{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:6ED5YS57FLGQEFTIVPAHL2FPVS","short_pith_number":"pith:6ED5YS57","canonical_record":{"source":{"id":"2106.14863","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2021-06-28T17:29:33Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"8ed9daa140b40053340c66493bcc80518bc3cbee4ecedbb0a673626bfb4a458d","abstract_canon_sha256":"cb58a70772dad91ba3ea95b2868bd80a555fe8e771159a4c254e90ff8aa3f025"},"schema_version":"1.0"},"canonical_sha256":"f107dc4bbf2acd021668abc075e8afac8688967902c3bccd62063b06cf53fcff","source":{"kind":"arxiv","id":"2106.14863","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.14863","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"2106.14863v2","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.14863","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"6ED5YS57FLGQ","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_16","alias_value":"6ED5YS57FLGQEFTI","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_8","alias_value":"6ED5YS57","created_at":"2026-07-05T03:28:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:6ED5YS57FLGQEFTIVPAHL2FPVS","target":"record","payload":{"canonical_record":{"source":{"id":"2106.14863","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2021-06-28T17:29:33Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"8ed9daa140b40053340c66493bcc80518bc3cbee4ecedbb0a673626bfb4a458d","abstract_canon_sha256":"cb58a70772dad91ba3ea95b2868bd80a555fe8e771159a4c254e90ff8aa3f025"},"schema_version":"1.0"},"canonical_sha256":"f107dc4bbf2acd021668abc075e8afac8688967902c3bccd62063b06cf53fcff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:28:20.010492Z","signature_b64":"jkkC7C/j4w5x5zAq/Xgr06Bb/0pxPTafC/xv7/n8AJrd8QpuhD8WzdtPlaXr/bjU9skdp52WWTrG/tqgwdnEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f107dc4bbf2acd021668abc075e8afac8688967902c3bccd62063b06cf53fcff","last_reissued_at":"2026-07-05T03:28:20.009944Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:28:20.009944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.14863","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SA1GfcQpGK6UscREAtQNsXuZu4ECFSfo2gTK5c/eSsFkbF0/4v77PoyPWY2uEknchkSQcPx9kvYOKo0+kz6lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T13:50:10.093329Z"},"content_sha256":"cdf87b17e8eb69da2708badcfee5f02f2f73ba0ffe9eab5c1a33cb51ca9ab2e2","schema_version":"1.0","event_id":"sha256:cdf87b17e8eb69da2708badcfee5f02f2f73ba0ffe9eab5c1a33cb51ca9ab2e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:6ED5YS57FLGQEFTIVPAHL2FPVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"astro-ph.EP","authors_text":"Daniel Tamayo, Joshua Winn, Norman Murray, Scott Tremaine","submitted_at":"2021-06-28T17:29:33Z","abstract_excerpt":"We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near-symmetry strongly suppresses thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.14863","kind":"arxiv","version":2},"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/2106.14863/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":"2026-07-05T03:28:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0nZChmDRKoj8jOfuY8yExz4UMdqU2P9UXWrrvDYmE7Et1Mxv8B9nMuZsoyq0f2kwPI8YXNVaWBbIz6HFIbrrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T13:50:10.093721Z"},"content_sha256":"2a5ce8bab9512e4e18d1eb2f6af33f693a797a52b587646a43900e3f96a5f9ba","schema_version":"1.0","event_id":"sha256:2a5ce8bab9512e4e18d1eb2f6af33f693a797a52b587646a43900e3f96a5f9ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/bundle.json","state_url":"https://pith.science/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/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":"2026-08-03T13:50:10Z","links":{"resolver":"https://pith.science/pith/6ED5YS57FLGQEFTIVPAHL2FPVS","bundle":"https://pith.science/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/bundle.json","state":"https://pith.science/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ED5YS57FLGQEFTIVPAHL2FPVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6ED5YS57FLGQEFTIVPAHL2FPVS","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":"cb58a70772dad91ba3ea95b2868bd80a555fe8e771159a4c254e90ff8aa3f025","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2021-06-28T17:29:33Z","title_canon_sha256":"8ed9daa140b40053340c66493bcc80518bc3cbee4ecedbb0a673626bfb4a458d"},"schema_version":"1.0","source":{"id":"2106.14863","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.14863","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"2106.14863v2","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.14863","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"6ED5YS57FLGQ","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_16","alias_value":"6ED5YS57FLGQEFTI","created_at":"2026-07-05T03:28:20Z"},{"alias_kind":"pith_short_8","alias_value":"6ED5YS57","created_at":"2026-07-05T03:28:20Z"}],"graph_snapshots":[{"event_id":"sha256:2a5ce8bab9512e4e18d1eb2f6af33f693a797a52b587646a43900e3f96a5f9ba","target":"graph","created_at":"2026-07-05T03:28:20Z","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/2106.14863/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near-symmetry strongly suppresses thi","authors_text":"Daniel Tamayo, Joshua Winn, Norman Murray, Scott Tremaine","cross_cats":["nlin.CD"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2021-06-28T17:29:33Z","title":"A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.14863","kind":"arxiv","version":2},"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:cdf87b17e8eb69da2708badcfee5f02f2f73ba0ffe9eab5c1a33cb51ca9ab2e2","target":"record","created_at":"2026-07-05T03:28:20Z","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":"cb58a70772dad91ba3ea95b2868bd80a555fe8e771159a4c254e90ff8aa3f025","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2021-06-28T17:29:33Z","title_canon_sha256":"8ed9daa140b40053340c66493bcc80518bc3cbee4ecedbb0a673626bfb4a458d"},"schema_version":"1.0","source":{"id":"2106.14863","kind":"arxiv","version":2}},"canonical_sha256":"f107dc4bbf2acd021668abc075e8afac8688967902c3bccd62063b06cf53fcff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f107dc4bbf2acd021668abc075e8afac8688967902c3bccd62063b06cf53fcff","first_computed_at":"2026-07-05T03:28:20.009944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:28:20.009944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkkC7C/j4w5x5zAq/Xgr06Bb/0pxPTafC/xv7/n8AJrd8QpuhD8WzdtPlaXr/bjU9skdp52WWTrG/tqgwdnEDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:28:20.010492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.14863","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdf87b17e8eb69da2708badcfee5f02f2f73ba0ffe9eab5c1a33cb51ca9ab2e2","sha256:2a5ce8bab9512e4e18d1eb2f6af33f693a797a52b587646a43900e3f96a5f9ba"],"state_sha256":"7c719658f17dce90f84113b5160a56297e7fb2d86b27b26db41e7af679f83b74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBgmks9BlrC1yWrpcqGs3y9Fl0e/p36EE6dCMD0kKvNpM2Ga2QLd+G0vyStoPL3ozvmEgzBGbu5n6CoQ0XMQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T13:50:10.096950Z","bundle_sha256":"302300b5d2b0079de78d6e9865f4d5bafb232933c5e792106e1bb6e2943b98ff"}}