{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:VM25EDPS34ITQQBHKND4JUI6BH","short_pith_number":"pith:VM25EDPS","canonical_record":{"source":{"id":"2209.07471","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-15T17:10:11Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"title_canon_sha256":"92cac3a3b2197e176f3d3755b27115f0465316e80baec523498e0c10e63efa39","abstract_canon_sha256":"4bfd917c2cb7c1e0963ac169388ff6d6fec332a6b96618b6eb342a4de4a28c83"},"schema_version":"1.0"},"canonical_sha256":"ab35d20df2df113840275347c4d11e09f985ee6616247ca2a35c4e2f375f9deb","source":{"kind":"arxiv","id":"2209.07471","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.07471","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"2209.07471v4","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.07471","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"VM25EDPS34IT","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_16","alias_value":"VM25EDPS34ITQQBH","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_8","alias_value":"VM25EDPS","created_at":"2026-05-24T07:35:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:VM25EDPS34ITQQBHKND4JUI6BH","target":"record","payload":{"canonical_record":{"source":{"id":"2209.07471","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-15T17:10:11Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"title_canon_sha256":"92cac3a3b2197e176f3d3755b27115f0465316e80baec523498e0c10e63efa39","abstract_canon_sha256":"4bfd917c2cb7c1e0963ac169388ff6d6fec332a6b96618b6eb342a4de4a28c83"},"schema_version":"1.0"},"canonical_sha256":"ab35d20df2df113840275347c4d11e09f985ee6616247ca2a35c4e2f375f9deb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-24T07:35:35.524030Z","signature_b64":"tb2RcVeNcb+BD3WikkZkuVNkG9suaTOjljgRjPv7KzgL27abTclvfKXpmW+1kepVdwv870KLrZhsmu/D5bKkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab35d20df2df113840275347c4d11e09f985ee6616247ca2a35c4e2f375f9deb","last_reissued_at":"2026-05-24T07:35:35.521051Z","signature_status":"signed_v1","first_computed_at":"2026-05-24T07:35:35.521051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.07471","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":"2026-05-24T07:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wj6pbkjNNynITnpluMvgYEDOHzVlF83arS8ymSnxBWoCvYiwK1iypBf+15waYMhFS2WqNYdKJenihUvzKyg9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:26:55.116176Z"},"content_sha256":"aec91353c0a49d870fb3adf58f5d5a76c3ee8c804647093fa3a3e61517683d1d","schema_version":"1.0","event_id":"sha256:aec91353c0a49d870fb3adf58f5d5a76c3ee8c804647093fa3a3e61517683d1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:VM25EDPS34ITQQBHKND4JUI6BH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological symmetry in quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Constantin Teleman, Daniel S. Freed, Gregory W. Moore","submitted_at":"2022-09-15T17:10:11Z","abstract_excerpt":"We introduce a framework for internal topological symmetries in quantum field theory, including \"noninvertible symmetries\" and \"categorical symmetries\". This leads to a calculus of topological defects which takes full advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called \"gauging\" and \"condensation defects\"), finite electromagnetic duality, and duality defects, among other topics. We include an appendix o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.07471","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.07471/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":"2026-05-24T07:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwCbStH+2BAlNzBQy/kU3oF4QzwKXVlfwUCjZhRxmlITsBuIrReUckc22jgZ1BSSJbHifoZE4mf18K4IgbHeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:26:55.117031Z"},"content_sha256":"d7e504e3edceccf9f2e01ab49c7f5c1fe65589f7b909449283103016ca5b1daf","schema_version":"1.0","event_id":"sha256:d7e504e3edceccf9f2e01ab49c7f5c1fe65589f7b909449283103016ca5b1daf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VM25EDPS34ITQQBHKND4JUI6BH/bundle.json","state_url":"https://pith.science/pith/VM25EDPS34ITQQBHKND4JUI6BH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VM25EDPS34ITQQBHKND4JUI6BH/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":"2026-05-24T13:26:55Z","links":{"resolver":"https://pith.science/pith/VM25EDPS34ITQQBHKND4JUI6BH","bundle":"https://pith.science/pith/VM25EDPS34ITQQBHKND4JUI6BH/bundle.json","state":"https://pith.science/pith/VM25EDPS34ITQQBHKND4JUI6BH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VM25EDPS34ITQQBHKND4JUI6BH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VM25EDPS34ITQQBHKND4JUI6BH","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":"4bfd917c2cb7c1e0963ac169388ff6d6fec332a6b96618b6eb342a4de4a28c83","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-15T17:10:11Z","title_canon_sha256":"92cac3a3b2197e176f3d3755b27115f0465316e80baec523498e0c10e63efa39"},"schema_version":"1.0","source":{"id":"2209.07471","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.07471","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"2209.07471v4","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.07471","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"VM25EDPS34IT","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_16","alias_value":"VM25EDPS34ITQQBH","created_at":"2026-05-24T07:35:35Z"},{"alias_kind":"pith_short_8","alias_value":"VM25EDPS","created_at":"2026-05-24T07:35:35Z"}],"graph_snapshots":[{"event_id":"sha256:d7e504e3edceccf9f2e01ab49c7f5c1fe65589f7b909449283103016ca5b1daf","target":"graph","created_at":"2026-05-24T07:35:35Z","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/2209.07471/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a framework for internal topological symmetries in quantum field theory, including \"noninvertible symmetries\" and \"categorical symmetries\". This leads to a calculus of topological defects which takes full advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called \"gauging\" and \"condensation defects\"), finite electromagnetic duality, and duality defects, among other topics. We include an appendix o","authors_text":"Constantin Teleman, Daniel S. Freed, Gregory W. Moore","cross_cats":["math-ph","math.AT","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-15T17:10:11Z","title":"Topological symmetry in quantum field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.07471","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:aec91353c0a49d870fb3adf58f5d5a76c3ee8c804647093fa3a3e61517683d1d","target":"record","created_at":"2026-05-24T07:35:35Z","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":"4bfd917c2cb7c1e0963ac169388ff6d6fec332a6b96618b6eb342a4de4a28c83","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-15T17:10:11Z","title_canon_sha256":"92cac3a3b2197e176f3d3755b27115f0465316e80baec523498e0c10e63efa39"},"schema_version":"1.0","source":{"id":"2209.07471","kind":"arxiv","version":4}},"canonical_sha256":"ab35d20df2df113840275347c4d11e09f985ee6616247ca2a35c4e2f375f9deb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab35d20df2df113840275347c4d11e09f985ee6616247ca2a35c4e2f375f9deb","first_computed_at":"2026-05-24T07:35:35.521051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-24T07:35:35.521051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tb2RcVeNcb+BD3WikkZkuVNkG9suaTOjljgRjPv7KzgL27abTclvfKXpmW+1kepVdwv870KLrZhsmu/D5bKkCQ==","signature_status":"signed_v1","signed_at":"2026-05-24T07:35:35.524030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.07471","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aec91353c0a49d870fb3adf58f5d5a76c3ee8c804647093fa3a3e61517683d1d","sha256:d7e504e3edceccf9f2e01ab49c7f5c1fe65589f7b909449283103016ca5b1daf"],"state_sha256":"1dfc1fea2ec5d82861478e131a6f4303fe8e8951c420393f1d5aabc8680678ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEvjIwsdcGS4GjHgtF5Pjwi9CjL3prGbX0Mw7JiviQaVfny+gMsjN2CxJLge3AhH1qLHKijFhQQko5s5kscLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T13:26:55.121007Z","bundle_sha256":"55540ba6e3de9265d83d469bfbcaa2d008dbeda26e782825121a31432e1ee6f3"}}