{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:4F5WSCYVGFH3KDYHK6VAQYYZQD","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":"c084bd12a5255943edd5bad341d07b2cbb86f4ec43baf5e7261d65485c3eb77a","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2007-06-25T22:22:16Z","title_canon_sha256":"5c4959f84c26cf79ed74288e3cba336495ac2de2702e7d5fa99e26b9ca8fa86d"},"schema_version":"1.0","source":{"id":"0706.3721","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3721","created_at":"2026-07-04T23:57:42Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3721v1","created_at":"2026-07-04T23:57:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3721","created_at":"2026-07-04T23:57:42Z"},{"alias_kind":"pith_short_12","alias_value":"4F5WSCYVGFH3","created_at":"2026-07-04T23:57:42Z"},{"alias_kind":"pith_short_16","alias_value":"4F5WSCYVGFH3KDYH","created_at":"2026-07-04T23:57:42Z"},{"alias_kind":"pith_short_8","alias_value":"4F5WSCYV","created_at":"2026-07-04T23:57:42Z"}],"graph_snapshots":[{"event_id":"sha256:9a3709065822055f62e8e0a1dbca1fbe92f307411c4c70b249f2819769d03802","target":"graph","created_at":"2026-07-04T23:57:42Z","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/0706.3721/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the","authors_text":"Richard Greenberg, Rory Barnes","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2007-06-25T22:22:16Z","title":"Stability Limits in Resonant Planetary Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3721","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:b4828f768265bbd8cc83639699a5da4ad4605dcd252add1667932994c35cedcb","target":"record","created_at":"2026-07-04T23:57:42Z","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":"c084bd12a5255943edd5bad341d07b2cbb86f4ec43baf5e7261d65485c3eb77a","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2007-06-25T22:22:16Z","title_canon_sha256":"5c4959f84c26cf79ed74288e3cba336495ac2de2702e7d5fa99e26b9ca8fa86d"},"schema_version":"1.0","source":{"id":"0706.3721","kind":"arxiv","version":1}},"canonical_sha256":"e17b690b15314fb50f0757aa08631980c955e5d02d796604d32a1b7faa65d11b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e17b690b15314fb50f0757aa08631980c955e5d02d796604d32a1b7faa65d11b","first_computed_at":"2026-07-04T23:57:42.563041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:57:42.563041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QXkmM9CTiJH0JzfDFHI96jHxXUDMgf2ZlWBiDhauGtaFYjTVsDzQPbp0xAl7b1p7TsE2RzqBIhAoX7+s8W6YDw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:57:42.563409Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3721","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4828f768265bbd8cc83639699a5da4ad4605dcd252add1667932994c35cedcb","sha256:9a3709065822055f62e8e0a1dbca1fbe92f307411c4c70b249f2819769d03802"],"state_sha256":"31944351d581291b2f555d36d1ac91b39b7f242c6dfc032d9e3a573f308f8199"}