{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R7MHYOMW6AGKUJJIWBFPLIHJCK","short_pith_number":"pith:R7MHYOMW","canonical_record":{"source":{"id":"1809.10042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-09-26T14:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"27a184f1231b2dc2181f900c1c8e337d178f150a12277dbc92df35b8772c7faf","abstract_canon_sha256":"c3983f2331d7803d4c20e0f7854833a860143cd0d9139091e425d41fadd7472c"},"schema_version":"1.0"},"canonical_sha256":"8fd87c3996f00caa2528b04af5a0e912a802700368265e86a2a428e8141bfb3e","source":{"kind":"arxiv","id":"1809.10042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10042","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10042v1","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10042","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"R7MHYOMW6AGK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R7MHYOMW6AGKUJJI","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R7MHYOMW","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R7MHYOMW6AGKUJJIWBFPLIHJCK","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-09-26T14:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"27a184f1231b2dc2181f900c1c8e337d178f150a12277dbc92df35b8772c7faf","abstract_canon_sha256":"c3983f2331d7803d4c20e0f7854833a860143cd0d9139091e425d41fadd7472c"},"schema_version":"1.0"},"canonical_sha256":"8fd87c3996f00caa2528b04af5a0e912a802700368265e86a2a428e8141bfb3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:14.714362Z","signature_b64":"Zn5GfvC62LxENP6VZy1FMsChv2KzCQW1EwmzilxSsr50/mKZORw3WDRmLW2pZav2j2Cdo/DLPXX+JtqU5XPuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fd87c3996f00caa2528b04af5a0e912a802700368265e86a2a428e8141bfb3e","last_reissued_at":"2026-05-18T00:03:14.713730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:14.713730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10042","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":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kaiT/6abz0tfyc3KMdL7bevhV/SMJSqb3Km3MUN1wW9MX0lu2KjbhBNltqhOzrtXBxUP/rfUQvwhiT6bVN2hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:35:21.041385Z"},"content_sha256":"ffb08a6dd1b35f0a4f11c13a672d1c3dca9c946de855083977dc169863ddaa09","schema_version":"1.0","event_id":"sha256:ffb08a6dd1b35f0a4f11c13a672d1c3dca9c946de855083977dc169863ddaa09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R7MHYOMW6AGKUJJIWBFPLIHJCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-order mean motion resonances in two-planet systems: general analysis and observed systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Caroline Terquem, John Papaloizou","submitted_at":"2018-09-26T14:59:52Z","abstract_excerpt":"This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium eccentricities, mean motions and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that period ratio normally exceeds, but can also be less than, $ (q+1)/q.$ Departure from exact resonance as a function of time for systems starting in resonance and undergoing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10042","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":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tlo/cBU2Yw2Za9zlheLtgi8sOjsI4E9Qa+Yq5Z8DpDkA6/qF2XCia6ovJf6wtl4AjrxAabkK53RYSYZ7D68BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:35:21.042060Z"},"content_sha256":"77304a3239f92fb1eb302c70897d1f39a7edc33d6a0dddfaabbb0748aa243527","schema_version":"1.0","event_id":"sha256:77304a3239f92fb1eb302c70897d1f39a7edc33d6a0dddfaabbb0748aa243527"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/bundle.json","state_url":"https://pith.science/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/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":"2026-06-07T21:35:21Z","links":{"resolver":"https://pith.science/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK","bundle":"https://pith.science/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/bundle.json","state":"https://pith.science/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R7MHYOMW6AGKUJJIWBFPLIHJCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R7MHYOMW6AGKUJJIWBFPLIHJCK","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":"c3983f2331d7803d4c20e0f7854833a860143cd0d9139091e425d41fadd7472c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-09-26T14:59:52Z","title_canon_sha256":"27a184f1231b2dc2181f900c1c8e337d178f150a12277dbc92df35b8772c7faf"},"schema_version":"1.0","source":{"id":"1809.10042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10042","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10042v1","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10042","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"R7MHYOMW6AGK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R7MHYOMW6AGKUJJI","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R7MHYOMW","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:77304a3239f92fb1eb302c70897d1f39a7edc33d6a0dddfaabbb0748aa243527","target":"graph","created_at":"2026-05-18T00:03:14Z","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":"This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium eccentricities, mean motions and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that period ratio normally exceeds, but can also be less than, $ (q+1)/q.$ Departure from exact resonance as a function of time for systems starting in resonance and undergoing ","authors_text":"Caroline Terquem, John Papaloizou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-09-26T14:59:52Z","title":"First-order mean motion resonances in two-planet systems: general analysis and observed systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10042","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:ffb08a6dd1b35f0a4f11c13a672d1c3dca9c946de855083977dc169863ddaa09","target":"record","created_at":"2026-05-18T00:03:14Z","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":"c3983f2331d7803d4c20e0f7854833a860143cd0d9139091e425d41fadd7472c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-09-26T14:59:52Z","title_canon_sha256":"27a184f1231b2dc2181f900c1c8e337d178f150a12277dbc92df35b8772c7faf"},"schema_version":"1.0","source":{"id":"1809.10042","kind":"arxiv","version":1}},"canonical_sha256":"8fd87c3996f00caa2528b04af5a0e912a802700368265e86a2a428e8141bfb3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fd87c3996f00caa2528b04af5a0e912a802700368265e86a2a428e8141bfb3e","first_computed_at":"2026-05-18T00:03:14.713730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:14.713730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zn5GfvC62LxENP6VZy1FMsChv2KzCQW1EwmzilxSsr50/mKZORw3WDRmLW2pZav2j2Cdo/DLPXX+JtqU5XPuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:14.714362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffb08a6dd1b35f0a4f11c13a672d1c3dca9c946de855083977dc169863ddaa09","sha256:77304a3239f92fb1eb302c70897d1f39a7edc33d6a0dddfaabbb0748aa243527"],"state_sha256":"c819ba83488b5e4febc5d395b862aece4051e7369d5261686d3d52b981984208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xfWgNQLbyV4gX5eOG8OoIWzb9ErH4ZIy+0uWMZgTgAX9uV9VGcbH7TfcS+N1Sq7g//xo1JP5aVWiNM9bJAzmDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:35:21.045887Z","bundle_sha256":"9017671c1fb53d20be9a2f1ad84aef9d490a498a19e87e41febbc650605c4cce"}}