{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:3QOOXAYEPRM7FGWMPI6NOHEJ7J","short_pith_number":"pith:3QOOXAYE","canonical_record":{"source":{"id":"2212.07393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-14T18:22:06Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"06d3be86cef28159b1acfe6e792f33a0998b97f02f9ba0436470abaacce3be9b","abstract_canon_sha256":"3738c60b8c271e598bffda1bae781cf830e31cb1aadfefd63a6e575da6240bab"},"schema_version":"1.0"},"canonical_sha256":"dc1ceb83047c59f29acc7a3cd71c89fa71fc8c7a1d665b47e4c36dedee617ac7","source":{"kind":"arxiv","id":"2212.07393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.07393","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"2212.07393v2","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.07393","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"3QOOXAYEPRM7","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_16","alias_value":"3QOOXAYEPRM7FGWM","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_8","alias_value":"3QOOXAYE","created_at":"2026-07-05T08:59:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:3QOOXAYEPRM7FGWMPI6NOHEJ7J","target":"record","payload":{"canonical_record":{"source":{"id":"2212.07393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-14T18:22:06Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"06d3be86cef28159b1acfe6e792f33a0998b97f02f9ba0436470abaacce3be9b","abstract_canon_sha256":"3738c60b8c271e598bffda1bae781cf830e31cb1aadfefd63a6e575da6240bab"},"schema_version":"1.0"},"canonical_sha256":"dc1ceb83047c59f29acc7a3cd71c89fa71fc8c7a1d665b47e4c36dedee617ac7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:59:48.729233Z","signature_b64":"bpaP4ln1EafQaSdW9uwDqnLm2Zuth/8yD2++Q11MnuqzXKd+E9NJjjRypw1mqruEKIPEDi/UbK5nTdPy18kwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc1ceb83047c59f29acc7a3cd71c89fa71fc8c7a1d665b47e4c36dedee617ac7","last_reissued_at":"2026-07-05T08:59:48.728723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:59:48.728723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.07393","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYppYn2V9anGYfbZ2pfsq/vEfM7PgO8SE8OSrygrZsjTnO2hcPw8TjtFSQ7DxYAGlOQL5f2I0ulsLf8C/wP+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:40:15.626818Z"},"content_sha256":"f0e17a9b81747d1e6b0b4fe420ab3c94ec4e3a9a81169f29994ba4d2572ad55c","schema_version":"1.0","event_id":"sha256:f0e17a9b81747d1e6b0b4fe420ab3c94ec4e3a9a81169f29994ba4d2572ad55c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:3QOOXAYEPRM7FGWMPI6NOHEJ7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-invertible Symmetries and Higher Representation Theory II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Andrea E. V. Ferrari, Jamie Pearson, Mathew Bullimore, Thomas Bartsch","submitted_at":"2022-12-14T18:22:06Z","abstract_excerpt":"In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete appl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07393","kind":"arxiv","version":2},"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/2212.07393/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":"2026-07-05T08:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQu61NqHWhV3HJX1g3el9Uv9+q2zZrc83IyZyeBUmsRHEM3IRlE3O6tS4Slpz6DNzUBCE4sMQcZbVjv25Ct/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:40:15.627333Z"},"content_sha256":"fa0fa3c4da23132a5e0ddb507b9a74469c5eb4f5b8e5ebdc6b7242c77f347730","schema_version":"1.0","event_id":"sha256:fa0fa3c4da23132a5e0ddb507b9a74469c5eb4f5b8e5ebdc6b7242c77f347730"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/bundle.json","state_url":"https://pith.science/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/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":"2026-08-08T23:40:15Z","links":{"resolver":"https://pith.science/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J","bundle":"https://pith.science/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/bundle.json","state":"https://pith.science/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QOOXAYEPRM7FGWMPI6NOHEJ7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3QOOXAYEPRM7FGWMPI6NOHEJ7J","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":"3738c60b8c271e598bffda1bae781cf830e31cb1aadfefd63a6e575da6240bab","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-14T18:22:06Z","title_canon_sha256":"06d3be86cef28159b1acfe6e792f33a0998b97f02f9ba0436470abaacce3be9b"},"schema_version":"1.0","source":{"id":"2212.07393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.07393","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"2212.07393v2","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.07393","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"3QOOXAYEPRM7","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_16","alias_value":"3QOOXAYEPRM7FGWM","created_at":"2026-07-05T08:59:48Z"},{"alias_kind":"pith_short_8","alias_value":"3QOOXAYE","created_at":"2026-07-05T08:59:48Z"}],"graph_snapshots":[{"event_id":"sha256:fa0fa3c4da23132a5e0ddb507b9a74469c5eb4f5b8e5ebdc6b7242c77f347730","target":"graph","created_at":"2026-07-05T08:59:48Z","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/2212.07393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete appl","authors_text":"Andrea E. V. Ferrari, Jamie Pearson, Mathew Bullimore, Thomas Bartsch","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-14T18:22:06Z","title":"Non-invertible Symmetries and Higher Representation Theory II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07393","kind":"arxiv","version":2},"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:f0e17a9b81747d1e6b0b4fe420ab3c94ec4e3a9a81169f29994ba4d2572ad55c","target":"record","created_at":"2026-07-05T08:59:48Z","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":"3738c60b8c271e598bffda1bae781cf830e31cb1aadfefd63a6e575da6240bab","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-14T18:22:06Z","title_canon_sha256":"06d3be86cef28159b1acfe6e792f33a0998b97f02f9ba0436470abaacce3be9b"},"schema_version":"1.0","source":{"id":"2212.07393","kind":"arxiv","version":2}},"canonical_sha256":"dc1ceb83047c59f29acc7a3cd71c89fa71fc8c7a1d665b47e4c36dedee617ac7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc1ceb83047c59f29acc7a3cd71c89fa71fc8c7a1d665b47e4c36dedee617ac7","first_computed_at":"2026-07-05T08:59:48.728723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:59:48.728723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bpaP4ln1EafQaSdW9uwDqnLm2Zuth/8yD2++Q11MnuqzXKd+E9NJjjRypw1mqruEKIPEDi/UbK5nTdPy18kwCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:59:48.729233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.07393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0e17a9b81747d1e6b0b4fe420ab3c94ec4e3a9a81169f29994ba4d2572ad55c","sha256:fa0fa3c4da23132a5e0ddb507b9a74469c5eb4f5b8e5ebdc6b7242c77f347730"],"state_sha256":"c71fcaa5c4ae0cc9f7d820c866858287dc64bfa8ea8897b9f493b44c0c06c299"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i+4F0DLKemdEDK8yJMBl8qeQHYECrNlFsR3mvtaytVYif7XkqN+4jyXxq3+XvlbTkLiXp7n8pU2Bz2MbLv+CDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:40:15.631293Z","bundle_sha256":"8124682110046b7b3256dbb0e5215847eb77d2e9db6253a4b9eb41c9e59792ba"}}