{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VEYN62OHUS4CXYQYDE2L333HEW","short_pith_number":"pith:VEYN62OH","canonical_record":{"source":{"id":"2404.07264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2024-04-10T18:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"ed5e087fcd23a96a92be494b733ea434e90ca108a3cc9eea5e803fdb03687547","abstract_canon_sha256":"10bf375587ded27a9c32f083fa20060006ce878e49f7051f33a6a1c9cac69829"},"schema_version":"1.0"},"canonical_sha256":"a930df69c7a4b82be2181934bdef67258c7455e058180330282a148e519e0c2e","source":{"kind":"arxiv","id":"2404.07264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07264","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07264v1","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07264","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"VEYN62OHUS4C","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"VEYN62OHUS4CXYQY","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"VEYN62OH","created_at":"2026-07-05T08:06:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VEYN62OHUS4CXYQYDE2L333HEW","target":"record","payload":{"canonical_record":{"source":{"id":"2404.07264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2024-04-10T18:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"ed5e087fcd23a96a92be494b733ea434e90ca108a3cc9eea5e803fdb03687547","abstract_canon_sha256":"10bf375587ded27a9c32f083fa20060006ce878e49f7051f33a6a1c9cac69829"},"schema_version":"1.0"},"canonical_sha256":"a930df69c7a4b82be2181934bdef67258c7455e058180330282a148e519e0c2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:50.055074Z","signature_b64":"d4hnw5ICcp3DDpiHG7hOZiKtRDqC04EsuYsfhpEQ8V7UsdWH7G1NrSCekqkwbjheEOFVf3OpiyjB93QJAJT/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a930df69c7a4b82be2181934bdef67258c7455e058180330282a148e519e0c2e","last_reissued_at":"2026-07-05T08:06:50.054610Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:50.054610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.07264","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":"2026-07-05T08:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xq9T75WamWPmwWnyFqaZt3E6+Gz73M8VYY/DhUWGHWO4FBqjH7gq3a+KNoknsiKkoRjD5R+Hf9uVqSrr4TE5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T09:16:19.658249Z"},"content_sha256":"a3c5f2f61423bbdbf8ca5038a68bd96d908d268fe3889714b040c839ac4cad6b","schema_version":"1.0","event_id":"sha256:a3c5f2f61423bbdbf8ca5038a68bd96d908d268fe3889714b040c839ac4cad6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VEYN62OHUS4CXYQYDE2L333HEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical and Secular Stability of Mutually Inclined Planetary Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Hagai Perets, Hareesh Gautham Bhaskar","submitted_at":"2024-04-10T18:00:05Z","abstract_excerpt":"Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semi-major axis of the inner binary $\\beta=\\delta a_1/a_1$ caused by perturbations from th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07264","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.07264/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2S5BGRpTET3NSSjtjkVOyV+YY09J5iTHt0vV9WDIARZdBzBfo38122967YTvujCdpDasJKU7T9p56HGNSW3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T09:16:19.659066Z"},"content_sha256":"95631c6de06cc5ade7a79d54c4378fd906be14112a95bb78a1a51b5bedefb980","schema_version":"1.0","event_id":"sha256:95631c6de06cc5ade7a79d54c4378fd906be14112a95bb78a1a51b5bedefb980"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEYN62OHUS4CXYQYDE2L333HEW/bundle.json","state_url":"https://pith.science/pith/VEYN62OHUS4CXYQYDE2L333HEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEYN62OHUS4CXYQYDE2L333HEW/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":"2026-08-19T09:16:19Z","links":{"resolver":"https://pith.science/pith/VEYN62OHUS4CXYQYDE2L333HEW","bundle":"https://pith.science/pith/VEYN62OHUS4CXYQYDE2L333HEW/bundle.json","state":"https://pith.science/pith/VEYN62OHUS4CXYQYDE2L333HEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEYN62OHUS4CXYQYDE2L333HEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VEYN62OHUS4CXYQYDE2L333HEW","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":"10bf375587ded27a9c32f083fa20060006ce878e49f7051f33a6a1c9cac69829","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2024-04-10T18:00:05Z","title_canon_sha256":"ed5e087fcd23a96a92be494b733ea434e90ca108a3cc9eea5e803fdb03687547"},"schema_version":"1.0","source":{"id":"2404.07264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07264","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07264v1","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07264","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"VEYN62OHUS4C","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"VEYN62OHUS4CXYQY","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"VEYN62OH","created_at":"2026-07-05T08:06:50Z"}],"graph_snapshots":[{"event_id":"sha256:95631c6de06cc5ade7a79d54c4378fd906be14112a95bb78a1a51b5bedefb980","target":"graph","created_at":"2026-07-05T08:06:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.07264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semi-major axis of the inner binary $\\beta=\\delta a_1/a_1$ caused by perturbations from th","authors_text":"Hagai Perets, Hareesh Gautham Bhaskar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2024-04-10T18:00:05Z","title":"Dynamical and Secular Stability of Mutually Inclined Planetary Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07264","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:a3c5f2f61423bbdbf8ca5038a68bd96d908d268fe3889714b040c839ac4cad6b","target":"record","created_at":"2026-07-05T08:06:50Z","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":"10bf375587ded27a9c32f083fa20060006ce878e49f7051f33a6a1c9cac69829","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2024-04-10T18:00:05Z","title_canon_sha256":"ed5e087fcd23a96a92be494b733ea434e90ca108a3cc9eea5e803fdb03687547"},"schema_version":"1.0","source":{"id":"2404.07264","kind":"arxiv","version":1}},"canonical_sha256":"a930df69c7a4b82be2181934bdef67258c7455e058180330282a148e519e0c2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a930df69c7a4b82be2181934bdef67258c7455e058180330282a148e519e0c2e","first_computed_at":"2026-07-05T08:06:50.054610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:50.054610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4hnw5ICcp3DDpiHG7hOZiKtRDqC04EsuYsfhpEQ8V7UsdWH7G1NrSCekqkwbjheEOFVf3OpiyjB93QJAJT/AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:50.055074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.07264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3c5f2f61423bbdbf8ca5038a68bd96d908d268fe3889714b040c839ac4cad6b","sha256:95631c6de06cc5ade7a79d54c4378fd906be14112a95bb78a1a51b5bedefb980"],"state_sha256":"e3d40261fa72496810281b5fa582383d39e12d810e49de703b1634aeaa30d9ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OPk3sx2FES7umQRGWxojjRCYQKX0V4EJ/iTb7JXiSvseiK+m5LeMxuchByFGDuP1KRKVzcIZQBryEr+rKRRUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T09:16:19.667203Z","bundle_sha256":"70ea99664fdb9af4f3d2782b0f25d64b481f9c9b1162155e19a92c445d942a3d"}}