{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BNYCTSV22OIBM64O3TMEQNKBB7","short_pith_number":"pith:BNYCTSV2","canonical_record":{"source":{"id":"2104.07067","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-04-14T18:19:53Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"eada1272820af0780d37512a24e86c2266f9ac1d6006b36e565637429f334580","abstract_canon_sha256":"f14729c5162119beb24d4332edf825bc488fa9b34c94a9abc47fff67c6b0a880"},"schema_version":"1.0"},"canonical_sha256":"0b7029cabad390167b8edcd84835410fff874df5aad5aa69578be760ec953e19","source":{"kind":"arxiv","id":"2104.07067","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BNYCTSV22OIBM64O3TMEQNKBB7","target":"record","payload":{"canonical_record":{"source":{"id":"2104.07067","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-04-14T18:19:53Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"eada1272820af0780d37512a24e86c2266f9ac1d6006b36e565637429f334580","abstract_canon_sha256":"f14729c5162119beb24d4332edf825bc488fa9b34c94a9abc47fff67c6b0a880"},"schema_version":"1.0"},"canonical_sha256":"0b7029cabad390167b8edcd84835410fff874df5aad5aa69578be760ec953e19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:16:51.502833Z","signature_b64":"EshEVwNo3J2H0PecbvZNBkobogEECrxz53pvsLFwjiD9z3LYvqBCjpokoYPJFZFsZfDb6aJK+73z9vqGISowBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b7029cabad390167b8edcd84835410fff874df5aad5aa69578be760ec953e19","last_reissued_at":"2026-07-05T04:16:51.502428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:16:51.502428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.07067","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":"2026-07-05T04:16:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLc+oMdKBW9vN63gDt1OmZc5kQ6/vMv4vh+BgjZj0Ogqic/nsqzydwchtRCuLCpyzxvIOcP4XwCFsDbE0v5eAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:48:41.855411Z"},"content_sha256":"bc2db2fb144135ddd83bc39e2859322a6a6311fc192f8049a3e65cc2f6dfa7c6","schema_version":"1.0","event_id":"sha256:bc2db2fb144135ddd83bc39e2859322a6a6311fc192f8049a3e65cc2f6dfa7c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BNYCTSV22OIBM64O3TMEQNKBB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions","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":"Peng Ye, Zhi-Feng Zhang","submitted_at":"2021-04-14T18:19:53Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07067","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/2104.07067/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":"2026-07-05T04:16:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zK85SuurExWwD4wHVFqJWFCsvRojD+MJ2r/+6LcBlWiZY+816ciITeu3afpJdrUBXEJLFayXOWBGs8FCX3OfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:48:41.856324Z"},"content_sha256":"0e588265cab33e33c5837441997478a7b85fcff2d9b7249348a5ad071d61d5c8","schema_version":"1.0","event_id":"sha256:0e588265cab33e33c5837441997478a7b85fcff2d9b7249348a5ad071d61d5c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNYCTSV22OIBM64O3TMEQNKBB7/bundle.json","state_url":"https://pith.science/pith/BNYCTSV22OIBM64O3TMEQNKBB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNYCTSV22OIBM64O3TMEQNKBB7/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":"2026-08-03T20:48:41Z","links":{"resolver":"https://pith.science/pith/BNYCTSV22OIBM64O3TMEQNKBB7","bundle":"https://pith.science/pith/BNYCTSV22OIBM64O3TMEQNKBB7/bundle.json","state":"https://pith.science/pith/BNYCTSV22OIBM64O3TMEQNKBB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNYCTSV22OIBM64O3TMEQNKBB7/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrofRS3ZpGceUV1Y1zPY3XBvgGf5coteF3nv+C0g834tk7fHtftYHw1f6reJUOmD/fXBvigJ4pqWYU0K7bTMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:48:41.862602Z","bundle_sha256":"7445d767fa462e4f131887d7a11ffceae6677a8889e3f0b9cff179fda0a16577"}}