{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WPFTYRRNB2HL7XQI6FNS632ASK","short_pith_number":"pith:WPFTYRRN","schema_version":"1.0","canonical_sha256":"b3cb3c462d0e8ebfde08f15b2f6f40928eff5be017bdefe25731552650b7d36e","source":{"kind":"arxiv","id":"1703.06308","version":2},"attestation_state":"computed","paper":{"title":"On the construction of Wannier functions in topological insulators: the 3D case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.mtrl-sci","math.MP"],"primary_cat":"math-ph","authors_text":"Domenico Monaco, Horia D. Cornean","submitted_at":"2017-03-18T15:37:39Z","abstract_excerpt":"We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for 3-dimensional time-reversal symmetric topological insulators, both of bosonic and of fermionic type, so that the bases in question are also compatible with time-reversal symmetry. This problem is translated in the study, of independent interest, of homotopy classes of continuous, periodic, and time-reversal symmetric families of unitary matrices. We identify three $\\mathbb{Z}_2$-valued complete invariants for these homotopy classes. When these invari"},"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":"1703.06308","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-18T15:37:39Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.mtrl-sci","math.MP"],"title_canon_sha256":"91cec1349735b528ae9ead4ee7cec748c8222bf2936d0aac9d15c151a29fefe2","abstract_canon_sha256":"e293a019c2c409f08930cb62e26dbee3574fe5114d55585b4c061ba13486034e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:30.565803Z","signature_b64":"WkWLwyLgJfQWuXzuMJsmRIitD6o5u4x/bPF51NwkDG7JdDLiQpQwmEW3b6FXiO2Xz5YtYdDJCn7u42+/klFgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3cb3c462d0e8ebfde08f15b2f6f40928eff5be017bdefe25731552650b7d36e","last_reissued_at":"2026-05-18T00:30:30.565101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:30.565101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the construction of Wannier functions in topological insulators: the 3D case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.mtrl-sci","math.MP"],"primary_cat":"math-ph","authors_text":"Domenico Monaco, Horia D. Cornean","submitted_at":"2017-03-18T15:37:39Z","abstract_excerpt":"We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for 3-dimensional time-reversal symmetric topological insulators, both of bosonic and of fermionic type, so that the bases in question are also compatible with time-reversal symmetry. This problem is translated in the study, of independent interest, of homotopy classes of continuous, periodic, and time-reversal symmetric families of unitary matrices. We identify three $\\mathbb{Z}_2$-valued complete invariants for these homotopy classes. When these invari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06308","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":"1703.06308","created_at":"2026-05-18T00:30:30.565205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06308v2","created_at":"2026-05-18T00:30:30.565205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06308","created_at":"2026-05-18T00:30:30.565205+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPFTYRRNB2HL","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPFTYRRNB2HL7XQI","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPFTYRRN","created_at":"2026-05-18T12:31:53.515858+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/WPFTYRRNB2HL7XQI6FNS632ASK","json":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK.json","graph_json":"https://pith.science/api/pith-number/WPFTYRRNB2HL7XQI6FNS632ASK/graph.json","events_json":"https://pith.science/api/pith-number/WPFTYRRNB2HL7XQI6FNS632ASK/events.json","paper":"https://pith.science/paper/WPFTYRRN"},"agent_actions":{"view_html":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK","download_json":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK.json","view_paper":"https://pith.science/paper/WPFTYRRN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06308&json=true","fetch_graph":"https://pith.science/api/pith-number/WPFTYRRNB2HL7XQI6FNS632ASK/graph.json","fetch_events":"https://pith.science/api/pith-number/WPFTYRRNB2HL7XQI6FNS632ASK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK/action/storage_attestation","attest_author":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK/action/author_attestation","sign_citation":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK/action/citation_signature","submit_replication":"https://pith.science/pith/WPFTYRRNB2HL7XQI6FNS632ASK/action/replication_record"}},"created_at":"2026-05-18T00:30:30.565205+00:00","updated_at":"2026-05-18T00:30:30.565205+00:00"}