{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YH2INNBEAX4KDNB7CQWRIT7SA6","short_pith_number":"pith:YH2INNBE","canonical_record":{"source":{"id":"1307.5956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-23T06:45:06Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"085e24d56942a9a594120bdaaacd2cb2a5b2baaa662ccce7cf4ebdc9634976c6","abstract_canon_sha256":"449c15b26eb64f71e48ccb369c8e263d67bdff9b77e2c63bfda5567c281653fd"},"schema_version":"1.0"},"canonical_sha256":"c1f486b42405f8a1b43f142d144ff2079ac9c2f657895b68cc3c409202038443","source":{"kind":"arxiv","id":"1307.5956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5956","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5956v1","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5956","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"YH2INNBEAX4K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YH2INNBEAX4KDNB7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YH2INNBE","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YH2INNBEAX4KDNB7CQWRIT7SA6","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-23T06:45:06Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"085e24d56942a9a594120bdaaacd2cb2a5b2baaa662ccce7cf4ebdc9634976c6","abstract_canon_sha256":"449c15b26eb64f71e48ccb369c8e263d67bdff9b77e2c63bfda5567c281653fd"},"schema_version":"1.0"},"canonical_sha256":"c1f486b42405f8a1b43f142d144ff2079ac9c2f657895b68cc3c409202038443","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:04.117572Z","signature_b64":"3ZgqyzSKXxIEgm4p8DUWKdswB33KkZ3ApESolLSt3PhtNeYOqVoAVeoVgXd7xMMEh//dlIxhPNDrGfMeTlZLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1f486b42405f8a1b43f142d144ff2079ac9c2f657895b68cc3c409202038443","last_reissued_at":"2026-05-18T00:54:04.117009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:04.117009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5956","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8CEhh/s+NPvU82Mcq82Q1ZWixa91YHTS1le6jIyxiX/t8rfEvzI/maG04VLq8WYzHwpJz9MnEfgZfGMOOqKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:20:05.439381Z"},"content_sha256":"5e25298622135813ac38f44f119e5a0fef8d6f2d405118949377de8010c18fd4","schema_version":"1.0","event_id":"sha256:5e25298622135813ac38f44f119e5a0fef8d6f2d405118949377de8010c18fd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YH2INNBEAX4KDNB7CQWRIT7SA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functoriality of the center of an algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Alexei Davydov, Ingo Runkel, Liang Kong","submitted_at":"2013-07-23T06:45:06Z","abstract_excerpt":"The notion of the center of an algebra over a field k has a far reaching generalization to algebras in monoidal categories. The center then lives in the monoidal center of the original category. This generalization plays an important role in the study of bulk-boundary duality of rational conformal field theories. In this paper, we study functorial properties of the center. We show that it gives rise to a 2-functor from the bicategory of semisimple indecomposable module categories over a fusion category to the bicategory of commutative algebras in the monoidal center of this fusion category. Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5956","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":"2026-05-18T00:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oI+q/VNq6Tcx0jIMh5U7Yb2+5WBxGfYvTFu9oLZxAQ/GDaQSBP+ng0wDPSr7uQbSblYuHfiOdjtNIxJL2awNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:20:05.439751Z"},"content_sha256":"3a853585ab6e4455d86ac5ed950a68d28eaa8cc50d12748f33a06f7c7a9e9575","schema_version":"1.0","event_id":"sha256:3a853585ab6e4455d86ac5ed950a68d28eaa8cc50d12748f33a06f7c7a9e9575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/bundle.json","state_url":"https://pith.science/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/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":"2026-06-12T04:20:05Z","links":{"resolver":"https://pith.science/pith/YH2INNBEAX4KDNB7CQWRIT7SA6","bundle":"https://pith.science/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/bundle.json","state":"https://pith.science/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YH2INNBEAX4KDNB7CQWRIT7SA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YH2INNBEAX4KDNB7CQWRIT7SA6","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":"449c15b26eb64f71e48ccb369c8e263d67bdff9b77e2c63bfda5567c281653fd","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-23T06:45:06Z","title_canon_sha256":"085e24d56942a9a594120bdaaacd2cb2a5b2baaa662ccce7cf4ebdc9634976c6"},"schema_version":"1.0","source":{"id":"1307.5956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5956","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5956v1","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5956","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"YH2INNBEAX4K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YH2INNBEAX4KDNB7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YH2INNBE","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3a853585ab6e4455d86ac5ed950a68d28eaa8cc50d12748f33a06f7c7a9e9575","target":"graph","created_at":"2026-05-18T00:54:04Z","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":"The notion of the center of an algebra over a field k has a far reaching generalization to algebras in monoidal categories. The center then lives in the monoidal center of the original category. This generalization plays an important role in the study of bulk-boundary duality of rational conformal field theories. In this paper, we study functorial properties of the center. We show that it gives rise to a 2-functor from the bicategory of semisimple indecomposable module categories over a fusion category to the bicategory of commutative algebras in the monoidal center of this fusion category. Mo","authors_text":"Alexei Davydov, Ingo Runkel, Liang Kong","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-23T06:45:06Z","title":"Functoriality of the center of an algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5956","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":"sha256:5e25298622135813ac38f44f119e5a0fef8d6f2d405118949377de8010c18fd4","target":"record","created_at":"2026-05-18T00:54:04Z","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":"449c15b26eb64f71e48ccb369c8e263d67bdff9b77e2c63bfda5567c281653fd","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-23T06:45:06Z","title_canon_sha256":"085e24d56942a9a594120bdaaacd2cb2a5b2baaa662ccce7cf4ebdc9634976c6"},"schema_version":"1.0","source":{"id":"1307.5956","kind":"arxiv","version":1}},"canonical_sha256":"c1f486b42405f8a1b43f142d144ff2079ac9c2f657895b68cc3c409202038443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1f486b42405f8a1b43f142d144ff2079ac9c2f657895b68cc3c409202038443","first_computed_at":"2026-05-18T00:54:04.117009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.117009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZgqyzSKXxIEgm4p8DUWKdswB33KkZ3ApESolLSt3PhtNeYOqVoAVeoVgXd7xMMEh//dlIxhPNDrGfMeTlZLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.117572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e25298622135813ac38f44f119e5a0fef8d6f2d405118949377de8010c18fd4","sha256:3a853585ab6e4455d86ac5ed950a68d28eaa8cc50d12748f33a06f7c7a9e9575"],"state_sha256":"fedb496933af02a2d8bff248de66ff1eec249632e35c1a49963bffa7ae11c11b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NOoEPDT6rE2s3t+ofXzhMXLeu7oObPiIr+aCwJ9KDlWw3GhlfmOQFfbvB5gR9C67OO5kUA+3UmwgjcjLb80XBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:20:05.441908Z","bundle_sha256":"2c7adae1b958ae0a187d367d409a6108e7e07213cff0e0cd20db3eb2d67ab126"}}