{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HYBQG75V2M2AELZQGDOLF55F7K","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":"672c011645a75c68a9192088ae7749f04f576fb2437ea0f261a87e2a2a6f82f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-21T14:06:52Z","title_canon_sha256":"9665d3224fb573fcb433fbf9ea1baa1b19007c3854d9356f4a753f910496b891"},"schema_version":"1.0","source":{"id":"1109.4532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4532","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4532v1","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4532","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"HYBQG75V2M2A","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HYBQG75V2M2AELZQ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HYBQG75V","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f650eed7fdc806b72eaf4dd7234924276ef3f33aed1516a5b79a2c40358053ee","target":"graph","created_at":"2026-05-18T04:12:34Z","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":"We determine the space of algebraic pseudo-Hermitian K\\\"ahler-Weyl curvature tensors and the space of para-Hermitian K\\\"ahler-Weyl curvature tensors in dimension 4 and show that every algebraic possibility is geometrically realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds and for para-Hermitian Weyl manifolds in arbitrary dimension.","authors_text":"P. Gilkey, S. Nikcevic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-21T14:06:52Z","title":"K\\\"ahler-Weyl manifolds of dimension 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4532","kind":"arxiv","version":1},"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":"sha256:0d67f6164376a28c10d7a248c88e18710bd8739d7a6fe9590fed7046cc63872c","target":"record","created_at":"2026-05-18T04:12:34Z","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":"672c011645a75c68a9192088ae7749f04f576fb2437ea0f261a87e2a2a6f82f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-21T14:06:52Z","title_canon_sha256":"9665d3224fb573fcb433fbf9ea1baa1b19007c3854d9356f4a753f910496b891"},"schema_version":"1.0","source":{"id":"1109.4532","kind":"arxiv","version":1}},"canonical_sha256":"3e03037fb5d334022f3030dcb2f7a5fabfc0a65a817ba37bc932519756a9f3d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e03037fb5d334022f3030dcb2f7a5fabfc0a65a817ba37bc932519756a9f3d4","first_computed_at":"2026-05-18T04:12:34.507374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:34.507374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVGQ2UjfR74+DZ+kQzocP5scVCKgaWgV62cdva7JV2/py2DTCPtTODjaMnW8Rp1rCq/LCqCRG3wQHRnQ2xQFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:34.507855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d67f6164376a28c10d7a248c88e18710bd8739d7a6fe9590fed7046cc63872c","sha256:f650eed7fdc806b72eaf4dd7234924276ef3f33aed1516a5b79a2c40358053ee"],"state_sha256":"3907a42c11db2d15a91f26c666b169491544f03f1794543fe68ebc8f3a912a4d"}