{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BNYCTSV22OIBM64O3TMEQNKBB7","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":"f14729c5162119beb24d4332edf825bc488fa9b34c94a9abc47fff67c6b0a880","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":"2021-04-14T18:19:53Z","title_canon_sha256":"eada1272820af0780d37512a24e86c2266f9ac1d6006b36e565637429f334580"},"schema_version":"1.0","source":{"id":"2104.07067","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07067","created_at":"2026-07-05T04:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07067v3","created_at":"2026-07-05T04:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07067","created_at":"2026-07-05T04:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"BNYCTSV22OIB","created_at":"2026-07-05T04:16:51Z"},{"alias_kind":"pith_short_16","alias_value":"BNYCTSV22OIBM64O","created_at":"2026-07-05T04:16:51Z"},{"alias_kind":"pith_short_8","alias_value":"BNYCTSV2","created_at":"2026-07-05T04:16:51Z"}],"graph_snapshots":[{"event_id":"sha256:0e588265cab33e33c5837441997478a7b85fcff2d9b7249348a5ad071d61d5c8","target":"graph","created_at":"2026-07-05T04:16:51Z","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/2104.07067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime ($5$D) in which \\textit{topological excitations} include not only point-like \\textit{particles}, but also two types of spatially extended objects: closed string-like \\textit{loops} and two-dimensional closed \\textit{membranes}. Especially, membranes have been rarely explored in the literature of topological orders. By introducing higher-form gauge fields, we cons","authors_text":"Peng Ye, Zhi-Feng Zhang","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":"2021-04-14T18:19:53Z","title":"Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07067","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:bc2db2fb144135ddd83bc39e2859322a6a6311fc192f8049a3e65cc2f6dfa7c6","target":"record","created_at":"2026-07-05T04:16:51Z","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":"f14729c5162119beb24d4332edf825bc488fa9b34c94a9abc47fff67c6b0a880","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":"2021-04-14T18:19:53Z","title_canon_sha256":"eada1272820af0780d37512a24e86c2266f9ac1d6006b36e565637429f334580"},"schema_version":"1.0","source":{"id":"2104.07067","kind":"arxiv","version":3}},"canonical_sha256":"0b7029cabad390167b8edcd84835410fff874df5aad5aa69578be760ec953e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b7029cabad390167b8edcd84835410fff874df5aad5aa69578be760ec953e19","first_computed_at":"2026-07-05T04:16:51.502428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:16:51.502428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EshEVwNo3J2H0PecbvZNBkobogEECrxz53pvsLFwjiD9z3LYvqBCjpokoYPJFZFsZfDb6aJK+73z9vqGISowBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:16:51.502833Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.07067","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc2db2fb144135ddd83bc39e2859322a6a6311fc192f8049a3e65cc2f6dfa7c6","sha256:0e588265cab33e33c5837441997478a7b85fcff2d9b7249348a5ad071d61d5c8"],"state_sha256":"e7e832d168bf259be175f625c80b2b10cef41807249c216e4998ce3d7355b04a"}