{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DEB6HLPOQIA7MRCZOKVXUATIVW","short_pith_number":"pith:DEB6HLPO","schema_version":"1.0","canonical_sha256":"1903e3adee8201f6445972ab7a0268adbccb671794633fd08da3f0f9af514064","source":{"kind":"arxiv","id":"1108.1229","version":3},"attestation_state":"computed","paper":{"title":"Relative equilibria in the 3-dimensional curved n-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Florin Diacu","submitted_at":"2011-08-04T23:19:15Z","abstract_excerpt":"We consider the 3-dimensional gravitational $n$-body problem, $n\\ge 2$, in spaces of constant Gaussian curvature $\\kappa\\ne 0$, i.e.\\ on spheres ${\\mathbb S}_\\kappa^3$, for $\\kappa>0$, and on hyperbolic manifolds ${\\mathbb H}_\\kappa^3$, for $\\kappa<0$. Our goal is to define and study relative equilibria, which are orbits whose mutual distances remain constant in time. We also briefly discuss the issue of singularities in order to avoid impossible configurations. We derive the equations of motion and define six classes of relative equilibria, which follow naturally from the geometric properties"},"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":"1108.1229","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-04T23:19:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a82980f0c614343aaed7cfdbe453bf02f96336a3fc7e727dc7cd5b9c74eb0d8","abstract_canon_sha256":"3ac5e385bbf2bd375baf4c73746daa75ba63300357f6ef4f011e68fe12d308a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:47.364219Z","signature_b64":"p4NJSFwkDlgrymk1CNPWHhlhx1d4Purog1/cR+HhX/Q2f4weESTl4foazJRunI96BHYwwR5SObfpETqEihQ3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1903e3adee8201f6445972ab7a0268adbccb671794633fd08da3f0f9af514064","last_reissued_at":"2026-05-18T03:11:47.363584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:47.363584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative equilibria in the 3-dimensional curved n-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Florin Diacu","submitted_at":"2011-08-04T23:19:15Z","abstract_excerpt":"We consider the 3-dimensional gravitational $n$-body problem, $n\\ge 2$, in spaces of constant Gaussian curvature $\\kappa\\ne 0$, i.e.\\ on spheres ${\\mathbb S}_\\kappa^3$, for $\\kappa>0$, and on hyperbolic manifolds ${\\mathbb H}_\\kappa^3$, for $\\kappa<0$. Our goal is to define and study relative equilibria, which are orbits whose mutual distances remain constant in time. We also briefly discuss the issue of singularities in order to avoid impossible configurations. We derive the equations of motion and define six classes of relative equilibria, which follow naturally from the geometric properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1229","kind":"arxiv","version":3},"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":"1108.1229","created_at":"2026-05-18T03:11:47.363678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.1229v3","created_at":"2026-05-18T03:11:47.363678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1229","created_at":"2026-05-18T03:11:47.363678+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEB6HLPOQIA7","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEB6HLPOQIA7MRCZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEB6HLPO","created_at":"2026-05-18T12:26:26.731475+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/DEB6HLPOQIA7MRCZOKVXUATIVW","json":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW.json","graph_json":"https://pith.science/api/pith-number/DEB6HLPOQIA7MRCZOKVXUATIVW/graph.json","events_json":"https://pith.science/api/pith-number/DEB6HLPOQIA7MRCZOKVXUATIVW/events.json","paper":"https://pith.science/paper/DEB6HLPO"},"agent_actions":{"view_html":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW","download_json":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW.json","view_paper":"https://pith.science/paper/DEB6HLPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.1229&json=true","fetch_graph":"https://pith.science/api/pith-number/DEB6HLPOQIA7MRCZOKVXUATIVW/graph.json","fetch_events":"https://pith.science/api/pith-number/DEB6HLPOQIA7MRCZOKVXUATIVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW/action/storage_attestation","attest_author":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW/action/author_attestation","sign_citation":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW/action/citation_signature","submit_replication":"https://pith.science/pith/DEB6HLPOQIA7MRCZOKVXUATIVW/action/replication_record"}},"created_at":"2026-05-18T03:11:47.363678+00:00","updated_at":"2026-05-18T03:11:47.363678+00:00"}