{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5LFTDKGTPVWOY6G7RLEQEV6F42","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":"4af1374e1d773c718f6aba99105492f876aaa7e7f77b37665d6a1d36c9f0b9b5","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2021-05-20T02:10:55Z","title_canon_sha256":"5eae08dcfde8a9089dc8bfd99a47bbc00722df99faba45904a30a5de66c6c0b2"},"schema_version":"1.0","source":{"id":"2105.09454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.09454","created_at":"2026-07-05T03:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"2105.09454v2","created_at":"2026-07-05T03:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.09454","created_at":"2026-07-05T03:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"5LFTDKGTPVWO","created_at":"2026-07-05T03:46:02Z"},{"alias_kind":"pith_short_16","alias_value":"5LFTDKGTPVWOY6G7","created_at":"2026-07-05T03:46:02Z"},{"alias_kind":"pith_short_8","alias_value":"5LFTDKGT","created_at":"2026-07-05T03:46:02Z"}],"graph_snapshots":[{"event_id":"sha256:5304b430e0bc3334d8a48219b62efdb80ff7801a39411593ac580a3d1b4cb32f","target":"graph","created_at":"2026-07-05T03:46:02Z","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/2105.09454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d. The excitation has $\\mathbb{Z}_2$ higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the $\\mathbb{Z}_2$ one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric o","authors_text":"Chao-Ming Jian, Po-Shen Hsin, Wenjie Ji","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2021-05-20T02:10:55Z","title":"Exotic Invertible Phases with Higher-Group Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.09454","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":"sha256:72924211f9bc0e6b5276c784020d35d4983cceda0e296aee9f6cab4f9a1ac4ed","target":"record","created_at":"2026-07-05T03:46:02Z","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":"4af1374e1d773c718f6aba99105492f876aaa7e7f77b37665d6a1d36c9f0b9b5","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2021-05-20T02:10:55Z","title_canon_sha256":"5eae08dcfde8a9089dc8bfd99a47bbc00722df99faba45904a30a5de66c6c0b2"},"schema_version":"1.0","source":{"id":"2105.09454","kind":"arxiv","version":2}},"canonical_sha256":"eacb31a8d37d6cec78df8ac90257c5e6a87c45c0a99a881b0b587f2cb73842f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eacb31a8d37d6cec78df8ac90257c5e6a87c45c0a99a881b0b587f2cb73842f6","first_computed_at":"2026-07-05T03:46:02.115366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:46:02.115366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLHVmbH78vW38IKO+NEPxFG1X5A3sWVsFuaR7X7WUk5GiePJxY81wRam8QBumOytVu1beikDDji4LS4exJu9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:46:02.115768Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.09454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72924211f9bc0e6b5276c784020d35d4983cceda0e296aee9f6cab4f9a1ac4ed","sha256:5304b430e0bc3334d8a48219b62efdb80ff7801a39411593ac580a3d1b4cb32f"],"state_sha256":"07e1e5d27a161da7ff092e7f4adcf5a828a46caa2b8fd05b089288503c59343a"}