{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WWEZVTWNWGR52JXCSIZCMSOECJ","short_pith_number":"pith:WWEZVTWN","schema_version":"1.0","canonical_sha256":"b5899acecdb1a3dd26e292322649c4124b404695c72f3d2c15a8f48422b9533d","source":{"kind":"arxiv","id":"2212.10569","version":1},"attestation_state":"computed","paper":{"title":"The phase-space architecture in extrasolar systems with two planets in orbits of high mutual inclination","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Christos Efthymiopoulos, Rita Mastroianni","submitted_at":"2022-12-20T14:05:24Z","abstract_excerpt":"We revisit the secular 3D planetary three-body problem aiming to provide a unified formalism for studying the structure of the phase space for progressively higher values of the mutual inclination $i_{mut}$ between the two planets' orbits. We propose a `book-keeping' technique yielding (after Jacobi reduction) a clear decomposition of the secular Hamiltonian as $H_{sec}=H_{planar} +H_{space}$, where $H_{space}$ contains all terms depending on $i_{mut}$. We numerically compare several models obtained via expansion in the orbital eccentricities or via multipole expansion. We find the mimimum req"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2212.10569","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2022-12-20T14:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"8d302d16b946ff2b20bf892d96b1e7f949a8680904bdb39234f62af6f4d736fe","abstract_canon_sha256":"3575016c1cb55e17e17fa26e3601121bb1b4cb55b3592589db989b7c463a77f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:02:04.143408Z","signature_b64":"g5OadpritonxVUzdE98P4VvblNb4zVW9JAhEg+Qmdp/qQZEXwC+esnjonHdgj6WDySyYXSbLqg4klVV9zDfGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5899acecdb1a3dd26e292322649c4124b404695c72f3d2c15a8f48422b9533d","last_reissued_at":"2026-07-05T06:02:04.142962Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:02:04.142962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The phase-space architecture in extrasolar systems with two planets in orbits of high mutual inclination","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Christos Efthymiopoulos, Rita Mastroianni","submitted_at":"2022-12-20T14:05:24Z","abstract_excerpt":"We revisit the secular 3D planetary three-body problem aiming to provide a unified formalism for studying the structure of the phase space for progressively higher values of the mutual inclination $i_{mut}$ between the two planets' orbits. We propose a `book-keeping' technique yielding (after Jacobi reduction) a clear decomposition of the secular Hamiltonian as $H_{sec}=H_{planar} +H_{space}$, where $H_{space}$ contains all terms depending on $i_{mut}$. We numerically compare several models obtained via expansion in the orbital eccentricities or via multipole expansion. We find the mimimum req"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.10569","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/2212.10569/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2212.10569","created_at":"2026-07-05T06:02:04.143022+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.10569v1","created_at":"2026-07-05T06:02:04.143022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.10569","created_at":"2026-07-05T06:02:04.143022+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWEZVTWNWGR5","created_at":"2026-07-05T06:02:04.143022+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWEZVTWNWGR52JXC","created_at":"2026-07-05T06:02:04.143022+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWEZVTWN","created_at":"2026-07-05T06:02:04.143022+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.12124","citing_title":"Dynamical regimes of two eccentric and mutually inclined giant planets","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ","json":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ.json","graph_json":"https://pith.science/api/pith-number/WWEZVTWNWGR52JXCSIZCMSOECJ/graph.json","events_json":"https://pith.science/api/pith-number/WWEZVTWNWGR52JXCSIZCMSOECJ/events.json","paper":"https://pith.science/paper/WWEZVTWN"},"agent_actions":{"view_html":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ","download_json":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ.json","view_paper":"https://pith.science/paper/WWEZVTWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.10569&json=true","fetch_graph":"https://pith.science/api/pith-number/WWEZVTWNWGR52JXCSIZCMSOECJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WWEZVTWNWGR52JXCSIZCMSOECJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ/action/storage_attestation","attest_author":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ/action/author_attestation","sign_citation":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ/action/citation_signature","submit_replication":"https://pith.science/pith/WWEZVTWNWGR52JXCSIZCMSOECJ/action/replication_record"}},"created_at":"2026-07-05T06:02:04.143022+00:00","updated_at":"2026-07-05T06:02:04.143022+00:00"}