{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IZYBNT4U4X7S3NKTZGYYCX5KQG","short_pith_number":"pith:IZYBNT4U","schema_version":"1.0","canonical_sha256":"467016cf94e5ff2db553c9b1815faa81ba4bd17391b8b75dc9b00371879a86c6","source":{"kind":"arxiv","id":"2602.12588","version":2},"attestation_state":"computed","paper":{"title":"Topology and edge modes surviving criticality in non-Hermitian Floquet systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems.","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Longwen Zhou","submitted_at":"2026-02-13T04:01:55Z","abstract_excerpt":"The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases an"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2602.12588","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2026-02-13T04:01:55Z","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"title_canon_sha256":"879ab30b48ea064b8007039cd113304c2260cf1a82693a390c181752c1d9956f","abstract_canon_sha256":"5958050d0e95df1aaf6a9af0ec3ddfe0deb2be80ae5f7c448eaee3063ef9273d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:16.186609Z","signature_b64":"3MCFxjsr+DNU27ry9UmGmejJpP9LGJtHgxOsH4uQ9YJr1UM/5TVocFtJZqy2475ODKSGnqcy4kSdZRQWC6BsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"467016cf94e5ff2db553c9b1815faa81ba4bd17391b8b75dc9b00371879a86c6","last_reissued_at":"2026-05-17T23:39:16.185882Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:16.185882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology and edge modes surviving criticality in non-Hermitian Floquet systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems.","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Longwen Zhou","submitted_at":"2026-02-13T04:01:55Z","abstract_excerpt":"The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that sublattice symmetry in one-dimensional non-Hermitian Floquet models permits a well-defined generalized Brillouin zone to which Cauchy's argument principle can be applied without additional restrictions at criticality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-Hermitian Floquet systems host gapless symmetry-protected topological phases with unified winding numbers and robust edge modes surviving at criticality.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"76c7e56f2ae8995a4bcf386dafded729c26f7edc30b0894a6c13dd39560b3eda"},"source":{"id":"2602.12588","kind":"arxiv","version":2},"verdict":{"id":"9d00579e-85a5-4183-aac5-653a62ebbe75","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T22:51:09.147747Z","strongest_claim":"We introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points.","one_line_summary":"Non-Hermitian Floquet systems host gapless symmetry-protected topological phases with unified winding numbers and robust edge modes surviving at criticality.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that sublattice symmetry in one-dimensional non-Hermitian Floquet models permits a well-defined generalized Brillouin zone to which Cauchy's argument principle can be applied without additional restrictions at criticality.","pith_extraction_headline":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems."},"references":{"count":91,"sample":[{"doi":"","year":null,"title":"The roles of disorder and interactions in non-Hermitian Floquet gSPTs also deserve more thorough explorations","work_id":"3e82c26b-9449-47c1-8388-0c6135269358","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"T. Scaffidi, D. E. Parker, and R. Vasseur, Gapless Symmetry-Protected Topological Order, Phys. Rev. X7, 041048 (2017)","work_id":"b110b6f6-ccd6-4a39-971a-c5a77d009645","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"R. Verresen, R. Thorngren, N. G. Jones, and F. Pollmann, Gapless Topological Phases and Symmetry- Enriched Quantum Criticality, Phys. Rev. X11, 041059 (2021)","work_id":"9c111808-7cf7-4a28-9cd0-69185264f5e1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Y. Baum, T. Posske, I. C. Fulga, B. Trauzettel, and A. Stern, Coexisting Edge States and Gapless Bulk in Topo- logical States of Matter, Phys. Rev. Lett.114, 136801 (2015)","work_id":"7c70e4d3-6d80-4036-a8c4-0352fdfd41c7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"A. Keselman and E. Berg, Gapless symmetry-protected topological phase of fermions in one dimension, Phys. Rev. B91, 235309 (2015)","work_id":"b21d03b4-6655-4177-9d17-079a8f481784","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":91,"snapshot_sha256":"7dafc59feb633765288dabb07a1c6dd5c32c9e80face9977a7d5bbe4fe37add5","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5e1bf7f0ded843da3883f50aa18dcd84561c9a22605511a1e75f016ad13abb99"},"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":"2602.12588","created_at":"2026-05-17T23:39:16.186012+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.12588v2","created_at":"2026-05-17T23:39:16.186012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.12588","created_at":"2026-05-17T23:39:16.186012+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZYBNT4U4X7S","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZYBNT4U4X7S3NKT","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZYBNT4U","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.22396","citing_title":"Boundary Floquet Control of Bulk non-Hermitian Systems","ref_index":104,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG","json":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG.json","graph_json":"https://pith.science/api/pith-number/IZYBNT4U4X7S3NKTZGYYCX5KQG/graph.json","events_json":"https://pith.science/api/pith-number/IZYBNT4U4X7S3NKTZGYYCX5KQG/events.json","paper":"https://pith.science/paper/IZYBNT4U"},"agent_actions":{"view_html":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG","download_json":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG.json","view_paper":"https://pith.science/paper/IZYBNT4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.12588&json=true","fetch_graph":"https://pith.science/api/pith-number/IZYBNT4U4X7S3NKTZGYYCX5KQG/graph.json","fetch_events":"https://pith.science/api/pith-number/IZYBNT4U4X7S3NKTZGYYCX5KQG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG/action/storage_attestation","attest_author":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG/action/author_attestation","sign_citation":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG/action/citation_signature","submit_replication":"https://pith.science/pith/IZYBNT4U4X7S3NKTZGYYCX5KQG/action/replication_record"}},"created_at":"2026-05-17T23:39:16.186012+00:00","updated_at":"2026-05-17T23:39:16.186012+00:00"}