{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Z2TM24VK7FZJ25A3GJVTZE5WQQ","short_pith_number":"pith:Z2TM24VK","schema_version":"1.0","canonical_sha256":"cea6cd72aaf9729d741b326b3c93b68414bf5a61dd2a0695c2c41483fe010416","source":{"kind":"arxiv","id":"2012.09460","version":2},"attestation_state":"computed","paper":{"title":"Takagi topological insulator with odd $\\mathcal P\\mathcal T$ pairs of corner states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Jia-Xiao Dai, Kai Wang, Shengyuan A. Yang, Y. X. Zhao","submitted_at":"2020-12-17T09:20:59Z","abstract_excerpt":"We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and spacetime inversion ($\\mathcal P\\mathcal T$) symmetry. The required symmetries for the TTIs can be realized on any bipartite lattice where the inversion exchanges sublattices. The protecting symmetries lead to the classifying space of Hamiltonians being unitary symmetric matrices, and therefore Takagi's factorization can be performed. Particularly, the global Takagi's factorization can (cannot) be done on a $3$D ($2$D) sphere. In 3D, there is a "},"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":"2012.09460","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2020-12-17T09:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"a9426d4913aa0c6633fd9f5b7a1140a4f55ac82b1a59b3802741b2d6557c7e67","abstract_canon_sha256":"716b6ee7c2fd53ff4408cdf4932657da2403b81cd59347c5afcfd74dc5c330ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:38.270937Z","signature_b64":"X5aPFojCUn/8634zXhVJFZI3DQnTq7UnGMzv1uVt9Hga/ewj4xLdgQvM8qhgJb+hBvearbk2qImoLMCW4Rx1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea6cd72aaf9729d741b326b3c93b68414bf5a61dd2a0695c2c41483fe010416","last_reissued_at":"2026-07-05T03:26:38.270590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:38.270590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Takagi topological insulator with odd $\\mathcal P\\mathcal T$ pairs of corner states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Jia-Xiao Dai, Kai Wang, Shengyuan A. Yang, Y. X. Zhao","submitted_at":"2020-12-17T09:20:59Z","abstract_excerpt":"We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and spacetime inversion ($\\mathcal P\\mathcal T$) symmetry. The required symmetries for the TTIs can be realized on any bipartite lattice where the inversion exchanges sublattices. The protecting symmetries lead to the classifying space of Hamiltonians being unitary symmetric matrices, and therefore Takagi's factorization can be performed. Particularly, the global Takagi's factorization can (cannot) be done on a $3$D ($2$D) sphere. In 3D, there is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.09460","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.09460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2012.09460","created_at":"2026-07-05T03:26:38.270647+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.09460v2","created_at":"2026-07-05T03:26:38.270647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.09460","created_at":"2026-07-05T03:26:38.270647+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2TM24VK7FZJ","created_at":"2026-07-05T03:26:38.270647+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2TM24VK7FZJ25A3","created_at":"2026-07-05T03:26:38.270647+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2TM24VK","created_at":"2026-07-05T03:26:38.270647+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/Z2TM24VK7FZJ25A3GJVTZE5WQQ","json":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ.json","graph_json":"https://pith.science/api/pith-number/Z2TM24VK7FZJ25A3GJVTZE5WQQ/graph.json","events_json":"https://pith.science/api/pith-number/Z2TM24VK7FZJ25A3GJVTZE5WQQ/events.json","paper":"https://pith.science/paper/Z2TM24VK"},"agent_actions":{"view_html":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ","download_json":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ.json","view_paper":"https://pith.science/paper/Z2TM24VK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.09460&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2TM24VK7FZJ25A3GJVTZE5WQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2TM24VK7FZJ25A3GJVTZE5WQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ/action/storage_attestation","attest_author":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ/action/author_attestation","sign_citation":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ/action/citation_signature","submit_replication":"https://pith.science/pith/Z2TM24VK7FZJ25A3GJVTZE5WQQ/action/replication_record"}},"created_at":"2026-07-05T03:26:38.270647+00:00","updated_at":"2026-07-05T03:26:38.270647+00:00"}