{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JDX442RVENQ2TGBTXI7KD5BMAN","short_pith_number":"pith:JDX442RV","canonical_record":{"source":{"id":"2404.00515","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T01:25:50Z","cross_cats_sorted":[],"title_canon_sha256":"2405712f8492f42daf77dd0018760d3f05c13aad15bdc18aa28fc4d26c98566d","abstract_canon_sha256":"658ed84939d425fb2bf9a0f0f5338878dafe5d678f92d58ae476f32ee809b869"},"schema_version":"1.0"},"canonical_sha256":"48efce6a352361a99833ba3ea1f42c0369aeef1ff3da6a2d573ebc28047093aa","source":{"kind":"arxiv","id":"2404.00515","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.00515","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2404.00515v1","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00515","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"JDX442RVENQ2","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"JDX442RVENQ2TGBT","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"JDX442RV","created_at":"2026-07-05T08:02:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JDX442RVENQ2TGBTXI7KD5BMAN","target":"record","payload":{"canonical_record":{"source":{"id":"2404.00515","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T01:25:50Z","cross_cats_sorted":[],"title_canon_sha256":"2405712f8492f42daf77dd0018760d3f05c13aad15bdc18aa28fc4d26c98566d","abstract_canon_sha256":"658ed84939d425fb2bf9a0f0f5338878dafe5d678f92d58ae476f32ee809b869"},"schema_version":"1.0"},"canonical_sha256":"48efce6a352361a99833ba3ea1f42c0369aeef1ff3da6a2d573ebc28047093aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:02:34.469371Z","signature_b64":"ZoOeJkmnAxPiWjor76N8yA17kBY+31BDIIcIWbfw6NnB5z6F18JTXba/mBTkI+3zbIZOYQaEt6bHLCtPIGvbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48efce6a352361a99833ba3ea1f42c0369aeef1ff3da6a2d573ebc28047093aa","last_reissued_at":"2026-07-05T08:02:34.468860Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:02:34.468860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.00515","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":"2026-07-05T08:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEMhlmnDaCU8MtpQieNY3vA8gAHp6RRkyu+CZQCrEvIm8Ss3wsnnn25DiQVvv0VxNyzDiqsfpC8tkZy1nECEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:15:45.675996Z"},"content_sha256":"11f69b050b93ae2eea37b16125644d2e8784957bf4e9fa6ff9712daf3cd2f3b5","schema_version":"1.0","event_id":"sha256:11f69b050b93ae2eea37b16125644d2e8784957bf4e9fa6ff9712daf3cd2f3b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JDX442RVENQ2TGBTXI7KD5BMAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polar Brauer categories, infinitesimal braids and Lie superalgebra representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gustav Lehrer, Ruibin Zhang","submitted_at":"2024-03-31T01:25:50Z","abstract_excerpt":"We define a class of monoidal categories whose morphisms are diagrams, and which are enhancements and generalisations of the Brauer category obtained by adjoining infinitesimal braids, \"coupons\" and poles. Properties of these categories are explored, particularly diagrammatic equations. We construct functors from certain of them to categories of representations of Lie algebras and superalgebras. Applications include a diagrammatic construction of the centre of the universal enveloping superalgebra and certain \"characteristic identities\", as well as an analysis of certain tensor representations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00515","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00515/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UNhyffUJ+nwfu391TP5242luayiCtQs12ihyoSOgWI6cHAMOKOxwfzTPMIP7BSDSbfb797zwLx1EdQ5UW19mDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:15:45.676549Z"},"content_sha256":"9e773f2666fb743e4b21f249df4b09681f985aaac76d6a8ebbaca0c95638dd32","schema_version":"1.0","event_id":"sha256:9e773f2666fb743e4b21f249df4b09681f985aaac76d6a8ebbaca0c95638dd32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDX442RVENQ2TGBTXI7KD5BMAN/bundle.json","state_url":"https://pith.science/pith/JDX442RVENQ2TGBTXI7KD5BMAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDX442RVENQ2TGBTXI7KD5BMAN/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":"2026-08-13T18:15:45Z","links":{"resolver":"https://pith.science/pith/JDX442RVENQ2TGBTXI7KD5BMAN","bundle":"https://pith.science/pith/JDX442RVENQ2TGBTXI7KD5BMAN/bundle.json","state":"https://pith.science/pith/JDX442RVENQ2TGBTXI7KD5BMAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDX442RVENQ2TGBTXI7KD5BMAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JDX442RVENQ2TGBTXI7KD5BMAN","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":"658ed84939d425fb2bf9a0f0f5338878dafe5d678f92d58ae476f32ee809b869","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T01:25:50Z","title_canon_sha256":"2405712f8492f42daf77dd0018760d3f05c13aad15bdc18aa28fc4d26c98566d"},"schema_version":"1.0","source":{"id":"2404.00515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.00515","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2404.00515v1","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00515","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"JDX442RVENQ2","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"JDX442RVENQ2TGBT","created_at":"2026-07-05T08:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"JDX442RV","created_at":"2026-07-05T08:02:34Z"}],"graph_snapshots":[{"event_id":"sha256:9e773f2666fb743e4b21f249df4b09681f985aaac76d6a8ebbaca0c95638dd32","target":"graph","created_at":"2026-07-05T08:02:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.00515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a class of monoidal categories whose morphisms are diagrams, and which are enhancements and generalisations of the Brauer category obtained by adjoining infinitesimal braids, \"coupons\" and poles. Properties of these categories are explored, particularly diagrammatic equations. We construct functors from certain of them to categories of representations of Lie algebras and superalgebras. Applications include a diagrammatic construction of the centre of the universal enveloping superalgebra and certain \"characteristic identities\", as well as an analysis of certain tensor representations","authors_text":"Gustav Lehrer, Ruibin Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T01:25:50Z","title":"Polar Brauer categories, infinitesimal braids and Lie superalgebra representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00515","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":"sha256:11f69b050b93ae2eea37b16125644d2e8784957bf4e9fa6ff9712daf3cd2f3b5","target":"record","created_at":"2026-07-05T08:02:34Z","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":"658ed84939d425fb2bf9a0f0f5338878dafe5d678f92d58ae476f32ee809b869","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-31T01:25:50Z","title_canon_sha256":"2405712f8492f42daf77dd0018760d3f05c13aad15bdc18aa28fc4d26c98566d"},"schema_version":"1.0","source":{"id":"2404.00515","kind":"arxiv","version":1}},"canonical_sha256":"48efce6a352361a99833ba3ea1f42c0369aeef1ff3da6a2d573ebc28047093aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48efce6a352361a99833ba3ea1f42c0369aeef1ff3da6a2d573ebc28047093aa","first_computed_at":"2026-07-05T08:02:34.468860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:02:34.468860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZoOeJkmnAxPiWjor76N8yA17kBY+31BDIIcIWbfw6NnB5z6F18JTXba/mBTkI+3zbIZOYQaEt6bHLCtPIGvbBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:02:34.469371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.00515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11f69b050b93ae2eea37b16125644d2e8784957bf4e9fa6ff9712daf3cd2f3b5","sha256:9e773f2666fb743e4b21f249df4b09681f985aaac76d6a8ebbaca0c95638dd32"],"state_sha256":"aaffbc5e4823b0a432bcd7a140fc7439431df8c4cfdd3a65095befbd83c2553d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRwwaHgy6etIuLHiwZi23q1m1QIibDHvzrJiz8Q1XkLVsygEbrAfK8CRDNlAd5GHXSXp5klcnVFFtboET0RZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:15:45.679830Z","bundle_sha256":"e0c10c6579b887e4384a3482b32856cc27b0f570304fa834a4e1bd07ebe6a54a"}}