{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WDXUWL7SXAXUKDHRA5GZEIB43Q","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":"6179c17c4b6c29a0b5feaf4b63e68f414c7399e79ec2c74b436745aff38c76d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-16T11:14:52Z","title_canon_sha256":"9ce1a9debd7da8b8d04798530dedd84e0a8c7e8534dbf1fa172b27fa4dbe7eb2"},"schema_version":"1.0","source":{"id":"0911.3007","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3007","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3007v2","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3007","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"WDXUWL7SXAXU","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WDXUWL7SXAXUKDHR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WDXUWL7S","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:567c10cbb2dd08e3fdb2a3cd82529f6f4701d3145982aef36761b44b14af03f5","target":"graph","created_at":"2026-05-18T04:32:34Z","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 2-form on a quaternionic-Kahler manifold (M, g) is called compatible (with the quaternionic structure) if it is a section of the direct sum bundle S^2(H) \\oplus S^2(E). We construct a connection D on S^2(H) \\oplus S^2(E)\\oplus TM, which is a prolongation of the conformal-Killing operator acting on compatible 2-forms. We show that D is flat if and only if the quaternionic-Weyl tensor of (M,g) is zero. Consequences of this result are developed. We construct a skew-symmetric multiplication on the space of conformal-Killing 2-forms on (M,g) and we study its properties in connection with the subs","authors_text":"Liana David","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-16T11:14:52Z","title":"A prolongation of the conformal-Killing operator on quaternionic-Kahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3007","kind":"arxiv","version":2},"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":"sha256:7eb91dd63b857eef5c2d01bb6a380a670443e97f9d6356321dbf30eb289d3e67","target":"record","created_at":"2026-05-18T04:32:34Z","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":"6179c17c4b6c29a0b5feaf4b63e68f414c7399e79ec2c74b436745aff38c76d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-16T11:14:52Z","title_canon_sha256":"9ce1a9debd7da8b8d04798530dedd84e0a8c7e8534dbf1fa172b27fa4dbe7eb2"},"schema_version":"1.0","source":{"id":"0911.3007","kind":"arxiv","version":2}},"canonical_sha256":"b0ef4b2ff2b82f450cf1074d92203cdc373aa9504658dfdf335e46d2d465fa98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0ef4b2ff2b82f450cf1074d92203cdc373aa9504658dfdf335e46d2d465fa98","first_computed_at":"2026-05-18T04:32:34.097504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:34.097504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1cOxR1DvuYEEvCUpmEunZN8O1Iu0WBIQaUCG3ZjNmhRA5fjZpdTjT/iQD5NfNWVmuM6d4MfTmk98fiZho13rDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:34.098040Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3007","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7eb91dd63b857eef5c2d01bb6a380a670443e97f9d6356321dbf30eb289d3e67","sha256:567c10cbb2dd08e3fdb2a3cd82529f6f4701d3145982aef36761b44b14af03f5"],"state_sha256":"31b551834e9cc0039b2e611180dc23798af038db106fca998da41be85a97b804"}