{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OM6UNUH4XJ2LUTG2NBFVCA3IRX","short_pith_number":"pith:OM6UNUH4","canonical_record":{"source":{"id":"0907.2500","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-15T06:41:07Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0ab211c5457ab076d9bf81449a037c4b4e106d21e69c5d47022b0809cf38433b","abstract_canon_sha256":"6153ad723876dc777a1580b3f1038cf91e1b4f298c5d31b41349a6bcccb1c21e"},"schema_version":"1.0"},"canonical_sha256":"733d46d0fcba74ba4cda684b5103688de8f2d20f2e01493a62740c5f626504cf","source":{"kind":"arxiv","id":"0907.2500","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2500","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2500v2","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2500","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"pith_short_12","alias_value":"OM6UNUH4XJ2L","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OM6UNUH4XJ2LUTG2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OM6UNUH4","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OM6UNUH4XJ2LUTG2NBFVCA3IRX","target":"record","payload":{"canonical_record":{"source":{"id":"0907.2500","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-15T06:41:07Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0ab211c5457ab076d9bf81449a037c4b4e106d21e69c5d47022b0809cf38433b","abstract_canon_sha256":"6153ad723876dc777a1580b3f1038cf91e1b4f298c5d31b41349a6bcccb1c21e"},"schema_version":"1.0"},"canonical_sha256":"733d46d0fcba74ba4cda684b5103688de8f2d20f2e01493a62740c5f626504cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:02.995769Z","signature_b64":"bNLA0zZppmlHgM1t6sKq0mDYkB5AQ8ROrrfh+izM4bn3ULbYz6/09Y3OwAzB25YelvbFHju4KnlN5JkdfQNOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"733d46d0fcba74ba4cda684b5103688de8f2d20f2e01493a62740c5f626504cf","last_reissued_at":"2026-05-18T02:13:02.994988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:02.994988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.2500","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65gt60N7tscTht972V1wMPZYW1fgMDxuNyQB2gAVg0AZWPY/OxVxodsnIvE35CTq4DVo96pBIL2b5k17XX0rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:42:42.515008Z"},"content_sha256":"ecd5aef5dbb3aa1be0b1a25f1c7c8fdac3b679d4cbae0fba6f907c0a1509b9b8","schema_version":"1.0","event_id":"sha256:ecd5aef5dbb3aa1be0b1a25f1c7c8fdac3b679d4cbae0fba6f907c0a1509b9b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OM6UNUH4XJ2LUTG2NBFVCA3IRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular Lie algebras and the Gelfand-Kirillov conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Alexander Premet","submitted_at":"2009-07-15T06:41:07Z","abstract_excerpt":"Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2500","kind":"arxiv","version":2},"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":"2026-05-18T02:13:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7PCW8m2v4tlGMxgUS3gikx9z9KYV0l4JeBxMz80K1cRJ265+gQY476itBXejYBrl5kBFCM0U/zaOcV4W2sXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:42:42.515360Z"},"content_sha256":"326f7e2f5df9741a145f1959253d1342693bb1910e091cf5fcd3355d1466efd4","schema_version":"1.0","event_id":"sha256:326f7e2f5df9741a145f1959253d1342693bb1910e091cf5fcd3355d1466efd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/bundle.json","state_url":"https://pith.science/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/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":"2026-06-22T22:42:42Z","links":{"resolver":"https://pith.science/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX","bundle":"https://pith.science/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/bundle.json","state":"https://pith.science/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OM6UNUH4XJ2LUTG2NBFVCA3IRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OM6UNUH4XJ2LUTG2NBFVCA3IRX","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":"6153ad723876dc777a1580b3f1038cf91e1b4f298c5d31b41349a6bcccb1c21e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-15T06:41:07Z","title_canon_sha256":"0ab211c5457ab076d9bf81449a037c4b4e106d21e69c5d47022b0809cf38433b"},"schema_version":"1.0","source":{"id":"0907.2500","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2500","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2500v2","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2500","created_at":"2026-05-18T02:13:02Z"},{"alias_kind":"pith_short_12","alias_value":"OM6UNUH4XJ2L","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OM6UNUH4XJ2LUTG2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OM6UNUH4","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:326f7e2f5df9741a145f1959253d1342693bb1910e091cf5fcd3355d1466efd4","target":"graph","created_at":"2026-05-18T02:13:02Z","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 g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.","authors_text":"Alexander Premet","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-15T06:41:07Z","title":"Modular Lie algebras and the Gelfand-Kirillov conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2500","kind":"arxiv","version":2},"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:ecd5aef5dbb3aa1be0b1a25f1c7c8fdac3b679d4cbae0fba6f907c0a1509b9b8","target":"record","created_at":"2026-05-18T02:13:02Z","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":"6153ad723876dc777a1580b3f1038cf91e1b4f298c5d31b41349a6bcccb1c21e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-15T06:41:07Z","title_canon_sha256":"0ab211c5457ab076d9bf81449a037c4b4e106d21e69c5d47022b0809cf38433b"},"schema_version":"1.0","source":{"id":"0907.2500","kind":"arxiv","version":2}},"canonical_sha256":"733d46d0fcba74ba4cda684b5103688de8f2d20f2e01493a62740c5f626504cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"733d46d0fcba74ba4cda684b5103688de8f2d20f2e01493a62740c5f626504cf","first_computed_at":"2026-05-18T02:13:02.994988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:02.994988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNLA0zZppmlHgM1t6sKq0mDYkB5AQ8ROrrfh+izM4bn3ULbYz6/09Y3OwAzB25YelvbFHju4KnlN5JkdfQNOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:02.995769Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2500","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecd5aef5dbb3aa1be0b1a25f1c7c8fdac3b679d4cbae0fba6f907c0a1509b9b8","sha256:326f7e2f5df9741a145f1959253d1342693bb1910e091cf5fcd3355d1466efd4"],"state_sha256":"06d91524af2412b9d088a3605e64163a6cacb5518784de9ee38682ea877d139e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1046EJVuId/r6Z3DV5xFYbEfzL+nA6MT0W/5218+mYU96MsunHr7/0DvOXiBFXVAF+uA0At4thCKWldNm9GCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:42:42.517306Z","bundle_sha256":"6527aa529f84030f3ac040159a079e2c5fe6afdf7f6445e913675cd9c56bb32b"}}