{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YCVFTRCTIS3OASGJTZNVJNQD5H","short_pith_number":"pith:YCVFTRCT","canonical_record":{"source":{"id":"1711.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-11-07T01:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"7e2012fb6f25e316042329f1d758545d9af1f01920a949343cb3809e4ca27209","abstract_canon_sha256":"941188f562a53481508c86371477b244b9d7bbf712df946319300c8f588784b6"},"schema_version":"1.0"},"canonical_sha256":"c0aa59c45344b6e048c99e5b54b603e9c0d74dc24bf9b53bb9998658f4f7642e","source":{"kind":"arxiv","id":"1711.02252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02252","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02252v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02252","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"YCVFTRCTIS3O","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YCVFTRCTIS3OASGJ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YCVFTRCT","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YCVFTRCTIS3OASGJTZNVJNQD5H","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-11-07T01:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"7e2012fb6f25e316042329f1d758545d9af1f01920a949343cb3809e4ca27209","abstract_canon_sha256":"941188f562a53481508c86371477b244b9d7bbf712df946319300c8f588784b6"},"schema_version":"1.0"},"canonical_sha256":"c0aa59c45344b6e048c99e5b54b603e9c0d74dc24bf9b53bb9998658f4f7642e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:08.427048Z","signature_b64":"xX0dbxs8YgVOy1WF1u/x+RUP9QFfHHRlK6UjgdgbTMe4RtZ1svZQcc3tl1HglIqOn1NS/BtqZb9deH3KXYI2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0aa59c45344b6e048c99e5b54b603e9c0d74dc24bf9b53bb9998658f4f7642e","last_reissued_at":"2026-05-18T00:31:08.426447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:08.426447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02252","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":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkf2QbHnfDtLVOJKsA2qqQaUWtMBRgq+x5BumVO5erGvCFj0Q2Vqrd1DZ+2oWTLHU+xZYpp5Mr8x+KXQ9ZzDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:32:09.476194Z"},"content_sha256":"96cfe09bfb246da25d85fd80f20420b5f44e547f360cce7495ffce612b89d670","schema_version":"1.0","event_id":"sha256:96cfe09bfb246da25d85fd80f20420b5f44e547f360cce7495ffce612b89d670"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YCVFTRCTIS3OASGJTZNVJNQD5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secular Dynamics of Multiplanetary Circumbinary Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Eduardo Andrade-Ines, Philippe Robutel","submitted_at":"2017-11-07T01:46:48Z","abstract_excerpt":"We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadractic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02252","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":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEbNRVShZb4nT9AqSuBJq4ycB+/zax3hdSv0j5lrWic8vvp+mA2dWRmN3LJpC9SSRIc09WZcw4by0UxBftJjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:32:09.476567Z"},"content_sha256":"f791d809ad64ab855a9c20bcc47ad0eed484eb5313943e7b6a47c96264dfe9e4","schema_version":"1.0","event_id":"sha256:f791d809ad64ab855a9c20bcc47ad0eed484eb5313943e7b6a47c96264dfe9e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/bundle.json","state_url":"https://pith.science/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/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":"2026-06-26T12:32:09Z","links":{"resolver":"https://pith.science/pith/YCVFTRCTIS3OASGJTZNVJNQD5H","bundle":"https://pith.science/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/bundle.json","state":"https://pith.science/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCVFTRCTIS3OASGJTZNVJNQD5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YCVFTRCTIS3OASGJTZNVJNQD5H","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":"941188f562a53481508c86371477b244b9d7bbf712df946319300c8f588784b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-11-07T01:46:48Z","title_canon_sha256":"7e2012fb6f25e316042329f1d758545d9af1f01920a949343cb3809e4ca27209"},"schema_version":"1.0","source":{"id":"1711.02252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02252","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02252v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02252","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"YCVFTRCTIS3O","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YCVFTRCTIS3OASGJ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YCVFTRCT","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f791d809ad64ab855a9c20bcc47ad0eed484eb5313943e7b6a47c96264dfe9e4","target":"graph","created_at":"2026-05-18T00:31:08Z","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":"We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadractic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-","authors_text":"Eduardo Andrade-Ines, Philippe Robutel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-11-07T01:46:48Z","title":"Secular Dynamics of Multiplanetary Circumbinary Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02252","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":"sha256:96cfe09bfb246da25d85fd80f20420b5f44e547f360cce7495ffce612b89d670","target":"record","created_at":"2026-05-18T00:31:08Z","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":"941188f562a53481508c86371477b244b9d7bbf712df946319300c8f588784b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-11-07T01:46:48Z","title_canon_sha256":"7e2012fb6f25e316042329f1d758545d9af1f01920a949343cb3809e4ca27209"},"schema_version":"1.0","source":{"id":"1711.02252","kind":"arxiv","version":1}},"canonical_sha256":"c0aa59c45344b6e048c99e5b54b603e9c0d74dc24bf9b53bb9998658f4f7642e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0aa59c45344b6e048c99e5b54b603e9c0d74dc24bf9b53bb9998658f4f7642e","first_computed_at":"2026-05-18T00:31:08.426447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:08.426447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xX0dbxs8YgVOy1WF1u/x+RUP9QFfHHRlK6UjgdgbTMe4RtZ1svZQcc3tl1HglIqOn1NS/BtqZb9deH3KXYI2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:08.427048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96cfe09bfb246da25d85fd80f20420b5f44e547f360cce7495ffce612b89d670","sha256:f791d809ad64ab855a9c20bcc47ad0eed484eb5313943e7b6a47c96264dfe9e4"],"state_sha256":"423991a35e38c0c6c7745e68e245bf734794204c8e1e498efdadc60e9d71b40f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnGC5q1apUN4SEkQZauDbqDU4RzH9YjRIqPGi6O83JoNUSjX5XZiRUQ8wt+jksFhbJEGw9DkxYImgThRRacFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:32:09.478632Z","bundle_sha256":"12085c0d99d3f07f890cdddfd3e8e6569df5f3c9e451ef97f00e407ce6e4322a"}}