQcp6/bOLd8jAn/KesDG4VMXZ10JsRM57GCjLaqbevM9Jel2q7kYmS8UyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbafb9a05c0ebddaf3cc1569c56c23226b36f8e2ecb4ba9d47dcf8af16b3c660","last_reissued_at":"2026-05-18T00:10:34.069043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:34.069043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06095","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":"2026-05-18T00:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/lW5k2f9xe6FuJZw3lPW81ClelXgWzJuMC8r1YqfyiHQsdUVBPMXI0wxf7D7kr5ftOfDCM8sK6hAnttjLWGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:54:40.090538Z"},"content_sha256":"a0f3a7ab613c56063b4c496250c00c5f303b3ae947d9132324daf2db854ec488","schema_version":"1.0","event_id":"sha256:a0f3a7ab613c56063b4c496250c00c5f303b3ae947d9132324daf2db854ec488"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZOX3TIC4B265V46MCVU4K3BDEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear librations of distant retrograde orbits: a perturbative approach -- The Hill problem case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP"],"primary_cat":"math.DS","authors_text":"Martin Lara","submitted_at":"2018-07-16T20:26:53Z","abstract_excerpt":"The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear dynamics of the Hill problem close to the origin, and the libration point dynamics have been thoroughly investigated by perturbation methods. Out of the Hill sphere, the analytical approach is also feasible, at least in the case of distant retrograde orbits. Previous analytical investigations of this last case succeeded in the qualitative description of the dynamic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06095","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":"2026-05-18T00:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWPBToFZ0rr/sO1JP6xsqBc+AbPGf/GxTJRe0wXecUm2dWaeHqvptcr9gRhV29j+2TJR0rbkPut/+S8Sc/NOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:54:40.091264Z"},"content_sha256":"5b84d0b9c6408f8fb09ea4c261f615f0c19c4407bb8a42021e2650f7dea9c53e","schema_version":"1.0","event_id":"sha256:5b84d0b9c6408f8fb09ea4c261f615f0c19c4407bb8a42021e2650f7dea9c53e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/bundle.json","state_url":"https://pith.science/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/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":"2026-06-07T22:54:40Z","links":{"resolver":"https://pith.science/pith/ZOX3TIC4B265V46MCVU4K3BDEJ","bundle":"https://pith.science/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/bundle.json","state":"https://pith.science/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOX3TIC4B265V46MCVU4K3BDEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZOX3TIC4B265V46MCVU4K3BDEJ","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":"64a0831a3a5c3c7e87d972c8890b994bc24ac9b5e4bed1fafc7738e8853e9a6e","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T20:26:53Z","title_canon_sha256":"0ef2f47f0d44443292219f00ec540cb375dfbb0c64721a52cf21ef01b0c29f4f"},"schema_version":"1.0","source":{"id":"1807.06095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06095","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06095v1","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06095","created_at":"2026-05-18T00:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZOX3TIC4B265","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZOX3TIC4B265V46M","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZOX3TIC4","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:5b84d0b9c6408f8fb09ea4c261f615f0c19c4407bb8a42021e2650f7dea9c53e","target":"graph","created_at":"2026-05-18T00:10:34Z","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":"The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear dynamics of the Hill problem close to the origin, and the libration point dynamics have been thoroughly investigated by perturbation methods. Out of the Hill sphere, the analytical approach is also feasible, at least in the case of distant retrograde orbits. Previous analytical investigations of this last case succeeded in the qualitative description of the dynamic","authors_text":"Martin Lara","cross_cats":["astro-ph.EP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T20:26:53Z","title":"Nonlinear librations of distant retrograde orbits: a perturbative approach -- The Hill problem case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06095","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:a0f3a7ab613c56063b4c496250c00c5f303b3ae947d9132324daf2db854ec488","target":"record","created_at":"2026-05-18T00:10:34Z","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":"64a0831a3a5c3c7e87d972c8890b994bc24ac9b5e4bed1fafc7738e8853e9a6e","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T20:26:53Z","title_canon_sha256":"0ef2f47f0d44443292219f00ec540cb375dfbb0c64721a52cf21ef01b0c29f4f"},"schema_version":"1.0","source":{"id":"1807.06095","kind":"arxiv","version":1}},"canonical_sha256":"cbafb9a05c0ebddaf3cc1569c56c23226b36f8e2ecb4ba9d47dcf8af16b3c660","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbafb9a05c0ebddaf3cc1569c56c23226b36f8e2ecb4ba9d47dcf8af16b3c660","first_computed_at":"2026-05-18T00:10:34.069043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:34.069043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4JvzZB5DZfHGiSl/TwP8RTgsdkhQcp6/bOLd8jAn/KesDG4VMXZ10JsRM57GCjLaqbevM9Jel2q7kYmS8UyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:34.069775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0f3a7ab613c56063b4c496250c00c5f303b3ae947d9132324daf2db854ec488","sha256:5b84d0b9c6408f8fb09ea4c261f615f0c19c4407bb8a42021e2650f7dea9c53e"],"state_sha256":"728b33b5e934f5feaaaf5936e4ef24cbb8d358d3849232c896edb2b408bac556"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CnOGIpG3qJbMohpu7hfexI2eG0B5aKJTPOpg5TIUwAi2Yk1UzoXxXcPH3/kC8oZ0Kgmorxaf7e9ugmNB1YCZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:54:40.095639Z","bundle_sha256":"987ec6925bf9cf508d3b9ed3c9693887ede2c491dd351b55260554168178da64"}}