{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5FSXJ7X2S7YUFZ3XDX46ZTXIPX","short_pith_number":"pith:5FSXJ7X2","canonical_record":{"source":{"id":"1211.4453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-19T15:04:16Z","cross_cats_sorted":[],"title_canon_sha256":"c7bf6d950f9f7b0de07fd298d5d17ec4a367a3904d816577769463d55b03247b","abstract_canon_sha256":"b5cc0f7cca28c573d3a2158939aa1b15a0851412a28ce4dc5193b8856a3f1801"},"schema_version":"1.0"},"canonical_sha256":"e96574fefa97f142e7771df9eccee87dd90da11afee8376055760f40a472781b","source":{"kind":"arxiv","id":"1211.4453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4453","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4453v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4453","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"5FSXJ7X2S7YU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5FSXJ7X2S7YUFZ3X","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5FSXJ7X2","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5FSXJ7X2S7YUFZ3XDX46ZTXIPX","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-19T15:04:16Z","cross_cats_sorted":[],"title_canon_sha256":"c7bf6d950f9f7b0de07fd298d5d17ec4a367a3904d816577769463d55b03247b","abstract_canon_sha256":"b5cc0f7cca28c573d3a2158939aa1b15a0851412a28ce4dc5193b8856a3f1801"},"schema_version":"1.0"},"canonical_sha256":"e96574fefa97f142e7771df9eccee87dd90da11afee8376055760f40a472781b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.842659Z","signature_b64":"61SDI3maGEZwVaz9JXaqcg7y6691ZA85FZcGb1x3G+qGZTua8yjOzzoEApUUqnZmgfnjMTU6PR1lKZgjvyfrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e96574fefa97f142e7771df9eccee87dd90da11afee8376055760f40a472781b","last_reissued_at":"2026-05-18T03:40:26.841816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.841816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4453","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzVkoYaArAuwB0QJVpW8EcIC+ow0105ilUwD4mtoJ7ksimtUD/ZkomngkXSoWHoyFrljS4WZ/81URoFqMy8FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:40:17.581255Z"},"content_sha256":"c02bfaf35cf92cc240f423c933daf9f4b37748d71d036fcd81c053c7a8259f64","schema_version":"1.0","event_id":"sha256:c02bfaf35cf92cc240f423c933daf9f4b37748d71d036fcd81c053c7a8259f64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5FSXJ7X2S7YUFZ3XDX46ZTXIPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogeneous 4-dimensional Kaehler--Weyl Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"E. Garcia-Rio, M. Brozos-Vazquez, P. Gilkey, R. Vazquez-Lorenzo","submitted_at":"2012-11-19T15:04:16Z","abstract_excerpt":"Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes values in a certain representation space. In this paper, we show that any algebraic possibility in this representation space can in fact be geometrically realized by a left-invariant Kaehler-Weyl structure on a 4-dimensional Lie group in either the Hermitian or the para-Hermitian setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4453","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vjHMC61HvR3cDx639GqbLUlI/Bdalpw97Wks6M1mO3OfEzR33XfetFjo8r3dv5VAVtTxkiPAPQKJ8xbuaqhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:40:17.581913Z"},"content_sha256":"9cb053a666ecd6704c30fd0b1a18a0989d38e0c7d65b6aaad9ac9fdb3eb0a8f5","schema_version":"1.0","event_id":"sha256:9cb053a666ecd6704c30fd0b1a18a0989d38e0c7d65b6aaad9ac9fdb3eb0a8f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/bundle.json","state_url":"https://pith.science/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/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":"2026-05-30T15:40:17Z","links":{"resolver":"https://pith.science/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX","bundle":"https://pith.science/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/bundle.json","state":"https://pith.science/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FSXJ7X2S7YUFZ3XDX46ZTXIPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5FSXJ7X2S7YUFZ3XDX46ZTXIPX","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":"b5cc0f7cca28c573d3a2158939aa1b15a0851412a28ce4dc5193b8856a3f1801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-19T15:04:16Z","title_canon_sha256":"c7bf6d950f9f7b0de07fd298d5d17ec4a367a3904d816577769463d55b03247b"},"schema_version":"1.0","source":{"id":"1211.4453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4453","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4453v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4453","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"5FSXJ7X2S7YU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5FSXJ7X2S7YUFZ3X","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5FSXJ7X2","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:9cb053a666ecd6704c30fd0b1a18a0989d38e0c7d65b6aaad9ac9fdb3eb0a8f5","target":"graph","created_at":"2026-05-18T03:40:26Z","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":"Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes values in a certain representation space. In this paper, we show that any algebraic possibility in this representation space can in fact be geometrically realized by a left-invariant Kaehler-Weyl structure on a 4-dimensional Lie group in either the Hermitian or the para-Hermitian setting.","authors_text":"E. Garcia-Rio, M. Brozos-Vazquez, P. Gilkey, R. Vazquez-Lorenzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-19T15:04:16Z","title":"Homogeneous 4-dimensional Kaehler--Weyl Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4453","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:c02bfaf35cf92cc240f423c933daf9f4b37748d71d036fcd81c053c7a8259f64","target":"record","created_at":"2026-05-18T03:40:26Z","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":"b5cc0f7cca28c573d3a2158939aa1b15a0851412a28ce4dc5193b8856a3f1801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-19T15:04:16Z","title_canon_sha256":"c7bf6d950f9f7b0de07fd298d5d17ec4a367a3904d816577769463d55b03247b"},"schema_version":"1.0","source":{"id":"1211.4453","kind":"arxiv","version":1}},"canonical_sha256":"e96574fefa97f142e7771df9eccee87dd90da11afee8376055760f40a472781b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e96574fefa97f142e7771df9eccee87dd90da11afee8376055760f40a472781b","first_computed_at":"2026-05-18T03:40:26.841816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.841816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61SDI3maGEZwVaz9JXaqcg7y6691ZA85FZcGb1x3G+qGZTua8yjOzzoEApUUqnZmgfnjMTU6PR1lKZgjvyfrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.842659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c02bfaf35cf92cc240f423c933daf9f4b37748d71d036fcd81c053c7a8259f64","sha256:9cb053a666ecd6704c30fd0b1a18a0989d38e0c7d65b6aaad9ac9fdb3eb0a8f5"],"state_sha256":"3ba0c8c9b2c96ed6e75e6e7ab4b47cbc35aad05db08f205825bcfba60073a472"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xEpG/ImcsxLo+7KAQZ6CYBZr+sI+AIDeJbx28UN3foEXRuSD+1pQ+g4hGbSTsNudMgEMEUDM4ViQXVkGNnHDCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:40:17.585963Z","bundle_sha256":"063b8582d4888aa2f85790c96d7ed95dc6ebb68b5a1c39eb70d090a48252434d"}}