{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CTDNLM3BSFMYBKTYPVCUOBKDCY","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":"bc317b30bf803a34eb24699c1415572b7111dced0dbda31ee39165086a70745d","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-12-31T18:53:27Z","title_canon_sha256":"182da90ca9b7020004ac745a954c218d9f62d72656ca6876da1c634c404315f8"},"schema_version":"1.0","source":{"id":"1912.13505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13505","created_at":"2026-07-05T07:28:24Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13505v2","created_at":"2026-07-05T07:28:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13505","created_at":"2026-07-05T07:28:24Z"},{"alias_kind":"pith_short_12","alias_value":"CTDNLM3BSFMY","created_at":"2026-07-05T07:28:24Z"},{"alias_kind":"pith_short_16","alias_value":"CTDNLM3BSFMYBKTY","created_at":"2026-07-05T07:28:24Z"},{"alias_kind":"pith_short_8","alias_value":"CTDNLM3B","created_at":"2026-07-05T07:28:24Z"}],"graph_snapshots":[{"event_id":"sha256:580e5ab4612a530a691791778038e83c7ec6fe629f22f3e3aeac7c3ac722155b","target":"graph","created_at":"2026-07-05T07:28:24Z","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/1912.13505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing universal topological quantum computation. Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics. In this work, we systematically study the so-called three-loop braiding statistics for loop-like excitations for 3D fermionic topological phases. Most surprisingly, we discovered new types of non-Abelian three-loop","authors_text":"Chenjie Wang, Jing-Ren Zhou, Qing-Rui Wang, Zheng-Cheng Gu","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-12-31T18:53:27Z","title":"Non-Abelian Three-Loop Braiding Statistics for 3D Fermionic Topological Phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13505","kind":"arxiv","version":2},"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:dda3ce6098a07370fb93e9bd7fd71c93e7a75adfe3f3a6ecff0765496319f3f6","target":"record","created_at":"2026-07-05T07:28:24Z","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":"bc317b30bf803a34eb24699c1415572b7111dced0dbda31ee39165086a70745d","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-12-31T18:53:27Z","title_canon_sha256":"182da90ca9b7020004ac745a954c218d9f62d72656ca6876da1c634c404315f8"},"schema_version":"1.0","source":{"id":"1912.13505","kind":"arxiv","version":2}},"canonical_sha256":"14c6d5b361915980aa787d45470543161a075a180dfb6eb570d8771685ff2564","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14c6d5b361915980aa787d45470543161a075a180dfb6eb570d8771685ff2564","first_computed_at":"2026-07-05T07:28:24.705716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:28:24.705716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CKQsvum7ZCJrUOCS4o7gVCp18CT6Cbq2cNjOz8zr9YvPV9jM3JL4mMxwu74JAHZ0JEFg9JLewSS+L1u6wihyBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:28:24.706244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.13505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dda3ce6098a07370fb93e9bd7fd71c93e7a75adfe3f3a6ecff0765496319f3f6","sha256:580e5ab4612a530a691791778038e83c7ec6fe629f22f3e3aeac7c3ac722155b"],"state_sha256":"c3105434b3f4a424aadcea451b51ad58fe8fbf58955668818f7881ab60dee69a"}