{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QXQWZJYDA37ZBKQNTELSGIV5AJ","short_pith_number":"pith:QXQWZJYD","canonical_record":{"source":{"id":"1905.01687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-05T14:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"9de35cdf3d11b017f297894ebdf89a3ce18031fd1c13bc525b0e1f6ef3670131","abstract_canon_sha256":"2c90121757615896202919ef66acd551c7990065b560a34d46edbed4eada0d27"},"schema_version":"1.0"},"canonical_sha256":"85e16ca70306ff90aa0d99172322bd0260ffcd67705c5b5a49fb4193e465b62b","source":{"kind":"arxiv","id":"1905.01687","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01687","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01687v1","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01687","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"QXQWZJYDA37Z","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QXQWZJYDA37ZBKQN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QXQWZJYD","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QXQWZJYDA37ZBKQNTELSGIV5AJ","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-05T14:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"9de35cdf3d11b017f297894ebdf89a3ce18031fd1c13bc525b0e1f6ef3670131","abstract_canon_sha256":"2c90121757615896202919ef66acd551c7990065b560a34d46edbed4eada0d27"},"schema_version":"1.0"},"canonical_sha256":"85e16ca70306ff90aa0d99172322bd0260ffcd67705c5b5a49fb4193e465b62b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:57.763075Z","signature_b64":"wg1/JwH7IZrilgbHuVh2AfEHaD0scsdW3Vg/M1n48txchPWXIdjNu1jOHNG1ZzZ3lQ2p9sKfP2nMBFD6DKthCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85e16ca70306ff90aa0d99172322bd0260ffcd67705c5b5a49fb4193e465b62b","last_reissued_at":"2026-05-17T23:46:57.762344Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:57.762344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01687","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":"2026-05-17T23:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tv61JdkpMfSxiFrbg3Cfiuu5hT+hpj4uh6zberM2kny5Wo8f3qDoG5CH06p7cW8JRl5s0foLkp3XkPTeZdBPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:16:03.609398Z"},"content_sha256":"65f2eaf8e95eafb51b7257bda78f296389225c2b06887156236a710b5d7c578c","schema_version":"1.0","event_id":"sha256:65f2eaf8e95eafb51b7257bda78f296389225c2b06887156236a710b5d7c578c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QXQWZJYDA37ZBKQNTELSGIV5AJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex fuzzy Lie Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Shadi Shaqaqha","submitted_at":"2019-05-05T14:07:47Z","abstract_excerpt":"A complex fuzzy Lie algebra is a fuzzy Lie algebra whose membership function takes values in the unit circle in the complex plane. In this paper, we deine the complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras. Then, we investigate some of characteristics of complex fuzzy Lie subalgebras. The relationship between complex fuzzy Lie subalgebras and fuzzy Lie subalgebras is also investigated. Finally, we define the image and the inverse image of complex fuzzy Lie subalgebra under Lie algebra homomorphism. The properties of complex fuzzy Lie subalgebras and complex fuzzy ideals"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01687","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":"2026-05-17T23:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3nGDa7/V4DiGthjOYze1+amvh+2mVHbrfkYY6YKRqx53Q8LeWaYZpr2/HKVxIVnSNgxwQX0BwbO3CgBFGRaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:16:03.609733Z"},"content_sha256":"9e255062e78e09ec73c28efae498ca698e2fd784c5601a92187dd5724069a7a1","schema_version":"1.0","event_id":"sha256:9e255062e78e09ec73c28efae498ca698e2fd784c5601a92187dd5724069a7a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/bundle.json","state_url":"https://pith.science/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/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":"2026-06-22T18:16:03Z","links":{"resolver":"https://pith.science/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ","bundle":"https://pith.science/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/bundle.json","state":"https://pith.science/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXQWZJYDA37ZBKQNTELSGIV5AJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QXQWZJYDA37ZBKQNTELSGIV5AJ","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":"2c90121757615896202919ef66acd551c7990065b560a34d46edbed4eada0d27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-05T14:07:47Z","title_canon_sha256":"9de35cdf3d11b017f297894ebdf89a3ce18031fd1c13bc525b0e1f6ef3670131"},"schema_version":"1.0","source":{"id":"1905.01687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01687","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01687v1","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01687","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"QXQWZJYDA37Z","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QXQWZJYDA37ZBKQN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QXQWZJYD","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:9e255062e78e09ec73c28efae498ca698e2fd784c5601a92187dd5724069a7a1","target":"graph","created_at":"2026-05-17T23:46:57Z","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 complex fuzzy Lie algebra is a fuzzy Lie algebra whose membership function takes values in the unit circle in the complex plane. In this paper, we deine the complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras. Then, we investigate some of characteristics of complex fuzzy Lie subalgebras. The relationship between complex fuzzy Lie subalgebras and fuzzy Lie subalgebras is also investigated. Finally, we define the image and the inverse image of complex fuzzy Lie subalgebra under Lie algebra homomorphism. The properties of complex fuzzy Lie subalgebras and complex fuzzy ideals","authors_text":"Shadi Shaqaqha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-05T14:07:47Z","title":"Complex fuzzy Lie Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01687","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":"sha256:65f2eaf8e95eafb51b7257bda78f296389225c2b06887156236a710b5d7c578c","target":"record","created_at":"2026-05-17T23:46:57Z","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":"2c90121757615896202919ef66acd551c7990065b560a34d46edbed4eada0d27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-05T14:07:47Z","title_canon_sha256":"9de35cdf3d11b017f297894ebdf89a3ce18031fd1c13bc525b0e1f6ef3670131"},"schema_version":"1.0","source":{"id":"1905.01687","kind":"arxiv","version":1}},"canonical_sha256":"85e16ca70306ff90aa0d99172322bd0260ffcd67705c5b5a49fb4193e465b62b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85e16ca70306ff90aa0d99172322bd0260ffcd67705c5b5a49fb4193e465b62b","first_computed_at":"2026-05-17T23:46:57.762344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:57.762344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wg1/JwH7IZrilgbHuVh2AfEHaD0scsdW3Vg/M1n48txchPWXIdjNu1jOHNG1ZzZ3lQ2p9sKfP2nMBFD6DKthCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:57.763075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65f2eaf8e95eafb51b7257bda78f296389225c2b06887156236a710b5d7c578c","sha256:9e255062e78e09ec73c28efae498ca698e2fd784c5601a92187dd5724069a7a1"],"state_sha256":"0328d521e1ef6bbebebf7a9b794bb0e1ca1582565308ab18c175cf7ae7befb20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gBKjP0VeUKsMmM6LmI9qiOrjfmsftRUmpn9CCTIYxiCtL8L4BK7QU0HLtCN4/gHg9Lm4g0uaKmpkGu0r85UtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:16:03.611645Z","bundle_sha256":"77dbeb9acb3821fbfb7fc5f781ae47bd6cd91b6c068564a51f5a3ac31cd38b1c"}}