{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HYBQG75V2M2AELZQGDOLF55F7K","short_pith_number":"pith:HYBQG75V","canonical_record":{"source":{"id":"1109.4532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-21T14:06:52Z","cross_cats_sorted":[],"title_canon_sha256":"9665d3224fb573fcb433fbf9ea1baa1b19007c3854d9356f4a753f910496b891","abstract_canon_sha256":"672c011645a75c68a9192088ae7749f04f576fb2437ea0f261a87e2a2a6f82f9"},"schema_version":"1.0"},"canonical_sha256":"3e03037fb5d334022f3030dcb2f7a5fabfc0a65a817ba37bc932519756a9f3d4","source":{"kind":"arxiv","id":"1109.4532","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HYBQG75V2M2AELZQGDOLF55F7K","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-21T14:06:52Z","cross_cats_sorted":[],"title_canon_sha256":"9665d3224fb573fcb433fbf9ea1baa1b19007c3854d9356f4a753f910496b891","abstract_canon_sha256":"672c011645a75c68a9192088ae7749f04f576fb2437ea0f261a87e2a2a6f82f9"},"schema_version":"1.0"},"canonical_sha256":"3e03037fb5d334022f3030dcb2f7a5fabfc0a65a817ba37bc932519756a9f3d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:34.507855Z","signature_b64":"fVGQ2UjfR74+DZ+kQzocP5scVCKgaWgV62cdva7JV2/py2DTCPtTODjaMnW8Rp1rCq/LCqCRG3wQHRnQ2xQFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e03037fb5d334022f3030dcb2f7a5fabfc0a65a817ba37bc932519756a9f3d4","last_reissued_at":"2026-05-18T04:12:34.507374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:34.507374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4532","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTkyh+2GWX64wcrw34Zsb9Fw5kFusBKeXafG9UWZZDthgmJ2LkjCLD42wHVK6UF8AREU7VCGRlDlpcuogYLEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:39:15.966302Z"},"content_sha256":"0d67f6164376a28c10d7a248c88e18710bd8739d7a6fe9590fed7046cc63872c","schema_version":"1.0","event_id":"sha256:0d67f6164376a28c10d7a248c88e18710bd8739d7a6fe9590fed7046cc63872c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HYBQG75V2M2AELZQGDOLF55F7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K\\\"ahler-Weyl manifolds of dimension 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"P. Gilkey, S. Nikcevic","submitted_at":"2011-09-21T14:06:52Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4532","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMi8E00pyR7+8L2+3OU8ixQ99OmOa6LnFHDsZBuQXXb0cLBx5FOiQUvHoCqQr0QpwDE3dEMUz1sP3pXdRdN3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:39:15.966803Z"},"content_sha256":"f650eed7fdc806b72eaf4dd7234924276ef3f33aed1516a5b79a2c40358053ee","schema_version":"1.0","event_id":"sha256:f650eed7fdc806b72eaf4dd7234924276ef3f33aed1516a5b79a2c40358053ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYBQG75V2M2AELZQGDOLF55F7K/bundle.json","state_url":"https://pith.science/pith/HYBQG75V2M2AELZQGDOLF55F7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYBQG75V2M2AELZQGDOLF55F7K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T03:39:15Z","links":{"resolver":"https://pith.science/pith/HYBQG75V2M2AELZQGDOLF55F7K","bundle":"https://pith.science/pith/HYBQG75V2M2AELZQGDOLF55F7K/bundle.json","state":"https://pith.science/pith/HYBQG75V2M2AELZQGDOLF55F7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYBQG75V2M2AELZQGDOLF55F7K/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zWKmK+SgNC2ZQ5r5ao5Q7+h3bN4cYgadui3VS49XXP3FeWGESSHRnkJBTDX2LXsda9QAp/om1gaC2xhmLRhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:39:15.971064Z","bundle_sha256":"d8f385a6032241dcb877901240ad4c0e917f17bcc39cc6d417bdb846c475636b"}}