{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GZ5ZHNQWLZVG7XUXO6ORD4E4QH","short_pith_number":"pith:GZ5ZHNQW","canonical_record":{"source":{"id":"1807.08854","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-23T22:46:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"07bef125d4ebae1fbfe7fddd2d13c153da2c468f64dd09c965412c168a9e793a","abstract_canon_sha256":"e23ccb62aec4171076413497bd1f904d3bc5d8b4bdde4b4d3d21bf2b0187f017"},"schema_version":"1.0"},"canonical_sha256":"367b93b6165e6a6fde97779d11f09c81e4b1a71923bbaae9898586bf87c81e07","source":{"kind":"arxiv","id":"1807.08854","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08854","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08854v4","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08854","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"GZ5ZHNQWLZVG","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZ5ZHNQWLZVG7XUX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZ5ZHNQW","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GZ5ZHNQWLZVG7XUXO6ORD4E4QH","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08854","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-23T22:46:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"07bef125d4ebae1fbfe7fddd2d13c153da2c468f64dd09c965412c168a9e793a","abstract_canon_sha256":"e23ccb62aec4171076413497bd1f904d3bc5d8b4bdde4b4d3d21bf2b0187f017"},"schema_version":"1.0"},"canonical_sha256":"367b93b6165e6a6fde97779d11f09c81e4b1a71923bbaae9898586bf87c81e07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:02.891527Z","signature_b64":"pXog5pDQ8ce/W+f7ewr9JyH9zTyQQgWZTQdP/wCLmtZZPC+urL6/QOivO6d1GiUXXTw+OM//3egNMtbK406oCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"367b93b6165e6a6fde97779d11f09c81e4b1a71923bbaae9898586bf87c81e07","last_reissued_at":"2026-05-17T23:44:02.891093Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:02.891093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08854","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lH+2ai7JO3Joy3OwZhBPHAWQV9eB51cNAiRzQ06kRvw2+TvPqjuBIsXf+oNRdIesKFEgAAyPPH2EfuRhes8IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:20:49.220796Z"},"content_sha256":"002bcddfc99fccac500aea585039270decc1871c9399af3b531f4b042c873459","schema_version":"1.0","event_id":"sha256:002bcddfc99fccac500aea585039270decc1871c9399af3b531f4b042c873459"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GZ5ZHNQWLZVG7XUXO6ORD4E4QH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of finite tensor categories: duality and Drinfeld centers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Cris Negron, Julia Yael Plavnik","submitted_at":"2018-07-23T22:46:22Z","abstract_excerpt":"We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded extension group Ext*_C(1,V) is a finitely generated module over the aforementioned algebra. We prove that this cohomological finiteness property is preserved under duality (with respect to exact module categories) and taking the Drinfeld center, under suitable restrictions on C. For example, the stated result holds when C is a braided tensor category of odd Fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08854","kind":"arxiv","version":4},"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":"2026-05-17T23:44:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtiA2PhMAzDGIOHVnntndtH1P+Et/dk19I0BH2x6r2g/NxesctI9R9TM5OLmebAIztHiP23r1Ro8ABhqWJ10DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:20:49.221218Z"},"content_sha256":"f1bfc4133bd427bf643f1ec56b5e2785be29ab9d6d41f704fcaee1a02bc5673a","schema_version":"1.0","event_id":"sha256:f1bfc4133bd427bf643f1ec56b5e2785be29ab9d6d41f704fcaee1a02bc5673a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/bundle.json","state_url":"https://pith.science/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/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":"2026-07-03T12:20:49Z","links":{"resolver":"https://pith.science/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH","bundle":"https://pith.science/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/bundle.json","state":"https://pith.science/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZ5ZHNQWLZVG7XUXO6ORD4E4QH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GZ5ZHNQWLZVG7XUXO6ORD4E4QH","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":"e23ccb62aec4171076413497bd1f904d3bc5d8b4bdde4b4d3d21bf2b0187f017","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-23T22:46:22Z","title_canon_sha256":"07bef125d4ebae1fbfe7fddd2d13c153da2c468f64dd09c965412c168a9e793a"},"schema_version":"1.0","source":{"id":"1807.08854","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08854","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08854v4","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08854","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"GZ5ZHNQWLZVG","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZ5ZHNQWLZVG7XUX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZ5ZHNQW","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:f1bfc4133bd427bf643f1ec56b5e2785be29ab9d6d41f704fcaee1a02bc5673a","target":"graph","created_at":"2026-05-17T23:44:02Z","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":"We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded extension group Ext*_C(1,V) is a finitely generated module over the aforementioned algebra. We prove that this cohomological finiteness property is preserved under duality (with respect to exact module categories) and taking the Drinfeld center, under suitable restrictions on C. For example, the stated result holds when C is a braided tensor category of odd Fro","authors_text":"Cris Negron, Julia Yael Plavnik","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-23T22:46:22Z","title":"Cohomology of finite tensor categories: duality and Drinfeld centers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08854","kind":"arxiv","version":4},"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":"sha256:002bcddfc99fccac500aea585039270decc1871c9399af3b531f4b042c873459","target":"record","created_at":"2026-05-17T23:44:02Z","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":"e23ccb62aec4171076413497bd1f904d3bc5d8b4bdde4b4d3d21bf2b0187f017","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-07-23T22:46:22Z","title_canon_sha256":"07bef125d4ebae1fbfe7fddd2d13c153da2c468f64dd09c965412c168a9e793a"},"schema_version":"1.0","source":{"id":"1807.08854","kind":"arxiv","version":4}},"canonical_sha256":"367b93b6165e6a6fde97779d11f09c81e4b1a71923bbaae9898586bf87c81e07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"367b93b6165e6a6fde97779d11f09c81e4b1a71923bbaae9898586bf87c81e07","first_computed_at":"2026-05-17T23:44:02.891093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:02.891093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pXog5pDQ8ce/W+f7ewr9JyH9zTyQQgWZTQdP/wCLmtZZPC+urL6/QOivO6d1GiUXXTw+OM//3egNMtbK406oCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:02.891527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08854","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:002bcddfc99fccac500aea585039270decc1871c9399af3b531f4b042c873459","sha256:f1bfc4133bd427bf643f1ec56b5e2785be29ab9d6d41f704fcaee1a02bc5673a"],"state_sha256":"e629ff91d22a34157be85f23e84182e76a534c3d566858e2601eca6be0b95fee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K39YXWzuLMpAv4EOaRdhvCZPulSP8tkeDYcwEmuBL0WPry9G/SzY7APwu1Xf3F6k+dYLEuQCHQDt4ejDIuV/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T12:20:49.223120Z","bundle_sha256":"a50bb90812d7a0d1bae4a9a13297485473417ccef0ee8b972d81a600c29d9fb6"}}