{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YRCMAWQ7TXBLNQKABID3IL37ZH","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":"f894173eb3393312a1f9e70cfa79d1740756b91bf4d74768fcc97e7e845d9295","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-05-13T09:15:37Z","title_canon_sha256":"d24203b7a9cdc352c49f6e7c71b1d8afc04f43ef29aedfb4e6b95614e4d97c0e"},"schema_version":"1.0","source":{"id":"1905.04924","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04924","created_at":"2026-07-05T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04924v4","created_at":"2026-07-05T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04924","created_at":"2026-07-05T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"YRCMAWQ7TXBL","created_at":"2026-07-05T00:51:02Z"},{"alias_kind":"pith_short_16","alias_value":"YRCMAWQ7TXBLNQKA","created_at":"2026-07-05T00:51:02Z"},{"alias_kind":"pith_short_8","alias_value":"YRCMAWQ7","created_at":"2026-07-05T00:51:02Z"}],"graph_snapshots":[{"event_id":"sha256:542c9ed519c7fde4816dcc98bc427175e8e55f6f67221b41ac6b6070edd52eb9","target":"graph","created_at":"2026-07-05T00:51:02Z","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/1905.04924/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e. a unitary fusion category) as a special case. Therefore, we obtain a unif","authors_text":"Hao Zheng, Liang Kong","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-05-13T09:15:37Z","title":"A mathematical theory of gapless edges of 2d topological orders. Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04924","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:b6e7377bf39ff1197f472b023211ca4a449c0d52c5bdaf3edbd090ffd71cdec4","target":"record","created_at":"2026-07-05T00:51:02Z","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":"f894173eb3393312a1f9e70cfa79d1740756b91bf4d74768fcc97e7e845d9295","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-05-13T09:15:37Z","title_canon_sha256":"d24203b7a9cdc352c49f6e7c71b1d8afc04f43ef29aedfb4e6b95614e4d97c0e"},"schema_version":"1.0","source":{"id":"1905.04924","kind":"arxiv","version":4}},"canonical_sha256":"c444c05a1f9dc2b6c1400a07b42f7fc9ca2bd9115e06cf28aef88cebce963b0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c444c05a1f9dc2b6c1400a07b42f7fc9ca2bd9115e06cf28aef88cebce963b0c","first_computed_at":"2026-07-05T00:51:02.398889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:51:02.398889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ychns0BreWppdunw+Q2nsitGEb67Fvq3L2gogSMgk6Gq7iu+4L/cBKh4q0pZvNEWFa1D9WKE0eNdVdJiFQZ8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:51:02.399377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04924","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e7377bf39ff1197f472b023211ca4a449c0d52c5bdaf3edbd090ffd71cdec4","sha256:542c9ed519c7fde4816dcc98bc427175e8e55f6f67221b41ac6b6070edd52eb9"],"state_sha256":"eb43f5d657b18d4af1f377c59c426740f6ee1e6a623e44e66d89ee4944316061"}