{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:33IJXYZ6IFAW7AVUPCWEH5FZT5","short_pith_number":"pith:33IJXYZ6","canonical_record":{"source":{"id":"2111.13697","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-26T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"6c71f6f8fdb321574a57003e29e755e94bb8eb5a40cff2543dce47ca56289f9e","abstract_canon_sha256":"ca637c7f11b7af37a178be7d0166908db3f37090da88f578ac56254df5b9aaa4"},"schema_version":"1.0"},"canonical_sha256":"ded09be33e41416f82b478ac43f4b99f622d7e498392af96489e06df150fac8d","source":{"kind":"arxiv","id":"2111.13697","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.13697","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"2111.13697v3","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.13697","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"33IJXYZ6IFAW","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_16","alias_value":"33IJXYZ6IFAW7AVU","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_8","alias_value":"33IJXYZ6","created_at":"2026-07-05T05:59:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:33IJXYZ6IFAW7AVUPCWEH5FZT5","target":"record","payload":{"canonical_record":{"source":{"id":"2111.13697","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-26T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"6c71f6f8fdb321574a57003e29e755e94bb8eb5a40cff2543dce47ca56289f9e","abstract_canon_sha256":"ca637c7f11b7af37a178be7d0166908db3f37090da88f578ac56254df5b9aaa4"},"schema_version":"1.0"},"canonical_sha256":"ded09be33e41416f82b478ac43f4b99f622d7e498392af96489e06df150fac8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:59:19.789884Z","signature_b64":"++X6JChZFTIIxQNJI3IoKwg617nr2lJqwpLfZ8cmnr1ARSn6QqHgZVNIC+qIWMoBy/S0lEH8HQHEPmypZdtLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ded09be33e41416f82b478ac43f4b99f622d7e498392af96489e06df150fac8d","last_reissued_at":"2026-07-05T05:59:19.789527Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:59:19.789527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.13697","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":"2026-07-05T05:59:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bO8saGySAGaDX100t5ieC20CLzb28dgfLla6gYHJVePs/NpMbuQKuRSWBlpJrDH4fMYMkYgynogrGh/Eq6CYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:05:08.048181Z"},"content_sha256":"82a27276b946cb48add47d6006084bd01277c2d9ccfa5c504bbbf11cd8b362f5","schema_version":"1.0","event_id":"sha256:82a27276b946cb48add47d6006084bd01277c2d9ccfa5c504bbbf11cd8b362f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:33IJXYZ6IFAW7AVUPCWEH5FZT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction","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":"Matthew Yu","submitted_at":"2021-11-26T19:00:00Z","abstract_excerpt":"We use the language of categorical condensation to give a procedure for gauging nonabelian anyons, which are the manifestations of categorical symmetries in three spacetime dimensions. We also describe how the condensation procedure can be used in other contexts such as for topological cosets and constructing modular invariants. By studying a generalization of which anyons are condensable, we arrive at representations of congruence subgroups of the modular group. We finally present an analysis for ungauging anyons, which is related to the problem of constructing a Drinfeld center for a fusion "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.13697","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.13697/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":"2026-07-05T05:59:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1v2hbX4GNd6iNLmOC7kHMnliPDgb/OIAETrPeBgbBhhlmdGmMEFKQ5DmiCTZSFsaX4fhydJ6TVrY/pUcvxjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:05:08.049113Z"},"content_sha256":"18b404496712ada78ff9d62b36db1964fc2ead773c94b1cbd24022d436e976cf","schema_version":"1.0","event_id":"sha256:18b404496712ada78ff9d62b36db1964fc2ead773c94b1cbd24022d436e976cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/bundle.json","state_url":"https://pith.science/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/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":"2026-08-03T22:05:08Z","links":{"resolver":"https://pith.science/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5","bundle":"https://pith.science/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/bundle.json","state":"https://pith.science/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33IJXYZ6IFAW7AVUPCWEH5FZT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:33IJXYZ6IFAW7AVUPCWEH5FZT5","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":"ca637c7f11b7af37a178be7d0166908db3f37090da88f578ac56254df5b9aaa4","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":"2021-11-26T19:00:00Z","title_canon_sha256":"6c71f6f8fdb321574a57003e29e755e94bb8eb5a40cff2543dce47ca56289f9e"},"schema_version":"1.0","source":{"id":"2111.13697","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.13697","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"2111.13697v3","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.13697","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"33IJXYZ6IFAW","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_16","alias_value":"33IJXYZ6IFAW7AVU","created_at":"2026-07-05T05:59:19Z"},{"alias_kind":"pith_short_8","alias_value":"33IJXYZ6","created_at":"2026-07-05T05:59:19Z"}],"graph_snapshots":[{"event_id":"sha256:18b404496712ada78ff9d62b36db1964fc2ead773c94b1cbd24022d436e976cf","target":"graph","created_at":"2026-07-05T05:59:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.13697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the language of categorical condensation to give a procedure for gauging nonabelian anyons, which are the manifestations of categorical symmetries in three spacetime dimensions. We also describe how the condensation procedure can be used in other contexts such as for topological cosets and constructing modular invariants. By studying a generalization of which anyons are condensable, we arrive at representations of congruence subgroups of the modular group. We finally present an analysis for ungauging anyons, which is related to the problem of constructing a Drinfeld center for a fusion ","authors_text":"Matthew Yu","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":"2021-11-26T19:00:00Z","title":"Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.13697","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":"sha256:82a27276b946cb48add47d6006084bd01277c2d9ccfa5c504bbbf11cd8b362f5","target":"record","created_at":"2026-07-05T05:59:19Z","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":"ca637c7f11b7af37a178be7d0166908db3f37090da88f578ac56254df5b9aaa4","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":"2021-11-26T19:00:00Z","title_canon_sha256":"6c71f6f8fdb321574a57003e29e755e94bb8eb5a40cff2543dce47ca56289f9e"},"schema_version":"1.0","source":{"id":"2111.13697","kind":"arxiv","version":3}},"canonical_sha256":"ded09be33e41416f82b478ac43f4b99f622d7e498392af96489e06df150fac8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ded09be33e41416f82b478ac43f4b99f622d7e498392af96489e06df150fac8d","first_computed_at":"2026-07-05T05:59:19.789527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:59:19.789527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"++X6JChZFTIIxQNJI3IoKwg617nr2lJqwpLfZ8cmnr1ARSn6QqHgZVNIC+qIWMoBy/S0lEH8HQHEPmypZdtLDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:59:19.789884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.13697","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82a27276b946cb48add47d6006084bd01277c2d9ccfa5c504bbbf11cd8b362f5","sha256:18b404496712ada78ff9d62b36db1964fc2ead773c94b1cbd24022d436e976cf"],"state_sha256":"7da4de5b5aaf9006fa1ca4295b1d8163a7edb05a2e0475d7dbd427cd637ca8f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ik9V87BeT7kXNcm29upjF9gogX/OviAeCwJP3bdOjFHX0RziFISo5tcuIl+Z2eO0HANl3NgIAeq6zQ6tPTvzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:05:08.054110Z","bundle_sha256":"3a1d24af0ea819bc64afda80e1871f2a9a7ba8e01c95d32fb1e3a046da53c1e8"}}