{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DEBSGFDXFPXVOS3NTIS2534Y7J","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":"3fa6dd0b29ae479a583f2c978458906c0b86023fe0014e5726b7cce9e2a7dfcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-06-29T07:55:12Z","title_canon_sha256":"4de5ae8111d39bc4a42234d9c4f2e8e4209ca3c77cd1755b09e3c65553f20800"},"schema_version":"1.0","source":{"id":"1706.09613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09613","created_at":"2026-05-18T00:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09613v1","created_at":"2026-05-18T00:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09613","created_at":"2026-05-18T00:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"DEBSGFDXFPXV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DEBSGFDXFPXVOS3N","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DEBSGFDX","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:6cda2f706252b6a942dfc6f4047e3fb34b1ae48ded5336003bd6b39064792731","target":"graph","created_at":"2026-05-18T00:34:47Z","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":"Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of convergent migration of the planets in the proto-planetary disk. In this article, I present an analytical model of resonant chains of any number of planets. Using this model, I show that a system captured in a resonant chain can librate around several possible equilibrium configurations. The probability of capture around each equilibrium depends on how the chain formed, and especially on the order in which","authors_text":"J.-B. Delisle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-06-29T07:55:12Z","title":"Analytical model of multi-planetary resonant chains and constraints on migration scenarios"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09613","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":"sha256:0241f537126fa55d5a54526d1e2b1cf159e69ac9a373fa58f11d5cab90d7575a","target":"record","created_at":"2026-05-18T00:34:47Z","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":"3fa6dd0b29ae479a583f2c978458906c0b86023fe0014e5726b7cce9e2a7dfcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-06-29T07:55:12Z","title_canon_sha256":"4de5ae8111d39bc4a42234d9c4f2e8e4209ca3c77cd1755b09e3c65553f20800"},"schema_version":"1.0","source":{"id":"1706.09613","kind":"arxiv","version":1}},"canonical_sha256":"19032314772bef574b6d9a25aeef98fa5b3055c9a5c2a1fccae1216066614849","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19032314772bef574b6d9a25aeef98fa5b3055c9a5c2a1fccae1216066614849","first_computed_at":"2026-05-18T00:34:47.555074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:47.555074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uldoXegC+o1iY4que6prs+RoNpCxBYv8vXPVW9msrtR99DEtntpelddFlX4/egi6axZphZPQ2vO+bcOJ4CPHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:47.555656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0241f537126fa55d5a54526d1e2b1cf159e69ac9a373fa58f11d5cab90d7575a","sha256:6cda2f706252b6a942dfc6f4047e3fb34b1ae48ded5336003bd6b39064792731"],"state_sha256":"796c80661690aa5d0cde2407baf9d6a0a2dd8630f24f49a8db2bb3c1658d51d6"}