{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ENMF4NGKVIRMLD2ZWAKZDQZLK3","short_pith_number":"pith:ENMF4NGK","schema_version":"1.0","canonical_sha256":"23585e34caaa22c58f59b01591c32b56efaf8c954300456cf5943af268ce7eb7","source":{"kind":"arxiv","id":"1902.01533","version":2},"attestation_state":"computed","paper":{"title":"Toeplitz operators on concave corners and topologically protected corner states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.KT","math.MP"],"primary_cat":"math-ph","authors_text":"Shin Hayashi","submitted_at":"2019-02-05T04:00:36Z","abstract_excerpt":"We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz operator of index one. By using this, a relation between Fredholm indices of quarter-plane and concave corner Toeplitz operators is clarified. As an application, topological invariants and corner states for some bulk-edges gapped Hamiltonians on two-dimensional (2-D) class AIII and 3-D class A systems with concave corners are studied. Explicit examples clarify th"},"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":"1902.01533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-05T04:00:36Z","cross_cats_sorted":["cond-mat.mes-hall","math.KT","math.MP"],"title_canon_sha256":"f2f84ef21d90a43a57148d16e04161ec04f895f5a9d63791ecf70f01f40dfb18","abstract_canon_sha256":"fde207b4509b73a79658c88709f192dec9e2d181cd546fb7810581c83e6e1c8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:01.941949Z","signature_b64":"gQxWB12qH1tm09gyyekh8EI7gGjH3okB/2fyE4Y/d3BpVNrrijksBH/0GNg8tqFfzNTAF9yN8dzKxYRkWQ51DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23585e34caaa22c58f59b01591c32b56efaf8c954300456cf5943af268ce7eb7","last_reissued_at":"2026-05-17T23:47:01.941126Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:01.941126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toeplitz operators on concave corners and topologically protected corner states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.KT","math.MP"],"primary_cat":"math-ph","authors_text":"Shin Hayashi","submitted_at":"2019-02-05T04:00:36Z","abstract_excerpt":"We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz operator of index one. By using this, a relation between Fredholm indices of quarter-plane and concave corner Toeplitz operators is clarified. As an application, topological invariants and corner states for some bulk-edges gapped Hamiltonians on two-dimensional (2-D) class AIII and 3-D class A systems with concave corners are studied. Explicit examples clarify th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01533","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":"1902.01533","created_at":"2026-05-17T23:47:01.941267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.01533v2","created_at":"2026-05-17T23:47:01.941267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01533","created_at":"2026-05-17T23:47:01.941267+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENMF4NGKVIRM","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENMF4NGKVIRMLD2Z","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENMF4NGK","created_at":"2026-05-18T12:33:15.570797+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/ENMF4NGKVIRMLD2ZWAKZDQZLK3","json":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3.json","graph_json":"https://pith.science/api/pith-number/ENMF4NGKVIRMLD2ZWAKZDQZLK3/graph.json","events_json":"https://pith.science/api/pith-number/ENMF4NGKVIRMLD2ZWAKZDQZLK3/events.json","paper":"https://pith.science/paper/ENMF4NGK"},"agent_actions":{"view_html":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3","download_json":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3.json","view_paper":"https://pith.science/paper/ENMF4NGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.01533&json=true","fetch_graph":"https://pith.science/api/pith-number/ENMF4NGKVIRMLD2ZWAKZDQZLK3/graph.json","fetch_events":"https://pith.science/api/pith-number/ENMF4NGKVIRMLD2ZWAKZDQZLK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3/action/storage_attestation","attest_author":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3/action/author_attestation","sign_citation":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3/action/citation_signature","submit_replication":"https://pith.science/pith/ENMF4NGKVIRMLD2ZWAKZDQZLK3/action/replication_record"}},"created_at":"2026-05-17T23:47:01.941267+00:00","updated_at":"2026-05-17T23:47:01.941267+00:00"}