{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XQUCJCB2PBXLYW5FCXF7K6KBQD","short_pith_number":"pith:XQUCJCB2","schema_version":"1.0","canonical_sha256":"bc2824883a786ebc5ba515cbf5794180cd2bf1bd1a966d7fdf5a18edc20a40ed","source":{"kind":"arxiv","id":"1803.10697","version":1},"attestation_state":"computed","paper":{"title":"Large deviations of the Lyapunov exponent and localization for the 1D Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Svetlana Jitomirskaya, Xiaowen Zhu","submitted_at":"2018-03-28T15:54:36Z","abstract_excerpt":"The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized that for one-dimensional models with positive Lyapunov exponents some parts of multi-scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle, leading to nonperturbative proofs for 1D quasiperiodic models. In this paper we present a short proof along these lines, for the Anderson mode"},"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":"1803.10697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-28T15:54:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4284945953d91719097224b9216da504a9c4f00d5c23106ca019f48c5919b46b","abstract_canon_sha256":"c55162b43d9a12d3d321647ed369a5ed6c75d963763049b3ac1b4f82c9d3c136"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:58.703524Z","signature_b64":"R5mfFH5obG9FvtQ1IOotKjVQ50Kp++3EQ1pyIc4W9UYXF8GOZoyMKkBg4n4yr113Fi5qj5UcD3TXCU5AyGHrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc2824883a786ebc5ba515cbf5794180cd2bf1bd1a966d7fdf5a18edc20a40ed","last_reissued_at":"2026-05-17T23:39:58.703075Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:58.703075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations of the Lyapunov exponent and localization for the 1D Anderson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Svetlana Jitomirskaya, Xiaowen Zhu","submitted_at":"2018-03-28T15:54:36Z","abstract_excerpt":"The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized that for one-dimensional models with positive Lyapunov exponents some parts of multi-scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle, leading to nonperturbative proofs for 1D quasiperiodic models. In this paper we present a short proof along these lines, for the Anderson mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10697","kind":"arxiv","version":1},"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":"1803.10697","created_at":"2026-05-17T23:39:58.703141+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10697v1","created_at":"2026-05-17T23:39:58.703141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10697","created_at":"2026-05-17T23:39:58.703141+00:00"},{"alias_kind":"pith_short_12","alias_value":"XQUCJCB2PBXL","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XQUCJCB2PBXLYW5F","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XQUCJCB2","created_at":"2026-05-18T12:33:01.666342+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/XQUCJCB2PBXLYW5FCXF7K6KBQD","json":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD.json","graph_json":"https://pith.science/api/pith-number/XQUCJCB2PBXLYW5FCXF7K6KBQD/graph.json","events_json":"https://pith.science/api/pith-number/XQUCJCB2PBXLYW5FCXF7K6KBQD/events.json","paper":"https://pith.science/paper/XQUCJCB2"},"agent_actions":{"view_html":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD","download_json":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD.json","view_paper":"https://pith.science/paper/XQUCJCB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10697&json=true","fetch_graph":"https://pith.science/api/pith-number/XQUCJCB2PBXLYW5FCXF7K6KBQD/graph.json","fetch_events":"https://pith.science/api/pith-number/XQUCJCB2PBXLYW5FCXF7K6KBQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD/action/storage_attestation","attest_author":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD/action/author_attestation","sign_citation":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD/action/citation_signature","submit_replication":"https://pith.science/pith/XQUCJCB2PBXLYW5FCXF7K6KBQD/action/replication_record"}},"created_at":"2026-05-17T23:39:58.703141+00:00","updated_at":"2026-05-17T23:39:58.703141+00:00"}