{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5P4JHAGI5XERORWYROW66BN2SF","short_pith_number":"pith:5P4JHAGI","canonical_record":{"source":{"id":"1701.00768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T18:25:39Z","cross_cats_sorted":[],"title_canon_sha256":"7498dd7c808eb03d168e4e2adf837d614a01828f443c13a712b8485217627182","abstract_canon_sha256":"946f3b0e35d4ef9926fc38338fec14b0296f97828c83c98a052f2ea821b0e646"},"schema_version":"1.0"},"canonical_sha256":"ebf89380c8edc91746d88badef05ba915504d24607c200c291e3c5404ef2ee15","source":{"kind":"arxiv","id":"1701.00768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00768","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00768v1","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00768","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"5P4JHAGI5XER","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5P4JHAGI5XERORWY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5P4JHAGI","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5P4JHAGI5XERORWYROW66BN2SF","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T18:25:39Z","cross_cats_sorted":[],"title_canon_sha256":"7498dd7c808eb03d168e4e2adf837d614a01828f443c13a712b8485217627182","abstract_canon_sha256":"946f3b0e35d4ef9926fc38338fec14b0296f97828c83c98a052f2ea821b0e646"},"schema_version":"1.0"},"canonical_sha256":"ebf89380c8edc91746d88badef05ba915504d24607c200c291e3c5404ef2ee15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:28.230774Z","signature_b64":"6XBQT+U3jPgX2Y+wXdcYY2v6aLcQqzHvxsMe38csE1oIKiX/CPc//aaRNnKsrbf3peTicHYvZOT1+mTKU9b/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebf89380c8edc91746d88badef05ba915504d24607c200c291e3c5404ef2ee15","last_reissued_at":"2026-05-18T00:53:28.230433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:28.230433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00768","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":"2026-05-18T00:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVodJXWRxnM/yFECVPCYHEYK5RD/vsdp7dioLC86zu30EJ9P0PGKSWA/m242JZaitPTvBP8xMVFVyU3221MlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:39:52.651002Z"},"content_sha256":"c9e553609e2d4041c7aad0cea4524b51101273685d782edaed45794b0c0e43b6","schema_version":"1.0","event_id":"sha256:c9e553609e2d4041c7aad0cea4524b51101273685d782edaed45794b0c0e43b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5P4JHAGI5XERORWYROW66BN2SF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enveloping algebras that are principal ideal rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hamid Usefi, Salvatore Siciliano","submitted_at":"2017-01-03T18:25:39Z","abstract_excerpt":"Let $L$ be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of $L$ is a principal ideal ring if and only if $L$ is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00768","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":"2026-05-18T00:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARkh8kuONtU25icNXspKLDX9kDyM1x4BpopsdKG0h4fgpI8B7vsD8E42FZQzubgp6xx805npu3NMDy1AcYa7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:39:52.651354Z"},"content_sha256":"500354354463abaa4b26acc98161807acdd7d703839ed7ce0cc2d15387f79c22","schema_version":"1.0","event_id":"sha256:500354354463abaa4b26acc98161807acdd7d703839ed7ce0cc2d15387f79c22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5P4JHAGI5XERORWYROW66BN2SF/bundle.json","state_url":"https://pith.science/pith/5P4JHAGI5XERORWYROW66BN2SF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5P4JHAGI5XERORWYROW66BN2SF/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":"2026-06-03T03:39:52Z","links":{"resolver":"https://pith.science/pith/5P4JHAGI5XERORWYROW66BN2SF","bundle":"https://pith.science/pith/5P4JHAGI5XERORWYROW66BN2SF/bundle.json","state":"https://pith.science/pith/5P4JHAGI5XERORWYROW66BN2SF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5P4JHAGI5XERORWYROW66BN2SF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5P4JHAGI5XERORWYROW66BN2SF","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":"946f3b0e35d4ef9926fc38338fec14b0296f97828c83c98a052f2ea821b0e646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T18:25:39Z","title_canon_sha256":"7498dd7c808eb03d168e4e2adf837d614a01828f443c13a712b8485217627182"},"schema_version":"1.0","source":{"id":"1701.00768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00768","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00768v1","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00768","created_at":"2026-05-18T00:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"5P4JHAGI5XER","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5P4JHAGI5XERORWY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5P4JHAGI","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:500354354463abaa4b26acc98161807acdd7d703839ed7ce0cc2d15387f79c22","target":"graph","created_at":"2026-05-18T00:53:28Z","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":"Let $L$ be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of $L$ is a principal ideal ring if and only if $L$ is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.","authors_text":"Hamid Usefi, Salvatore Siciliano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T18:25:39Z","title":"Enveloping algebras that are principal ideal rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00768","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:c9e553609e2d4041c7aad0cea4524b51101273685d782edaed45794b0c0e43b6","target":"record","created_at":"2026-05-18T00:53:28Z","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":"946f3b0e35d4ef9926fc38338fec14b0296f97828c83c98a052f2ea821b0e646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-01-03T18:25:39Z","title_canon_sha256":"7498dd7c808eb03d168e4e2adf837d614a01828f443c13a712b8485217627182"},"schema_version":"1.0","source":{"id":"1701.00768","kind":"arxiv","version":1}},"canonical_sha256":"ebf89380c8edc91746d88badef05ba915504d24607c200c291e3c5404ef2ee15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebf89380c8edc91746d88badef05ba915504d24607c200c291e3c5404ef2ee15","first_computed_at":"2026-05-18T00:53:28.230433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:28.230433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6XBQT+U3jPgX2Y+wXdcYY2v6aLcQqzHvxsMe38csE1oIKiX/CPc//aaRNnKsrbf3peTicHYvZOT1+mTKU9b/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:28.230774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e553609e2d4041c7aad0cea4524b51101273685d782edaed45794b0c0e43b6","sha256:500354354463abaa4b26acc98161807acdd7d703839ed7ce0cc2d15387f79c22"],"state_sha256":"244b0a8e183d2e0b9217259b12e39c89632e6252fbd5a9f325b3a3f887fc20fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZTiYKbAXs+Pi9NQz1XSwlcQhvyCZfl17pYPGzccvLqr99kOmXu5V5VN+/86Awingw9pEy+wIDgnqgqqgIIn2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:39:52.653304Z","bundle_sha256":"fa455b76e7e978ee9dc320f4b939bd79845f1fa8541db037d71642799ea71226"}}