{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:L6TGJTYPFABYR2CITMIXB3XAU4","short_pith_number":"pith:L6TGJTYP","schema_version":"1.0","canonical_sha256":"5fa664cf0f280388e8489b1170eee0a73aa23ca99b26f6053633dc7bb7ecdd4c","source":{"kind":"arxiv","id":"1106.5062","version":1},"attestation_state":"computed","paper":{"title":"The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP"],"primary_cat":"astro-ph.SR","authors_text":"B. Quarles, J. Eberle, M. Cuntz, Z. E. Musielak","submitted_at":"2011-06-24T20:32:03Z","abstract_excerpt":"We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.5062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2011-06-24T20:32:03Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"3db6a45d6676443b5902a8b10edeeb8fe06eb5aa2e8cfd07aa1023fae0b3ee19","abstract_canon_sha256":"f949b9d8a5d1822a24742d75f8f6689f46a6b327a73500b5031a6c4daec95fc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:22.646129Z","signature_b64":"tYKCZy6NtQCgX+bVxZGiuEDI4EI/Urd0x9pwv9xMnBKXVoX8cRIj9qDoiq8y+Ks7prwJiVtsrBFMFwlLpmUBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fa664cf0f280388e8489b1170eee0a73aa23ca99b26f6053633dc7bb7ecdd4c","last_reissued_at":"2026-05-18T03:56:22.645457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:22.645457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP"],"primary_cat":"astro-ph.SR","authors_text":"B. Quarles, J. Eberle, M. Cuntz, Z. E. Musielak","submitted_at":"2011-06-24T20:32:03Z","abstract_excerpt":"We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5062","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.5062","created_at":"2026-05-18T03:56:22.645557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5062v1","created_at":"2026-05-18T03:56:22.645557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5062","created_at":"2026-05-18T03:56:22.645557+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6TGJTYPFABY","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6TGJTYPFABYR2CI","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6TGJTYP","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4","json":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4.json","graph_json":"https://pith.science/api/pith-number/L6TGJTYPFABYR2CITMIXB3XAU4/graph.json","events_json":"https://pith.science/api/pith-number/L6TGJTYPFABYR2CITMIXB3XAU4/events.json","paper":"https://pith.science/paper/L6TGJTYP"},"agent_actions":{"view_html":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4","download_json":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4.json","view_paper":"https://pith.science/paper/L6TGJTYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5062&json=true","fetch_graph":"https://pith.science/api/pith-number/L6TGJTYPFABYR2CITMIXB3XAU4/graph.json","fetch_events":"https://pith.science/api/pith-number/L6TGJTYPFABYR2CITMIXB3XAU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4/action/storage_attestation","attest_author":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4/action/author_attestation","sign_citation":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4/action/citation_signature","submit_replication":"https://pith.science/pith/L6TGJTYPFABYR2CITMIXB3XAU4/action/replication_record"}},"created_at":"2026-05-18T03:56:22.645557+00:00","updated_at":"2026-05-18T03:56:22.645557+00:00"}