{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZR46AFM6OBKP6YOZNWRZWQOCEE","short_pith_number":"pith:ZR46AFM6","schema_version":"1.0","canonical_sha256":"cc79e0159e7054ff61d96da39b41c2210f49f460ecdbcfc488b95f84ad0d6144","source":{"kind":"arxiv","id":"1312.6525","version":1},"attestation_state":"computed","paper":{"title":"Reduction the secular solution to the periodic solution in the generalized restricted three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP","math-ph","math.DS","math.MP"],"primary_cat":"astro-ph.SR","authors_text":"Elbaz I. Abouelmagd, E. M. A. Elzayat, Ibrahim A. Abbas, M.E. Awad","submitted_at":"2013-12-23T11:29:47Z","abstract_excerpt":"The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some num"},"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":"1312.6525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2013-12-23T11:29:47Z","cross_cats_sorted":["astro-ph.EP","math-ph","math.DS","math.MP"],"title_canon_sha256":"738e3a94d4d3a21b3b98fc14045db4e204591f466917a3178848df4111fdec22","abstract_canon_sha256":"4623bd45ad57eab3033afe2d17befab23a7594fc57ca7e257967bc0201923509"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:42.521995Z","signature_b64":"f2jRvugqYx3hMK+BCFi+6b1mVC2S+29mFgYQL6gGjDg++Oj9Aix+8+0wWS9g0IEGb4ripaIaFoJz0QcoVUIWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc79e0159e7054ff61d96da39b41c2210f49f460ecdbcfc488b95f84ad0d6144","last_reissued_at":"2026-05-18T01:45:42.520737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:42.520737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduction the secular solution to the periodic solution in the generalized restricted three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP","math-ph","math.DS","math.MP"],"primary_cat":"astro-ph.SR","authors_text":"Elbaz I. Abouelmagd, E. M. A. Elzayat, Ibrahim A. Abbas, M.E. Awad","submitted_at":"2013-12-23T11:29:47Z","abstract_excerpt":"The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6525","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":"1312.6525","created_at":"2026-05-18T01:45:42.520911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6525v1","created_at":"2026-05-18T01:45:42.520911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6525","created_at":"2026-05-18T01:45:42.520911+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZR46AFM6OBKP","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZR46AFM6OBKP6YOZ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZR46AFM6","created_at":"2026-05-18T12:28:09.283467+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/ZR46AFM6OBKP6YOZNWRZWQOCEE","json":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE.json","graph_json":"https://pith.science/api/pith-number/ZR46AFM6OBKP6YOZNWRZWQOCEE/graph.json","events_json":"https://pith.science/api/pith-number/ZR46AFM6OBKP6YOZNWRZWQOCEE/events.json","paper":"https://pith.science/paper/ZR46AFM6"},"agent_actions":{"view_html":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE","download_json":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE.json","view_paper":"https://pith.science/paper/ZR46AFM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6525&json=true","fetch_graph":"https://pith.science/api/pith-number/ZR46AFM6OBKP6YOZNWRZWQOCEE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZR46AFM6OBKP6YOZNWRZWQOCEE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE/action/storage_attestation","attest_author":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE/action/author_attestation","sign_citation":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE/action/citation_signature","submit_replication":"https://pith.science/pith/ZR46AFM6OBKP6YOZNWRZWQOCEE/action/replication_record"}},"created_at":"2026-05-18T01:45:42.520911+00:00","updated_at":"2026-05-18T01:45:42.520911+00:00"}