{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:N7Y4BVOGEDDHEFDNKYYCGB74UO","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":"1578b84ac1c083706d5dc1a2cec40ec9d0e4e76b992c6947feb747c79635de65","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2006-11-22T17:19:00Z","title_canon_sha256":"612e2ea5f548ee3614fc80967d87d166708095b553680b59a2a79a27f9d1d1a3"},"schema_version":"1.0","source":{"id":"math/0611658","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611658","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611658v5","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611658","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"N7Y4BVOGEDDH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"N7Y4BVOGEDDHEFDN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"N7Y4BVOG","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:ca047c889ff140e99f993f29d6b453d3907f20d5272d94bbf68ca6a675a6475c","target":"graph","created_at":"2026-05-18T01:19:55Z","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":"A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolods. All conformal deformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A '3-Hamiltonian form' of infinitesimal co","authors_text":"Dimiter Vassilev, Ivan Minchev, Stefan Ivanov","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2006-11-22T17:19:00Z","title":"Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611658","kind":"arxiv","version":5},"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:a6d08a2fccfc741ae40e1301266ed8a4f139646b62de1362d0347fb4462c88c3","target":"record","created_at":"2026-05-18T01:19:55Z","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":"1578b84ac1c083706d5dc1a2cec40ec9d0e4e76b992c6947feb747c79635de65","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2006-11-22T17:19:00Z","title_canon_sha256":"612e2ea5f548ee3614fc80967d87d166708095b553680b59a2a79a27f9d1d1a3"},"schema_version":"1.0","source":{"id":"math/0611658","kind":"arxiv","version":5}},"canonical_sha256":"6ff1c0d5c620c672146d56302307fca3aeb02bfacb6dc9450dbc85fadb4dca76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff1c0d5c620c672146d56302307fca3aeb02bfacb6dc9450dbc85fadb4dca76","first_computed_at":"2026-05-18T01:19:55.978763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:55.978763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mrn2c7W8ul0h6P2hRO4aOQ3RwLVHd/dU2sKTInHRQQRPLzPmihgbBlRSo0Col+w0H48CwlxvrXz1+RvZPnchAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:55.979420Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611658","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6d08a2fccfc741ae40e1301266ed8a4f139646b62de1362d0347fb4462c88c3","sha256:ca047c889ff140e99f993f29d6b453d3907f20d5272d94bbf68ca6a675a6475c"],"state_sha256":"d1db2929b77e5e2fc501dab1905e7585c3bc511afb4ed5544c6151a36f876194"}