{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:R2QSWRUMKVAF3MKZG47IYWU2IR","short_pith_number":"pith:R2QSWRUM","canonical_record":{"source":{"id":"1906.04969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-12T07:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"7f172b8c9ae1a1ad2145885884eddd8e83516a79eb0159f68b1e690243c019b8","abstract_canon_sha256":"db37ece7d6dd2b5c86119f9e87d93b6e3315ba459ed64cd1d642b19d14a83e47"},"schema_version":"1.0"},"canonical_sha256":"8ea12b468c55405db159373e8c5a9a4468b9382b94e65a05462645e57ecf938f","source":{"kind":"arxiv","id":"1906.04969","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04969","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04969v1","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04969","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"R2QSWRUMKVAF","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"R2QSWRUMKVAF3MKZ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"R2QSWRUM","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:R2QSWRUMKVAF3MKZG47IYWU2IR","target":"record","payload":{"canonical_record":{"source":{"id":"1906.04969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-12T07:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"7f172b8c9ae1a1ad2145885884eddd8e83516a79eb0159f68b1e690243c019b8","abstract_canon_sha256":"db37ece7d6dd2b5c86119f9e87d93b6e3315ba459ed64cd1d642b19d14a83e47"},"schema_version":"1.0"},"canonical_sha256":"8ea12b468c55405db159373e8c5a9a4468b9382b94e65a05462645e57ecf938f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:29.922200Z","signature_b64":"92y0mNq0hwWs4tEXTq0jL5n+JZnsMfHN15mQq5gcdiYGq7wsb/nli1W7S7edMGN9czkvL+aEjv5oGfCbDCPzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ea12b468c55405db159373e8c5a9a4468b9382b94e65a05462645e57ecf938f","last_reissued_at":"2026-05-17T23:43:29.921535Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:29.921535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.04969","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":"2026-05-17T23:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLEah9f+FRW99xZ5s5oQO2et/7cT+n1JeKUYZb9U8XmZfOMKRCdQ73m6zCxTcgu2WGU7IdwKZcxO/jZZFGQqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:54:14.115925Z"},"content_sha256":"e2271ea66ee114197169d39742fc6a42e7b530b665417292cb1b3c97dd5f6154","schema_version":"1.0","event_id":"sha256:e2271ea66ee114197169d39742fc6a42e7b530b665417292cb1b3c97dd5f6154"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:R2QSWRUMKVAF3MKZG47IYWU2IR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure and classification of Hom-associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Ahmed Zahari","submitted_at":"2019-06-12T07:00:54Z","abstract_excerpt":"The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\\times 2$-matrix algebra to simple Hom-associative algebras. We provide a classification of $n$-dimensional Hom-associative algebras for $n\\leq3$. Then study their derivations and compute small Hom-Type Hochschild cohomology groups. Furthermore, we discuss their irreducible components."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04969","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":"2026-05-17T23:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"omDaNY37E8ThCUiFA23eBxdwff53R4cJxjkjGdjfOkKfJN0OOE/tImNTLaLg2itYFIoHiWAWU9OuNrkcnpQpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:54:14.116259Z"},"content_sha256":"d2ce530388233379cacbd1935b1e4005f7ec4e2e16844e71f420345dc268482f","schema_version":"1.0","event_id":"sha256:d2ce530388233379cacbd1935b1e4005f7ec4e2e16844e71f420345dc268482f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/bundle.json","state_url":"https://pith.science/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/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":"2026-06-02T07:54:14Z","links":{"resolver":"https://pith.science/pith/R2QSWRUMKVAF3MKZG47IYWU2IR","bundle":"https://pith.science/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/bundle.json","state":"https://pith.science/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R2QSWRUMKVAF3MKZG47IYWU2IR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:R2QSWRUMKVAF3MKZG47IYWU2IR","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":"db37ece7d6dd2b5c86119f9e87d93b6e3315ba459ed64cd1d642b19d14a83e47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-12T07:00:54Z","title_canon_sha256":"7f172b8c9ae1a1ad2145885884eddd8e83516a79eb0159f68b1e690243c019b8"},"schema_version":"1.0","source":{"id":"1906.04969","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04969","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04969v1","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04969","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"R2QSWRUMKVAF","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"R2QSWRUMKVAF3MKZ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"R2QSWRUM","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:d2ce530388233379cacbd1935b1e4005f7ec4e2e16844e71f420345dc268482f","target":"graph","created_at":"2026-05-17T23:43:29Z","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 purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\\times 2$-matrix algebra to simple Hom-associative algebras. We provide a classification of $n$-dimensional Hom-associative algebras for $n\\leq3$. Then study their derivations and compute small Hom-Type Hochschild cohomology groups. Furthermore, we discuss their irreducible components.","authors_text":"Abdenacer Makhlouf, Ahmed Zahari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-12T07:00:54Z","title":"Structure and classification of Hom-associative algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04969","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:e2271ea66ee114197169d39742fc6a42e7b530b665417292cb1b3c97dd5f6154","target":"record","created_at":"2026-05-17T23:43:29Z","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":"db37ece7d6dd2b5c86119f9e87d93b6e3315ba459ed64cd1d642b19d14a83e47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-12T07:00:54Z","title_canon_sha256":"7f172b8c9ae1a1ad2145885884eddd8e83516a79eb0159f68b1e690243c019b8"},"schema_version":"1.0","source":{"id":"1906.04969","kind":"arxiv","version":1}},"canonical_sha256":"8ea12b468c55405db159373e8c5a9a4468b9382b94e65a05462645e57ecf938f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ea12b468c55405db159373e8c5a9a4468b9382b94e65a05462645e57ecf938f","first_computed_at":"2026-05-17T23:43:29.921535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:29.921535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"92y0mNq0hwWs4tEXTq0jL5n+JZnsMfHN15mQq5gcdiYGq7wsb/nli1W7S7edMGN9czkvL+aEjv5oGfCbDCPzBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:29.922200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04969","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2271ea66ee114197169d39742fc6a42e7b530b665417292cb1b3c97dd5f6154","sha256:d2ce530388233379cacbd1935b1e4005f7ec4e2e16844e71f420345dc268482f"],"state_sha256":"4794af245b71e70936e095a3711fe8aec569040335d7938339ab85afc1195a70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTW+5/hddXkfoPmr7POhYOfWIaFExeAiABnGLWNEJ41YAPJJOwUDnqJTwhuy6vXjhRG0oDgnmY9naQFSv8I6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:54:14.118120Z","bundle_sha256":"ef6667eb38005a44ad6f01b2d2e5f76bd240f8b8799838030fc0594cb424b7de"}}