{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KW3ITKLDXHCD7NH23MAW4TBART","short_pith_number":"pith:KW3ITKLD","canonical_record":{"source":{"id":"1304.2229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-08T15:04:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1b90c5dc332919d3982530e6698f08ba17fe848a08654cbc456073405af6e29d","abstract_canon_sha256":"c6dd5ccda1667b4d46c728ecfa424266d1fadd32fd85566a251c12c5e473a8d7"},"schema_version":"1.0"},"canonical_sha256":"55b689a963b9c43fb4fadb016e4c208ce576c02d7c5ed2e54659c0f17dc80353","source":{"kind":"arxiv","id":"1304.2229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2229","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2229v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2229","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"KW3ITKLDXHCD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KW3ITKLDXHCD7NH2","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KW3ITKLD","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KW3ITKLDXHCD7NH23MAW4TBART","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-08T15:04:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1b90c5dc332919d3982530e6698f08ba17fe848a08654cbc456073405af6e29d","abstract_canon_sha256":"c6dd5ccda1667b4d46c728ecfa424266d1fadd32fd85566a251c12c5e473a8d7"},"schema_version":"1.0"},"canonical_sha256":"55b689a963b9c43fb4fadb016e4c208ce576c02d7c5ed2e54659c0f17dc80353","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:43.644306Z","signature_b64":"W/8JwYEkzIxN88j4a2KlYYtxnRK/EXSmomK8h0PzC9IcLThUfXiR2n+BWJ8YiQCduDMriDdQKk4Clnc/YETHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b689a963b9c43fb4fadb016e4c208ce576c02d7c5ed2e54659c0f17dc80353","last_reissued_at":"2026-05-18T03:28:43.643512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:43.643512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2229","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":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQUYNGlgfOK7t9KNxpzKsyAA6fYZbYjrT68PQdWnPPr6QLfJkcu8sCPC8kZOKn4xEA7VVqxdwpwQ4GM18jblDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:23:58.516421Z"},"content_sha256":"a8a984947e2ad93e2e26bd0c3c35223ab6309f095d4bbaf607e5acac70299961","schema_version":"1.0","event_id":"sha256:a8a984947e2ad93e2e26bd0c3c35223ab6309f095d4bbaf607e5acac70299961"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KW3ITKLDXHCD7NH23MAW4TBART","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization Of Left Artinian Algebras Through Pseudo Path Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Fang Li","submitted_at":"2013-04-08T15:04:45Z","abstract_excerpt":"In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field $k$ when it is splitting over its radical, in particular, when the dimension of the quotient algebra decided by the $n$'th Hochschild cohomology is less than 2 (for example, $k$ is finite or char$k=0$). Using generalized path algebras, the generalized Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebras are introduced as a new generalization of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2229","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":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8yO59wUWMJrTOUvErvT3VX0djwKQir7/f3OvVPx/8w3iIJFfrQMLrHKCaEZa9ugWNbWa3c2yEht/QU2u9/uAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:23:58.516765Z"},"content_sha256":"c21b5ffe63020e083ff25b2f1f0b9177c3f97c244017e81dfec14c0b1b688fb0","schema_version":"1.0","event_id":"sha256:c21b5ffe63020e083ff25b2f1f0b9177c3f97c244017e81dfec14c0b1b688fb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KW3ITKLDXHCD7NH23MAW4TBART/bundle.json","state_url":"https://pith.science/pith/KW3ITKLDXHCD7NH23MAW4TBART/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KW3ITKLDXHCD7NH23MAW4TBART/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":"2026-06-09T00:23:58Z","links":{"resolver":"https://pith.science/pith/KW3ITKLDXHCD7NH23MAW4TBART","bundle":"https://pith.science/pith/KW3ITKLDXHCD7NH23MAW4TBART/bundle.json","state":"https://pith.science/pith/KW3ITKLDXHCD7NH23MAW4TBART/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KW3ITKLDXHCD7NH23MAW4TBART/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KW3ITKLDXHCD7NH23MAW4TBART","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":"c6dd5ccda1667b4d46c728ecfa424266d1fadd32fd85566a251c12c5e473a8d7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-08T15:04:45Z","title_canon_sha256":"1b90c5dc332919d3982530e6698f08ba17fe848a08654cbc456073405af6e29d"},"schema_version":"1.0","source":{"id":"1304.2229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2229","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2229v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2229","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"KW3ITKLDXHCD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KW3ITKLDXHCD7NH2","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KW3ITKLD","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c21b5ffe63020e083ff25b2f1f0b9177c3f97c244017e81dfec14c0b1b688fb0","target":"graph","created_at":"2026-05-18T03:28:43Z","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":"In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field $k$ when it is splitting over its radical, in particular, when the dimension of the quotient algebra decided by the $n$'th Hochschild cohomology is less than 2 (for example, $k$ is finite or char$k=0$). Using generalized path algebras, the generalized Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebras are introduced as a new generalization of p","authors_text":"Fang Li","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-08T15:04:45Z","title":"Characterization Of Left Artinian Algebras Through Pseudo Path Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2229","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:a8a984947e2ad93e2e26bd0c3c35223ab6309f095d4bbaf607e5acac70299961","target":"record","created_at":"2026-05-18T03:28:43Z","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":"c6dd5ccda1667b4d46c728ecfa424266d1fadd32fd85566a251c12c5e473a8d7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-08T15:04:45Z","title_canon_sha256":"1b90c5dc332919d3982530e6698f08ba17fe848a08654cbc456073405af6e29d"},"schema_version":"1.0","source":{"id":"1304.2229","kind":"arxiv","version":1}},"canonical_sha256":"55b689a963b9c43fb4fadb016e4c208ce576c02d7c5ed2e54659c0f17dc80353","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55b689a963b9c43fb4fadb016e4c208ce576c02d7c5ed2e54659c0f17dc80353","first_computed_at":"2026-05-18T03:28:43.643512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.643512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W/8JwYEkzIxN88j4a2KlYYtxnRK/EXSmomK8h0PzC9IcLThUfXiR2n+BWJ8YiQCduDMriDdQKk4Clnc/YETHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.644306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8a984947e2ad93e2e26bd0c3c35223ab6309f095d4bbaf607e5acac70299961","sha256:c21b5ffe63020e083ff25b2f1f0b9177c3f97c244017e81dfec14c0b1b688fb0"],"state_sha256":"a20dd7ba6c02f3a331f0ad4c2c3666fc67126a1e8aab7cb5a0be3a323b5d3da6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVu4HLwBbXPja1eRDK9l78MD+PiWtud4lVWxyMETRLNSxkt30yJWfK2vtsRqREFTIGFoynhvov9IYrYNPM7bBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:23:58.518634Z","bundle_sha256":"fde37befd51d9014cda193ba3fe01384fff095d755ca3ba56f4a301874534eb0"}}