{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:X3VDAF3WSCFDSQ5TMXHTW2FIGG","short_pith_number":"pith:X3VDAF3W","canonical_record":{"source":{"id":"1806.08869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-06-22T22:26:18Z","cross_cats_sorted":[],"title_canon_sha256":"e78e84faa600c41537e86bf90201358d195d9bde7046c33f4d0fcc46c4c74421","abstract_canon_sha256":"746ae50baa6d47821e4d66aadd34e533f7a6e1c06d6f693e94e06cde491a6e6f"},"schema_version":"1.0"},"canonical_sha256":"beea301776908a3943b365cf3b68a831873c66d935217c9a2fe444f20bf496a3","source":{"kind":"arxiv","id":"1806.08869","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08869","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08869v1","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08869","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"X3VDAF3WSCFD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X3VDAF3WSCFDSQ5T","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X3VDAF3W","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:X3VDAF3WSCFDSQ5TMXHTW2FIGG","target":"record","payload":{"canonical_record":{"source":{"id":"1806.08869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-06-22T22:26:18Z","cross_cats_sorted":[],"title_canon_sha256":"e78e84faa600c41537e86bf90201358d195d9bde7046c33f4d0fcc46c4c74421","abstract_canon_sha256":"746ae50baa6d47821e4d66aadd34e533f7a6e1c06d6f693e94e06cde491a6e6f"},"schema_version":"1.0"},"canonical_sha256":"beea301776908a3943b365cf3b68a831873c66d935217c9a2fe444f20bf496a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:48.534901Z","signature_b64":"2UVVT/gRO6tdwpsW3SjOtsqCv1jlOVhDhaeCnswqCzcYCsd3c0X6shWU9rFYxlouW+xmxs744P/ge/FNhsYaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beea301776908a3943b365cf3b68a831873c66d935217c9a2fe444f20bf496a3","last_reissued_at":"2026-05-18T00:04:48.534148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:48.534148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.08869","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":"2026-05-18T00:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVgSAmB3fC6hDL9yqtrVHPqlhs9WUAITKiVcXRZQqF/fL5lG3NYPruPf7uSv76hTStR2Rf0oE3eSamhANycIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:41:30.291199Z"},"content_sha256":"3d911f8fb0be2b17badcad95c060475cd6f474c04c909c621c0d49b56a4c0838","schema_version":"1.0","event_id":"sha256:3d911f8fb0be2b17badcad95c060475cd6f474c04c909c621c0d49b56a4c0838"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:X3VDAF3WSCFDSQ5TMXHTW2FIGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hill stability in the AMD framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Antoine C. Petit, Gwena\\\"el Bou\\'e, Jacques Laskar","submitted_at":"2018-06-22T22:26:18Z","abstract_excerpt":"In a two-planet system, due to Sundman (1912) inequality, a topological boundary can forbid close encounters between the two planets for infinite time. A system is said Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extra solar planets dynamics. However people often use the coplanar and circular orbits approximation.\n  In this paper, we explain how the Hill stability can be understood in the framework of Angular Momentum Deficit (AMD). In the secular approximation, the AMD allows to discriminate between a priori stable systems and systems f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08869","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":"2026-05-18T00:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/Q2eQHSpZRnQhVQn4bAQlYpoohUmFXJORd7AF7FYWG5EGYBUa4CE7iNLLpbyY1AYwC10et649PrEzGIHqd4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:41:30.291903Z"},"content_sha256":"e56246eaab706d670b60384c7af16a2b174c3f00a88e60db3e031d0854bd3ae1","schema_version":"1.0","event_id":"sha256:e56246eaab706d670b60384c7af16a2b174c3f00a88e60db3e031d0854bd3ae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/bundle.json","state_url":"https://pith.science/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/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":"2026-05-27T16:41:30Z","links":{"resolver":"https://pith.science/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG","bundle":"https://pith.science/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/bundle.json","state":"https://pith.science/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3VDAF3WSCFDSQ5TMXHTW2FIGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X3VDAF3WSCFDSQ5TMXHTW2FIGG","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":"746ae50baa6d47821e4d66aadd34e533f7a6e1c06d6f693e94e06cde491a6e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-06-22T22:26:18Z","title_canon_sha256":"e78e84faa600c41537e86bf90201358d195d9bde7046c33f4d0fcc46c4c74421"},"schema_version":"1.0","source":{"id":"1806.08869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08869","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08869v1","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08869","created_at":"2026-05-18T00:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"X3VDAF3WSCFD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X3VDAF3WSCFDSQ5T","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X3VDAF3W","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:e56246eaab706d670b60384c7af16a2b174c3f00a88e60db3e031d0854bd3ae1","target":"graph","created_at":"2026-05-18T00:04:48Z","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":"In a two-planet system, due to Sundman (1912) inequality, a topological boundary can forbid close encounters between the two planets for infinite time. A system is said Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extra solar planets dynamics. However people often use the coplanar and circular orbits approximation.\n  In this paper, we explain how the Hill stability can be understood in the framework of Angular Momentum Deficit (AMD). In the secular approximation, the AMD allows to discriminate between a priori stable systems and systems f","authors_text":"Antoine C. Petit, Gwena\\\"el Bou\\'e, Jacques Laskar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-06-22T22:26:18Z","title":"Hill stability in the AMD framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08869","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":"sha256:3d911f8fb0be2b17badcad95c060475cd6f474c04c909c621c0d49b56a4c0838","target":"record","created_at":"2026-05-18T00:04:48Z","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":"746ae50baa6d47821e4d66aadd34e533f7a6e1c06d6f693e94e06cde491a6e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-06-22T22:26:18Z","title_canon_sha256":"e78e84faa600c41537e86bf90201358d195d9bde7046c33f4d0fcc46c4c74421"},"schema_version":"1.0","source":{"id":"1806.08869","kind":"arxiv","version":1}},"canonical_sha256":"beea301776908a3943b365cf3b68a831873c66d935217c9a2fe444f20bf496a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"beea301776908a3943b365cf3b68a831873c66d935217c9a2fe444f20bf496a3","first_computed_at":"2026-05-18T00:04:48.534148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:48.534148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UVVT/gRO6tdwpsW3SjOtsqCv1jlOVhDhaeCnswqCzcYCsd3c0X6shWU9rFYxlouW+xmxs744P/ge/FNhsYaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:48.534901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d911f8fb0be2b17badcad95c060475cd6f474c04c909c621c0d49b56a4c0838","sha256:e56246eaab706d670b60384c7af16a2b174c3f00a88e60db3e031d0854bd3ae1"],"state_sha256":"ebadaf31204f9ceaf968d550fdeeca996298be1fa45ff2d7044dd7583c707c35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iy7o1g8+JSRRhyZlb6BFbAPEQvXXPrhsIWwMNW2lMJRP0UIYdxKpNNc2cQhslk9O4N4Tu4P8RvmEwlt3mL7lDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:41:30.295641Z","bundle_sha256":"282556a5d6508e4ca63a8e044849603793b10b42bbad6af688b1bf9efaff911c"}}