{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6CQ4YIXGOVL3Q3L2R2VEOGWLS6","short_pith_number":"pith:6CQ4YIXG","canonical_record":{"source":{"id":"1905.13048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-29T09:28:27Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"e8a4ee57eade8fed197caa50bc0ebd2196baed7ac44d4ada8cc5d79d136e9028","abstract_canon_sha256":"de7fd2c0a9963c2d25b5d38f7b1d13733c42b4d03e06227295365a401d4f41b2"},"schema_version":"1.0"},"canonical_sha256":"f0a1cc22e67557b86d7a8eaa471acb97bf01476c82ad4009bcac8d18e75a0e34","source":{"kind":"arxiv","id":"1905.13048","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.13048","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.13048v1","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13048","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"6CQ4YIXGOVL3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6CQ4YIXGOVL3Q3L2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6CQ4YIXG","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6CQ4YIXGOVL3Q3L2R2VEOGWLS6","target":"record","payload":{"canonical_record":{"source":{"id":"1905.13048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-29T09:28:27Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"e8a4ee57eade8fed197caa50bc0ebd2196baed7ac44d4ada8cc5d79d136e9028","abstract_canon_sha256":"de7fd2c0a9963c2d25b5d38f7b1d13733c42b4d03e06227295365a401d4f41b2"},"schema_version":"1.0"},"canonical_sha256":"f0a1cc22e67557b86d7a8eaa471acb97bf01476c82ad4009bcac8d18e75a0e34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:39.060792Z","signature_b64":"eT0iMZpBQKCCrJrOL8YG/uwreDEPQ1pvAh8RxqsH7qPOPo6Msm+ZgtdsPszfwm7YF7xzQSvqzJo185f/j2mqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0a1cc22e67557b86d7a8eaa471acb97bf01476c82ad4009bcac8d18e75a0e34","last_reissued_at":"2026-05-17T23:44:39.060343Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:39.060343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.13048","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":"2026-05-17T23:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSkuiZHCrg3fT23/IYnR+FRf07v+nXIXaHHsR2DxILlr3bImvrnalsPJI3VLifwuFrGarsEGY4im29o4Mu/NCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:06.509374Z"},"content_sha256":"8c8b5c4d49886ed9bceb6f9752af7cce1f72efb107912a3101a7711bcecbda42","schema_version":"1.0","event_id":"sha256:8c8b5c4d49886ed9bceb6f9752af7cce1f72efb107912a3101a7711bcecbda42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6CQ4YIXGOVL3Q3L2R2VEOGWLS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized representations of 3-Hom-Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.RT","authors_text":"Abdenacer Makhlouf, Sami Mabrouk, Sonia Massoud","submitted_at":"2019-05-29T09:28:27Z","abstract_excerpt":"The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology theory and study semi-direct products. We provide a key construction, various examples and computation of 2-cocycles of the new cohomology. Also, we give a connection between a split abelian extension of a 3-Hom-Lie algebra and a generalized semidirect product 3-Hom-Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13048","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":"2026-05-17T23:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnJfhyzjUsMsy68VP/zPvJVgtTu31yKTf9rzqbl1PSMC6gelD3XR7XNsYw/5YfzJoIFmsnJVHvWZJ7ANC9Y7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:06.509884Z"},"content_sha256":"8432e1af80eef29368c4d5de44868bd8dab0cacd47b9d60ab6b5452c56854101","schema_version":"1.0","event_id":"sha256:8432e1af80eef29368c4d5de44868bd8dab0cacd47b9d60ab6b5452c56854101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/bundle.json","state_url":"https://pith.science/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/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":"2026-06-02T05:25:06Z","links":{"resolver":"https://pith.science/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6","bundle":"https://pith.science/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/bundle.json","state":"https://pith.science/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CQ4YIXGOVL3Q3L2R2VEOGWLS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6CQ4YIXGOVL3Q3L2R2VEOGWLS6","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":"de7fd2c0a9963c2d25b5d38f7b1d13733c42b4d03e06227295365a401d4f41b2","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-29T09:28:27Z","title_canon_sha256":"e8a4ee57eade8fed197caa50bc0ebd2196baed7ac44d4ada8cc5d79d136e9028"},"schema_version":"1.0","source":{"id":"1905.13048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.13048","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.13048v1","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13048","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"6CQ4YIXGOVL3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6CQ4YIXGOVL3Q3L2","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6CQ4YIXG","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:8432e1af80eef29368c4d5de44868bd8dab0cacd47b9d60ab6b5452c56854101","target":"graph","created_at":"2026-05-17T23:44:39Z","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":"The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology theory and study semi-direct products. We provide a key construction, various examples and computation of 2-cocycles of the new cohomology. Also, we give a connection between a split abelian extension of a 3-Hom-Lie algebra and a generalized semidirect product 3-Hom-Lie algebra.","authors_text":"Abdenacer Makhlouf, Sami Mabrouk, Sonia Massoud","cross_cats":["math-ph","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-29T09:28:27Z","title":"Generalized representations of 3-Hom-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13048","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":"sha256:8c8b5c4d49886ed9bceb6f9752af7cce1f72efb107912a3101a7711bcecbda42","target":"record","created_at":"2026-05-17T23:44:39Z","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":"de7fd2c0a9963c2d25b5d38f7b1d13733c42b4d03e06227295365a401d4f41b2","cross_cats_sorted":["math-ph","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-29T09:28:27Z","title_canon_sha256":"e8a4ee57eade8fed197caa50bc0ebd2196baed7ac44d4ada8cc5d79d136e9028"},"schema_version":"1.0","source":{"id":"1905.13048","kind":"arxiv","version":1}},"canonical_sha256":"f0a1cc22e67557b86d7a8eaa471acb97bf01476c82ad4009bcac8d18e75a0e34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a1cc22e67557b86d7a8eaa471acb97bf01476c82ad4009bcac8d18e75a0e34","first_computed_at":"2026-05-17T23:44:39.060343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:39.060343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eT0iMZpBQKCCrJrOL8YG/uwreDEPQ1pvAh8RxqsH7qPOPo6Msm+ZgtdsPszfwm7YF7xzQSvqzJo185f/j2mqDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:39.060792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.13048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c8b5c4d49886ed9bceb6f9752af7cce1f72efb107912a3101a7711bcecbda42","sha256:8432e1af80eef29368c4d5de44868bd8dab0cacd47b9d60ab6b5452c56854101"],"state_sha256":"9640f68b1909785bb77c89cc7a47d7c9689ec6b4a5a7303251d86921f281c19f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/tv4aUf9naP/cZYm7TpM+kOKJhcZSzi48LqiXPVlzyQY7cH/ENokQ9dsbCk19PNrHDSC1GcZVB2E2Dps7YyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:25:06.512189Z","bundle_sha256":"7a3f055ef1c95d8bc76a3b63ec293706c6426823528d58df0b91d3afc64c0f3e"}}