{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GXQZQ4MNJ3Q4ER7ZCIBADSFPWR","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":"ab006212a069110571f7a22dadf4afcbb8665fa0fe9294e64a70f3e1fe26ad68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-01T12:36:46Z","title_canon_sha256":"7d5b64a0d21970b2f912f38c65579959b831fd0432b4f7f496bfb8d387ccf274"},"schema_version":"1.0","source":{"id":"1812.00200","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00200","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00200v3","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00200","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"GXQZQ4MNJ3Q4","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GXQZQ4MNJ3Q4ER7Z","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GXQZQ4MN","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:4afa095eaf47edee2d1d99851956750a7a4272c6162c494a0cc784437dc29c46","target":"graph","created_at":"2026-05-17T23:52:26Z","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":"We classify the extensions of n-body central configurations to (n + 1)-body central configurations in R3, in both the collinear case and the non-collinear case. We completely solve the two open questions posed by Hampton (Nonlinearity 18: 2299- 2304, 2005). This classification is related with study on co-circular and co-spherical central configurations. We also obtain a general property of co-circular central configurations.","authors_text":"Shuqiang Zhu, Xiang Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-01T12:36:46Z","title":"Classification of stacked central configurations in R^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00200","kind":"arxiv","version":3},"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":"sha256:67dd10eac0fc1bca3147cbfe5c0dc63fb74a6ab94f8c667a4734f9208a004d5a","target":"record","created_at":"2026-05-17T23:52:26Z","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":"ab006212a069110571f7a22dadf4afcbb8665fa0fe9294e64a70f3e1fe26ad68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-01T12:36:46Z","title_canon_sha256":"7d5b64a0d21970b2f912f38c65579959b831fd0432b4f7f496bfb8d387ccf274"},"schema_version":"1.0","source":{"id":"1812.00200","kind":"arxiv","version":3}},"canonical_sha256":"35e198718d4ee1c247f9120201c8afb470bafb94727437c32502a1a271cece68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e198718d4ee1c247f9120201c8afb470bafb94727437c32502a1a271cece68","first_computed_at":"2026-05-17T23:52:26.951812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:26.951812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XEnNlR7jr99RWnByI1c7BuXQj5Fwm8y3DoGzi22P+I/A8NGC10ap3uboFfiQDyMwqY+jphytQ622EpdymVbpAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:26.952331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00200","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67dd10eac0fc1bca3147cbfe5c0dc63fb74a6ab94f8c667a4734f9208a004d5a","sha256:4afa095eaf47edee2d1d99851956750a7a4272c6162c494a0cc784437dc29c46"],"state_sha256":"1c6c99a91f279e0f0223f8e9434773e642c2cb8eb970dde87490dad3f23caa83"}