{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GGRT7C2TMPUJNHDTD7OACUA5FL","short_pith_number":"pith:GGRT7C2T","canonical_record":{"source":{"id":"1404.6497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-25T18:37:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"53597b47132e394d9be8def4a32db6c8ae56446685fd9b4665149acd16ba5094","abstract_canon_sha256":"75687805a4c3276ba9c51aadf117d9b1096b5b9b3a1d78fef84ee9b23da7078b"},"schema_version":"1.0"},"canonical_sha256":"31a33f8b5363e8969c731fdc01501d2ae88b1a69f13c6764ce08e813be2cfb2c","source":{"kind":"arxiv","id":"1404.6497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6497","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6497v1","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6497","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"GGRT7C2TMPUJ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GGRT7C2TMPUJNHDT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GGRT7C2T","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GGRT7C2TMPUJNHDTD7OACUA5FL","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-25T18:37:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"53597b47132e394d9be8def4a32db6c8ae56446685fd9b4665149acd16ba5094","abstract_canon_sha256":"75687805a4c3276ba9c51aadf117d9b1096b5b9b3a1d78fef84ee9b23da7078b"},"schema_version":"1.0"},"canonical_sha256":"31a33f8b5363e8969c731fdc01501d2ae88b1a69f13c6764ce08e813be2cfb2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:16.183340Z","signature_b64":"0KsRgyYAEQBzBWGesKd8YXY1WD/OFJwnFJu1xrO6KcGRbA2XDH3f7rzXJfy+gCSF7eBpGZMvj/AL5bk2hQuBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31a33f8b5363e8969c731fdc01501d2ae88b1a69f13c6764ce08e813be2cfb2c","last_reissued_at":"2026-05-18T02:53:16.182672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:16.182672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6497","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":"2026-05-18T02:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5B5KlA5D7yAQiOgzmckykimkWCXySy8uVuJE7htwsVSagW50Oi+ZUEmPpDGD8vvAC6uHtVrPrHE413sgWCE4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:33:04.299588Z"},"content_sha256":"47422fcd791122b9f6c2faf35f8a7956973ee36f15dfdb5ff6f96ac775286a32","schema_version":"1.0","event_id":"sha256:47422fcd791122b9f6c2faf35f8a7956973ee36f15dfdb5ff6f96ac775286a32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GGRT7C2TMPUJNHDTD7OACUA5FL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincare-Birkhoff-Witt Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Anne V. Shepler, Sarah Witherspoon","submitted_at":"2014-04-25T18:37:07Z","abstract_excerpt":"We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological approaches of Braverman and Gaitsgory and of Polishchuk and Positselski. We discuss several contexts for PBW theorems and their applications, such as Drinfeld-Jimbo quantum groups, graded Hecke algebras, and symplectic reflection and related algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6497","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":"2026-05-18T02:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxiQMtJs99dYPqd+yyBClJTsFvrcY4Ta+QujvQgZkVOa9+rNblSQcnu/5gWdYf/zF84XrDAvK+w1IuCW8FA7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:33:04.299918Z"},"content_sha256":"5a8ca19ffd9b34c7020b916f1e83fbef68e499d22919298930189de25ee3ebb0","schema_version":"1.0","event_id":"sha256:5a8ca19ffd9b34c7020b916f1e83fbef68e499d22919298930189de25ee3ebb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/bundle.json","state_url":"https://pith.science/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/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":"2026-06-05T12:33:04Z","links":{"resolver":"https://pith.science/pith/GGRT7C2TMPUJNHDTD7OACUA5FL","bundle":"https://pith.science/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/bundle.json","state":"https://pith.science/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGRT7C2TMPUJNHDTD7OACUA5FL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GGRT7C2TMPUJNHDTD7OACUA5FL","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":"75687805a4c3276ba9c51aadf117d9b1096b5b9b3a1d78fef84ee9b23da7078b","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-25T18:37:07Z","title_canon_sha256":"53597b47132e394d9be8def4a32db6c8ae56446685fd9b4665149acd16ba5094"},"schema_version":"1.0","source":{"id":"1404.6497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6497","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6497v1","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6497","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"GGRT7C2TMPUJ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GGRT7C2TMPUJNHDT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GGRT7C2T","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:5a8ca19ffd9b34c7020b916f1e83fbef68e499d22919298930189de25ee3ebb0","target":"graph","created_at":"2026-05-18T02:53:16Z","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":"We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological approaches of Braverman and Gaitsgory and of Polishchuk and Positselski. We discuss several contexts for PBW theorems and their applications, such as Drinfeld-Jimbo quantum groups, graded Hecke algebras, and symplectic reflection and related algebras.","authors_text":"Anne V. Shepler, Sarah Witherspoon","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-25T18:37:07Z","title":"Poincare-Birkhoff-Witt Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6497","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":"sha256:47422fcd791122b9f6c2faf35f8a7956973ee36f15dfdb5ff6f96ac775286a32","target":"record","created_at":"2026-05-18T02:53:16Z","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":"75687805a4c3276ba9c51aadf117d9b1096b5b9b3a1d78fef84ee9b23da7078b","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-25T18:37:07Z","title_canon_sha256":"53597b47132e394d9be8def4a32db6c8ae56446685fd9b4665149acd16ba5094"},"schema_version":"1.0","source":{"id":"1404.6497","kind":"arxiv","version":1}},"canonical_sha256":"31a33f8b5363e8969c731fdc01501d2ae88b1a69f13c6764ce08e813be2cfb2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31a33f8b5363e8969c731fdc01501d2ae88b1a69f13c6764ce08e813be2cfb2c","first_computed_at":"2026-05-18T02:53:16.182672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:16.182672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0KsRgyYAEQBzBWGesKd8YXY1WD/OFJwnFJu1xrO6KcGRbA2XDH3f7rzXJfy+gCSF7eBpGZMvj/AL5bk2hQuBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:16.183340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47422fcd791122b9f6c2faf35f8a7956973ee36f15dfdb5ff6f96ac775286a32","sha256:5a8ca19ffd9b34c7020b916f1e83fbef68e499d22919298930189de25ee3ebb0"],"state_sha256":"497919de8e72434623e32607ecfe01350b6abcc92337a8df4efe4fa3c30453b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"riUw4NG+8KsZoNBcTxuYv1r5ByR2QJ9PbyieA/DQkKjiUYbXHTeofhWLk8lEeAI0IRGuWfjSU5WdtzxEjgBiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:33:04.301767Z","bundle_sha256":"4c5e7f0e3526b9122682c12734fc18d82cdd6dd0f3afed9137e03d6ebe8194d2"}}