{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GB6SQGNYCU3DLG6RCIBZRPEOJ6","short_pith_number":"pith:GB6SQGNY","canonical_record":{"source":{"id":"1505.05389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-20T14:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"a56a7f5b30e72437152711daad81aab94d68a78d6111ebf2e17948fcab276d3e","abstract_canon_sha256":"1458b1a432520086d70f49f7758a18942369fa6dbe811748a197a5abfebf6ee0"},"schema_version":"1.0"},"canonical_sha256":"307d2819b81536359bd1120398bc8e4f90187122a6ceb84c91c53df6cd16e283","source":{"kind":"arxiv","id":"1505.05389","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05389","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05389v1","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05389","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"GB6SQGNYCU3D","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GB6SQGNYCU3DLG6R","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GB6SQGNY","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GB6SQGNYCU3DLG6RCIBZRPEOJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-20T14:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"a56a7f5b30e72437152711daad81aab94d68a78d6111ebf2e17948fcab276d3e","abstract_canon_sha256":"1458b1a432520086d70f49f7758a18942369fa6dbe811748a197a5abfebf6ee0"},"schema_version":"1.0"},"canonical_sha256":"307d2819b81536359bd1120398bc8e4f90187122a6ceb84c91c53df6cd16e283","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:33.757218Z","signature_b64":"1P9n3X2qjjVriKL/mougoLPGvYf1rN9GrIplVQcixLT29/eagraZ/ekh5Jb21X7NTOts/DjhY1zxwdE0OcD+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"307d2819b81536359bd1120398bc8e4f90187122a6ceb84c91c53df6cd16e283","last_reissued_at":"2026-05-18T01:18:33.756808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:33.756808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05389","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":"2026-05-18T01:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jDIuerrrXkfxZGfwU8cshzqGebUKgX0007jMANBoZxG9a5VaweMJhsJzL4yXMwo2MN9x1XbiUhToovr/spSOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:38:27.525645Z"},"content_sha256":"109f1023541dc70c5503cc116eff3f6711be3d9de0a459fcd13d79810c72b8ff","schema_version":"1.0","event_id":"sha256:109f1023541dc70c5503cc116eff3f6711be3d9de0a459fcd13d79810c72b8ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GB6SQGNYCU3DLG6RCIBZRPEOJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secular instability in the spatial three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jacques F\\'ejoz, Marcel Guardia","submitted_at":"2015-05-20T14:09:51Z","abstract_excerpt":"Consider the spatial three-body problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The so-called secular dynamics governs the slow evolution of the Keplerian ellipses. We show that it contains a horseshoe and all the chaotic dynamics which goes along with it, corresponding to motions along which the eccentricity of the inner ellipse undergoes large, random excursions. The proof goes through the surprisingly explicit computation of the homoclinic solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05389","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":"2026-05-18T01:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"19uljo12+1igKeYxSE/tRFMKyzcUjh4J25Z3pv7i3TMXnDg2jiDqlgu8z3tP/3y9KUR2YyJxEDVu8y32gLa+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:38:27.526341Z"},"content_sha256":"ed10a9fa10700260c102285b58257af98d8695acc385579b962d418a654548de","schema_version":"1.0","event_id":"sha256:ed10a9fa10700260c102285b58257af98d8695acc385579b962d418a654548de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/bundle.json","state_url":"https://pith.science/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/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":"2026-05-31T10:38:27Z","links":{"resolver":"https://pith.science/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6","bundle":"https://pith.science/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/bundle.json","state":"https://pith.science/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GB6SQGNYCU3DLG6RCIBZRPEOJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GB6SQGNYCU3DLG6RCIBZRPEOJ6","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":"1458b1a432520086d70f49f7758a18942369fa6dbe811748a197a5abfebf6ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-20T14:09:51Z","title_canon_sha256":"a56a7f5b30e72437152711daad81aab94d68a78d6111ebf2e17948fcab276d3e"},"schema_version":"1.0","source":{"id":"1505.05389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05389","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05389v1","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05389","created_at":"2026-05-18T01:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"GB6SQGNYCU3D","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GB6SQGNYCU3DLG6R","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GB6SQGNY","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:ed10a9fa10700260c102285b58257af98d8695acc385579b962d418a654548de","target":"graph","created_at":"2026-05-18T01:18:33Z","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":"Consider the spatial three-body problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The so-called secular dynamics governs the slow evolution of the Keplerian ellipses. We show that it contains a horseshoe and all the chaotic dynamics which goes along with it, corresponding to motions along which the eccentricity of the inner ellipse undergoes large, random excursions. The proof goes through the surprisingly explicit computation of the homoclinic solu","authors_text":"Jacques F\\'ejoz, Marcel Guardia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-20T14:09:51Z","title":"Secular instability in the spatial three-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05389","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":"sha256:109f1023541dc70c5503cc116eff3f6711be3d9de0a459fcd13d79810c72b8ff","target":"record","created_at":"2026-05-18T01:18:33Z","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":"1458b1a432520086d70f49f7758a18942369fa6dbe811748a197a5abfebf6ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-20T14:09:51Z","title_canon_sha256":"a56a7f5b30e72437152711daad81aab94d68a78d6111ebf2e17948fcab276d3e"},"schema_version":"1.0","source":{"id":"1505.05389","kind":"arxiv","version":1}},"canonical_sha256":"307d2819b81536359bd1120398bc8e4f90187122a6ceb84c91c53df6cd16e283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"307d2819b81536359bd1120398bc8e4f90187122a6ceb84c91c53df6cd16e283","first_computed_at":"2026-05-18T01:18:33.756808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:33.756808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1P9n3X2qjjVriKL/mougoLPGvYf1rN9GrIplVQcixLT29/eagraZ/ekh5Jb21X7NTOts/DjhY1zxwdE0OcD+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:33.757218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109f1023541dc70c5503cc116eff3f6711be3d9de0a459fcd13d79810c72b8ff","sha256:ed10a9fa10700260c102285b58257af98d8695acc385579b962d418a654548de"],"state_sha256":"2b4746ab5eb6a8a6fb6814c975980f781d458850ac8adcc2a9803f47451d1588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9P9kxOEvRE2JeO3Fg50lPF9AhDdpan2QJThc/ntLhcA+OHaSrsMx7B+zoPyqDknz8y/HNNwnUooeFz2v9ATCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:38:27.529712Z","bundle_sha256":"eeb5b9f641c525a29fcf925c8582243db918aef08984e55fb17aab9f640a3a81"}}