{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LBWMRPTKBU4FKTZEKAB5XI462A","short_pith_number":"pith:LBWMRPTK","canonical_record":{"source":{"id":"1709.06589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-19T18:15:51Z","cross_cats_sorted":[],"title_canon_sha256":"fb4f75a1f4113bae1011473b7086b32b3f40e7cf7d53db469a52872d41daad8e","abstract_canon_sha256":"a7723bf7367200ad3cb16cd9ea617e5234ede4ee802424f3c18d1821ca892451"},"schema_version":"1.0"},"canonical_sha256":"586cc8be6a0d38554f245003dba39ed03aa3e10e4cc3cea44135f256b242f140","source":{"kind":"arxiv","id":"1709.06589","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06589","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06589v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06589","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"LBWMRPTKBU4F","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LBWMRPTKBU4FKTZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LBWMRPTK","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LBWMRPTKBU4FKTZEKAB5XI462A","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-19T18:15:51Z","cross_cats_sorted":[],"title_canon_sha256":"fb4f75a1f4113bae1011473b7086b32b3f40e7cf7d53db469a52872d41daad8e","abstract_canon_sha256":"a7723bf7367200ad3cb16cd9ea617e5234ede4ee802424f3c18d1821ca892451"},"schema_version":"1.0"},"canonical_sha256":"586cc8be6a0d38554f245003dba39ed03aa3e10e4cc3cea44135f256b242f140","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.614860Z","signature_b64":"mSTgtuDvzydqc6ru34or6B7ygqwGG7GlL/OOKCCS2cZkpeQH9A6xkms0/gNu8/kQGLSNK6FKqIMdO4oolx4qCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"586cc8be6a0d38554f245003dba39ed03aa3e10e4cc3cea44135f256b242f140","last_reissued_at":"2026-05-17T23:58:19.614444Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.614444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06589","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5JXXkvxA9x3mXwnVlyViqB71ow8nBI3f9T77kfEiaPKMF9stAAPPI2dqFFCzUt2eGpkBnT8MmN00nwDjhUpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:16:33.922873Z"},"content_sha256":"e825e52dd6ec05f86cc97085f7c02b1b68c0c833d83bebb121de49653aa47bc0","schema_version":"1.0","event_id":"sha256:e825e52dd6ec05f86cc97085f7c02b1b68c0c833d83bebb121de49653aa47bc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LBWMRPTKBU4FKTZEKAB5XI462A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the definition of Heisenberg category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Brundan","submitted_at":"2017-09-19T18:15:51Z","abstract_excerpt":"We revisit the definition of the Heisenberg category of central charge k. For central charge -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. For other negative central charges, the definition is due to Mackaay and Savage, also with some redundant relations, while central charge zero recovers the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06589","kind":"arxiv","version":3},"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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghM4G6VdvJxdfwJFam9CJ6jMcnIb3bqjH8POpUUC3mZc0uKMSgK7ycvjgVL5LeUo620VaJt5KJ8uEaPt4fKOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:16:33.923210Z"},"content_sha256":"52389810f3e36b2dbe416df15ae98a86cb207ab7d8499e56392035790422963b","schema_version":"1.0","event_id":"sha256:52389810f3e36b2dbe416df15ae98a86cb207ab7d8499e56392035790422963b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBWMRPTKBU4FKTZEKAB5XI462A/bundle.json","state_url":"https://pith.science/pith/LBWMRPTKBU4FKTZEKAB5XI462A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBWMRPTKBU4FKTZEKAB5XI462A/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":"2026-06-29T13:16:33Z","links":{"resolver":"https://pith.science/pith/LBWMRPTKBU4FKTZEKAB5XI462A","bundle":"https://pith.science/pith/LBWMRPTKBU4FKTZEKAB5XI462A/bundle.json","state":"https://pith.science/pith/LBWMRPTKBU4FKTZEKAB5XI462A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBWMRPTKBU4FKTZEKAB5XI462A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LBWMRPTKBU4FKTZEKAB5XI462A","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":"a7723bf7367200ad3cb16cd9ea617e5234ede4ee802424f3c18d1821ca892451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-19T18:15:51Z","title_canon_sha256":"fb4f75a1f4113bae1011473b7086b32b3f40e7cf7d53db469a52872d41daad8e"},"schema_version":"1.0","source":{"id":"1709.06589","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06589","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06589v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06589","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"LBWMRPTKBU4F","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LBWMRPTKBU4FKTZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LBWMRPTK","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:52389810f3e36b2dbe416df15ae98a86cb207ab7d8499e56392035790422963b","target":"graph","created_at":"2026-05-17T23:58:19Z","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 revisit the definition of the Heisenberg category of central charge k. For central charge -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. For other negative central charges, the definition is due to Mackaay and Savage, also with some redundant relations, while central charge zero recovers the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.","authors_text":"Jonathan Brundan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-19T18:15:51Z","title":"On the definition of Heisenberg category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06589","kind":"arxiv","version":3},"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:e825e52dd6ec05f86cc97085f7c02b1b68c0c833d83bebb121de49653aa47bc0","target":"record","created_at":"2026-05-17T23:58:19Z","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":"a7723bf7367200ad3cb16cd9ea617e5234ede4ee802424f3c18d1821ca892451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-19T18:15:51Z","title_canon_sha256":"fb4f75a1f4113bae1011473b7086b32b3f40e7cf7d53db469a52872d41daad8e"},"schema_version":"1.0","source":{"id":"1709.06589","kind":"arxiv","version":3}},"canonical_sha256":"586cc8be6a0d38554f245003dba39ed03aa3e10e4cc3cea44135f256b242f140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"586cc8be6a0d38554f245003dba39ed03aa3e10e4cc3cea44135f256b242f140","first_computed_at":"2026-05-17T23:58:19.614444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.614444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mSTgtuDvzydqc6ru34or6B7ygqwGG7GlL/OOKCCS2cZkpeQH9A6xkms0/gNu8/kQGLSNK6FKqIMdO4oolx4qCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.614860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06589","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e825e52dd6ec05f86cc97085f7c02b1b68c0c833d83bebb121de49653aa47bc0","sha256:52389810f3e36b2dbe416df15ae98a86cb207ab7d8499e56392035790422963b"],"state_sha256":"f2bb48706911637cd530e4e28431959ca73438b7eb5802e7907bdd8afe4873b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NhrU7Dfsaav7DLHkRO5ieQw3eI5AIDkRcA8qWECJl2wv4hg9JOPqvsWpdd0Yzdv50YHTYyDTlv4gztmEMyEXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:16:33.926543Z","bundle_sha256":"28781ba93d2a40118cf372a31c39464af59aff4e7192e8d9cddf142eccc79bbf"}}