{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P3CTZGIO45DO335JRQ7PEKMQIF","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":"8cbec4d063e7cc23fa065bcf8d79f24bb4ff5a7a101b8afdaecab59b4c50ee46","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-05-26T18:29:26Z","title_canon_sha256":"a62cb292564c23b38594a2e565259c0bd2937ef654a5ba4cc2161fadee90e842"},"schema_version":"1.0","source":{"id":"1605.08398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08398","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08398v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08398","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"P3CTZGIO45DO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P3CTZGIO45DO335J","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P3CTZGIO","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:2b50edaf487b90e0abba0f603dd4acd2bdbbf49d2a27a601e130ae7307f9c512","target":"graph","created_at":"2026-05-18T01:12:41Z","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":"In this short mostly expository note, we sketch a program for gauging fully extended topological field theories in 3 dimensions. One begins with the spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro. One then computes a homotopic space with certain $\\pi_\\bullet$ given by autoequivalences, invertible objects and the ground (algebraic) field. Then for each desired symmetry group $G$ one looks at mapping $BG$ into that. This classifies equivalence classes of G-extended fusion categories. This is an equivalence at a fully extended level so will allow many defects rather","authors_text":"Ammar Husain","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-05-26T18:29:26Z","title":"G-Extensions of Quantum Group Categories and Functorial SPT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08398","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":"sha256:73b646c60d106be3a90c2b1b19566b114ebe5dee66c8edaa3d22a690129821ce","target":"record","created_at":"2026-05-18T01:12:41Z","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":"8cbec4d063e7cc23fa065bcf8d79f24bb4ff5a7a101b8afdaecab59b4c50ee46","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-05-26T18:29:26Z","title_canon_sha256":"a62cb292564c23b38594a2e565259c0bd2937ef654a5ba4cc2161fadee90e842"},"schema_version":"1.0","source":{"id":"1605.08398","kind":"arxiv","version":1}},"canonical_sha256":"7ec53c990ee746edefa98c3ef2299041657fcf10e3dc73aa72cfdcff5b08f270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ec53c990ee746edefa98c3ef2299041657fcf10e3dc73aa72cfdcff5b08f270","first_computed_at":"2026-05-18T01:12:41.643526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:41.643526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KqE1hQ8svkWB27FOcp9KZBZBbopXrQolTj8dRACB3RXrqwd3qacBjQs3z0i0mc+GwLVy8detiqQI2o6iXMfYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:41.643883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73b646c60d106be3a90c2b1b19566b114ebe5dee66c8edaa3d22a690129821ce","sha256:2b50edaf487b90e0abba0f603dd4acd2bdbbf49d2a27a601e130ae7307f9c512"],"state_sha256":"c1d36d588c475175760f8cde127fb546502d1263f707cbd91b4e67f19045013f"}