{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QVT3C4K44TYQD3D3FWPHGB44UU","short_pith_number":"pith:QVT3C4K4","schema_version":"1.0","canonical_sha256":"8567b1715ce4f101ec7b2d9e73079ca50beb80a918fafd837541cae80b23d216","source":{"kind":"arxiv","id":"1208.3183","version":2},"attestation_state":"computed","paper":{"title":"Stability of the Rhomboidal Symmetric-Mass Orbit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lennard Bakker, Skyler Simmons","submitted_at":"2012-08-15T19:20:26Z","abstract_excerpt":"We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable. Linear stability analysis is performed in both settings. For the two-degree-of-freedom setting, linear stability is established for a wide interval of mass ratios. A Poincar\\'{e} section analysis is also performed, showing stability. In the four-degree-of-freedom setting, linear stability fails except for a very small interval of mass ratios."},"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":"1208.3183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T19:20:26Z","cross_cats_sorted":[],"title_canon_sha256":"f69867d95458cd06fc913b4a5e3dfeee17c1ba14cec3e32c2c2c94ff2003ce9a","abstract_canon_sha256":"4a871e0c03adb7865ff327bfdc23d90517c535bb910c2bfe25b1ff36fd21650a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:52.892957Z","signature_b64":"5DbYDKc9b0u0B8feK5v5a4urGFXkD6vxKUTh45CmE+hQVPUFj2WPd1ln3bpsUm7rxonzQqhLRa5MkDpGTMmKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8567b1715ce4f101ec7b2d9e73079ca50beb80a918fafd837541cae80b23d216","last_reissued_at":"2026-05-18T03:26:52.892253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:52.892253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the Rhomboidal Symmetric-Mass Orbit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lennard Bakker, Skyler Simmons","submitted_at":"2012-08-15T19:20:26Z","abstract_excerpt":"We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable. Linear stability analysis is performed in both settings. For the two-degree-of-freedom setting, linear stability is established for a wide interval of mass ratios. A Poincar\\'{e} section analysis is also performed, showing stability. In the four-degree-of-freedom setting, linear stability fails except for a very small interval of mass ratios."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3183","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":""},"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":"1208.3183","created_at":"2026-05-18T03:26:52.892363+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3183v2","created_at":"2026-05-18T03:26:52.892363+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3183","created_at":"2026-05-18T03:26:52.892363+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVT3C4K44TYQ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVT3C4K44TYQD3D3","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVT3C4K4","created_at":"2026-05-18T12:27:20.899486+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/QVT3C4K44TYQD3D3FWPHGB44UU","json":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU.json","graph_json":"https://pith.science/api/pith-number/QVT3C4K44TYQD3D3FWPHGB44UU/graph.json","events_json":"https://pith.science/api/pith-number/QVT3C4K44TYQD3D3FWPHGB44UU/events.json","paper":"https://pith.science/paper/QVT3C4K4"},"agent_actions":{"view_html":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU","download_json":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU.json","view_paper":"https://pith.science/paper/QVT3C4K4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3183&json=true","fetch_graph":"https://pith.science/api/pith-number/QVT3C4K44TYQD3D3FWPHGB44UU/graph.json","fetch_events":"https://pith.science/api/pith-number/QVT3C4K44TYQD3D3FWPHGB44UU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU/action/storage_attestation","attest_author":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU/action/author_attestation","sign_citation":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU/action/citation_signature","submit_replication":"https://pith.science/pith/QVT3C4K44TYQD3D3FWPHGB44UU/action/replication_record"}},"created_at":"2026-05-18T03:26:52.892363+00:00","updated_at":"2026-05-18T03:26:52.892363+00:00"}