{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CZZU6JFGHVGG5LZ5GZXSWSVWR3","short_pith_number":"pith:CZZU6JFG","schema_version":"1.0","canonical_sha256":"16734f24a63d4c6eaf3d366f2b4ab68ec9e5fc83b15ca18f953326f290761db6","source":{"kind":"arxiv","id":"1009.1415","version":2},"attestation_state":"computed","paper":{"title":"Wannier representation of Z_2 topological insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.mes-hall","authors_text":"Alexey A. Soluyanov, David Vanderbilt","submitted_at":"2010-09-07T22:24:23Z","abstract_excerpt":"We consider the problem of constructing Wannier functions for Z_2 topological insulators in two dimensions. It is well known that there is a topological obstruction to the construction of Wannier functions for Chern insulators, but it has been unclear whether this is also true for the Z_2 case. We consider the Kane-Mele tight-binding model, which exhibits both normal (Z_2-even) and topological (Z_2-odd) phases as a function of the model parameters. In the Z_2-even phase, the usual projection-based scheme can be used to build the Wannier representation. In the Z_2-odd phase, we do find a topolo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.1415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2010-09-07T22:24:23Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"eb0b9d4a240d9cd554bdea05bc75260df8d93e446605f47afc42fb077b85a6ec","abstract_canon_sha256":"17f3db49622f8dd3a477a4617a4343c317a04d70819735128ae7b28245745c1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:09.618646Z","signature_b64":"O2+aWjUL5x1/3HX75bTvRKQbgc8qkuoavCr1/mdL0wIX6VUgqRiN0zFJM8+04vtUequzHD7LS6LaOi0dSQviBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16734f24a63d4c6eaf3d366f2b4ab68ec9e5fc83b15ca18f953326f290761db6","last_reissued_at":"2026-05-18T04:28:09.618060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:09.618060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wannier representation of Z_2 topological insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.mes-hall","authors_text":"Alexey A. Soluyanov, David Vanderbilt","submitted_at":"2010-09-07T22:24:23Z","abstract_excerpt":"We consider the problem of constructing Wannier functions for Z_2 topological insulators in two dimensions. It is well known that there is a topological obstruction to the construction of Wannier functions for Chern insulators, but it has been unclear whether this is also true for the Z_2 case. We consider the Kane-Mele tight-binding model, which exhibits both normal (Z_2-even) and topological (Z_2-odd) phases as a function of the model parameters. In the Z_2-even phase, the usual projection-based scheme can be used to build the Wannier representation. In the Z_2-odd phase, we do find a topolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1415","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.1415","created_at":"2026-05-18T04:28:09.618136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.1415v2","created_at":"2026-05-18T04:28:09.618136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1415","created_at":"2026-05-18T04:28:09.618136+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZZU6JFGHVGG","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZZU6JFGHVGG5LZ5","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZZU6JFG","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3","json":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3.json","graph_json":"https://pith.science/api/pith-number/CZZU6JFGHVGG5LZ5GZXSWSVWR3/graph.json","events_json":"https://pith.science/api/pith-number/CZZU6JFGHVGG5LZ5GZXSWSVWR3/events.json","paper":"https://pith.science/paper/CZZU6JFG"},"agent_actions":{"view_html":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3","download_json":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3.json","view_paper":"https://pith.science/paper/CZZU6JFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.1415&json=true","fetch_graph":"https://pith.science/api/pith-number/CZZU6JFGHVGG5LZ5GZXSWSVWR3/graph.json","fetch_events":"https://pith.science/api/pith-number/CZZU6JFGHVGG5LZ5GZXSWSVWR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3/action/storage_attestation","attest_author":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3/action/author_attestation","sign_citation":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3/action/citation_signature","submit_replication":"https://pith.science/pith/CZZU6JFGHVGG5LZ5GZXSWSVWR3/action/replication_record"}},"created_at":"2026-05-18T04:28:09.618136+00:00","updated_at":"2026-05-18T04:28:09.618136+00:00"}