{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:QNFYCUC7GA7YFX4ASODADFPKIL","short_pith_number":"pith:QNFYCUC7","schema_version":"1.0","canonical_sha256":"834b81505f303f82df8093860195ea42dc5b3ed0b4d3057616bb87e8af6a1b6d","source":{"kind":"arxiv","id":"2009.07605","version":2},"attestation_state":"computed","paper":{"title":"Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Qi Zhou, Shu Chen, Yanxia Liu","submitted_at":"2020-09-16T11:09:01Z","abstract_excerpt":"By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for the study of general non-Hermitian quasicrystals with both complex phase factor and non-reciprocal hopping. Specially, the localization-delocalization transition point, $\\mathcal{PT}$-symmetry-breaking point and the winding number transition points are determined by LEs of its dual Hermitian model. The analysis was based on Avila's global theory, and we found that winding number is directly related to the acceleration, the slope of the LE, while quantization of acceleration is the crucial ingredient of Avila"},"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":"2009.07605","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2020-09-16T11:09:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2c012cff331d3417a67c5a4ac56a3e268636680f6c65218070255bd507d3497e","abstract_canon_sha256":"567ab04c7af1ec958472ca4d28449ce7c2a4c9c8195118434e2728a53ca0a255"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:55:32.424421Z","signature_b64":"xihJQI5KBabuCsK1GVSn/DhcT3VHNKzc8HbF6RAkNoVIGLGQ3ZCx2Ij+ssNOPjDgBqmv48N1FIPzOXIIBXo4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"834b81505f303f82df8093860195ea42dc5b3ed0b4d3057616bb87e8af6a1b6d","last_reissued_at":"2026-07-05T02:55:32.423948Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:55:32.423948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Qi Zhou, Shu Chen, Yanxia Liu","submitted_at":"2020-09-16T11:09:01Z","abstract_excerpt":"By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for the study of general non-Hermitian quasicrystals with both complex phase factor and non-reciprocal hopping. Specially, the localization-delocalization transition point, $\\mathcal{PT}$-symmetry-breaking point and the winding number transition points are determined by LEs of its dual Hermitian model. The analysis was based on Avila's global theory, and we found that winding number is directly related to the acceleration, the slope of the LE, while quantization of acceleration is the crucial ingredient of Avila"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07605","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/2009.07605/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":"2009.07605","created_at":"2026-07-05T02:55:32.424006+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.07605v2","created_at":"2026-07-05T02:55:32.424006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07605","created_at":"2026-07-05T02:55:32.424006+00:00"},{"alias_kind":"pith_short_12","alias_value":"QNFYCUC7GA7Y","created_at":"2026-07-05T02:55:32.424006+00:00"},{"alias_kind":"pith_short_16","alias_value":"QNFYCUC7GA7YFX4A","created_at":"2026-07-05T02:55:32.424006+00:00"},{"alias_kind":"pith_short_8","alias_value":"QNFYCUC7","created_at":"2026-07-05T02:55:32.424006+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2411.16843","citing_title":"Mobility edges in pseudo-unitary quasiperiodic quantum walks","ref_index":62,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL","json":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL.json","graph_json":"https://pith.science/api/pith-number/QNFYCUC7GA7YFX4ASODADFPKIL/graph.json","events_json":"https://pith.science/api/pith-number/QNFYCUC7GA7YFX4ASODADFPKIL/events.json","paper":"https://pith.science/paper/QNFYCUC7"},"agent_actions":{"view_html":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL","download_json":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL.json","view_paper":"https://pith.science/paper/QNFYCUC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.07605&json=true","fetch_graph":"https://pith.science/api/pith-number/QNFYCUC7GA7YFX4ASODADFPKIL/graph.json","fetch_events":"https://pith.science/api/pith-number/QNFYCUC7GA7YFX4ASODADFPKIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL/action/storage_attestation","attest_author":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL/action/author_attestation","sign_citation":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL/action/citation_signature","submit_replication":"https://pith.science/pith/QNFYCUC7GA7YFX4ASODADFPKIL/action/replication_record"}},"created_at":"2026-07-05T02:55:32.424006+00:00","updated_at":"2026-07-05T02:55:32.424006+00:00"}