{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VRSAOLKSGTLJXMLBEHT2JDRA37","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":"5cca6faf564d7502d03696c830a91f86d5b7992988935a18430d033129853c0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-07-27T02:17:42Z","title_canon_sha256":"7c987468660cf09a7e5a6de0327684e15242a529b306a227d09875024fa3858d"},"schema_version":"1.0","source":{"id":"1307.7206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7206","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7206v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7206","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"VRSAOLKSGTLJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VRSAOLKSGTLJXMLB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VRSAOLKS","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:e6b61e976ccd2ba493c3d683d92a8df6867830b9d6d9ceb9c13dd41dfc83707f","target":"graph","created_at":"2026-05-18T03:06:54Z","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"},"paper":{"abstract_excerpt":"Three-dimensional (3D) topological insulators in general need to be protected by certain kinds of symmetries other than the presumed $U(1)$ charge conservation. A peculiar exception is the Hopf insulators which are 3D topological insulators characterized by an integer Hopf index. To demonstrate the existence and physical relevance of the Hopf insulators, we construct a class of tight-binding model Hamiltonians which realize all kinds of Hopf insulators with arbitrary integer Hopf index. These Hopf insulator phases have topologically protected surface states and we numerically demonstrate the r","authors_text":"Chao Shen, Dong-Ling Deng, Lu-Ming Duan, Sheng-Tao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-07-27T02:17:42Z","title":"Hopf Insulators and Their Topologically Protected Surface States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7206","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":"sha256:4d5df0ec15bc448a53fb863aa73b4b06db1543ba0a80299c2857afd2cee82361","target":"record","created_at":"2026-05-18T03:06:54Z","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":"5cca6faf564d7502d03696c830a91f86d5b7992988935a18430d033129853c0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-07-27T02:17:42Z","title_canon_sha256":"7c987468660cf09a7e5a6de0327684e15242a529b306a227d09875024fa3858d"},"schema_version":"1.0","source":{"id":"1307.7206","kind":"arxiv","version":2}},"canonical_sha256":"ac64072d5234d69bb16121e7a48e20dfc95d053770654e4998bcb1287fe9fa7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac64072d5234d69bb16121e7a48e20dfc95d053770654e4998bcb1287fe9fa7e","first_computed_at":"2026-05-18T03:06:54.706177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.706177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QezaTl7wcLn8t+caAKwafh2lVqC18lAXWc8ryqGuDlGFSsI0A4q3ZWcDLrc8XyWi52rJcMVoakV3/OG2hWpQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.706861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d5df0ec15bc448a53fb863aa73b4b06db1543ba0a80299c2857afd2cee82361","sha256:e6b61e976ccd2ba493c3d683d92a8df6867830b9d6d9ceb9c13dd41dfc83707f"],"state_sha256":"f5d09d4d60f2acc4c432a301f0351ffaedda8076115c0a4725b26d4d399b9f03"}