{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TRQ4GUJES2EOHJHRRPZW4OZGY2","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":"9ebe20e025f8f141bc12087751f72eb8404eb699e83ae6b2c1e55288e48e24e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2013-06-04T07:45:14Z","title_canon_sha256":"973794be7e2b952a5b210ad1314238d48d29790ffa8a2dd85cf5cdcd7c7cb7cd"},"schema_version":"1.0","source":{"id":"1306.0689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0689","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0689v2","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0689","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"TRQ4GUJES2EO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TRQ4GUJES2EOHJHR","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TRQ4GUJE","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:00ffd2e3fcb2ab7c3fd442bf8a1b37762ed5e2d3f412b4dda7d0c033f518769c","target":"graph","created_at":"2026-05-18T03:21:11Z","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":"Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet system shows complicated dynamics with mostly chaotic trajectories. We can determine possible stable configurations by computing resonant periodic trajectories of the general planar three body problem, which can be used for modeling a two-planet system. In this work, we review our model for both the planar and the spatial case. We present families of symmetr","authors_text":"George Voyatzis, John D. Hadjidemetriou, Kyriaki I. Antoniadou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2013-06-04T07:45:14Z","title":"Resonant planetary dynamics: Periodic orbits and long-term stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0689","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":"sha256:5e393e2ac45b797f6c0f25b360f1a12a14bf3eb4f8c26cf2de4d269493b1956e","target":"record","created_at":"2026-05-18T03:21:11Z","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":"9ebe20e025f8f141bc12087751f72eb8404eb699e83ae6b2c1e55288e48e24e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2013-06-04T07:45:14Z","title_canon_sha256":"973794be7e2b952a5b210ad1314238d48d29790ffa8a2dd85cf5cdcd7c7cb7cd"},"schema_version":"1.0","source":{"id":"1306.0689","kind":"arxiv","version":2}},"canonical_sha256":"9c61c351249688e3a4f18bf36e3b26c6adb6c587132410e37053208f86f0c9b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c61c351249688e3a4f18bf36e3b26c6adb6c587132410e37053208f86f0c9b6","first_computed_at":"2026-05-18T03:21:11.436923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:11.436923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIF2cEYHQdqs30k+UwMMAjMAkSz7wkOPJGw8YFSwpgH0NS3bzWlYZhxphLP9tWV+wlKcud8qciSbXx8u/RngDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:11.437776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e393e2ac45b797f6c0f25b360f1a12a14bf3eb4f8c26cf2de4d269493b1956e","sha256:00ffd2e3fcb2ab7c3fd442bf8a1b37762ed5e2d3f412b4dda7d0c033f518769c"],"state_sha256":"9eaa7921dd618424e3caab31c5d30865eea09cd8bd0ecd6c8c7843942299f450"}