{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:2CD7MQFJTCMPE53TARK3K3BCYV","short_pith_number":"pith:2CD7MQFJ","schema_version":"1.0","canonical_sha256":"d087f640a99898f277730455b56c22c5458ebd7adb2c5a43b26252beded20667","source":{"kind":"arxiv","id":"math-ph/0110040","version":1},"attestation_state":"computed","paper":{"title":"Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential","license":"","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"J. Bourgain, S. Jitomirskaya","submitted_at":"2001-10-31T18:32:54Z","abstract_excerpt":"We study regularity properties of the Lyapunov exponent L of quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove that L is jointly continuous, in frequency and energy, at every irrational frequency."},"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":"math-ph/0110040","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-10-31T18:32:54Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"d5cd029b682f8ea26914677edff1db7e299c6790fc61a55e9f1189df074a3664","abstract_canon_sha256":"1c8cfce9bb6ee3b5215ad6b2417b68932549b46bb24eb53ea6331a95bf784dbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:33:40.571544Z","signature_b64":"1FyFLyqbNVIKrKRJiuX+pMBdDUJ3Rwz1WlJYTvtQ6O3Zr9J135ZHiqRh2X9UsjG+xpYl0zWITKusMaQ7uVhKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d087f640a99898f277730455b56c22c5458ebd7adb2c5a43b26252beded20667","last_reissued_at":"2026-07-04T14:33:40.571168Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:33:40.571168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential","license":"","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"J. Bourgain, S. Jitomirskaya","submitted_at":"2001-10-31T18:32:54Z","abstract_excerpt":"We study regularity properties of the Lyapunov exponent L of quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove that L is jointly continuous, in frequency and energy, at every irrational frequency."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0110040","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0110040/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":"math-ph/0110040","created_at":"2026-07-04T14:33:40.571220+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0110040v1","created_at":"2026-07-04T14:33:40.571220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0110040","created_at":"2026-07-04T14:33:40.571220+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CD7MQFJTCMP","created_at":"2026-07-04T14:33:40.571220+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CD7MQFJTCMPE53T","created_at":"2026-07-04T14:33:40.571220+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CD7MQFJ","created_at":"2026-07-04T14:33:40.571220+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.04795","citing_title":"Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results","ref_index":84,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV","json":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV.json","graph_json":"https://pith.science/api/pith-number/2CD7MQFJTCMPE53TARK3K3BCYV/graph.json","events_json":"https://pith.science/api/pith-number/2CD7MQFJTCMPE53TARK3K3BCYV/events.json","paper":"https://pith.science/paper/2CD7MQFJ"},"agent_actions":{"view_html":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV","download_json":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV.json","view_paper":"https://pith.science/paper/2CD7MQFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0110040&json=true","fetch_graph":"https://pith.science/api/pith-number/2CD7MQFJTCMPE53TARK3K3BCYV/graph.json","fetch_events":"https://pith.science/api/pith-number/2CD7MQFJTCMPE53TARK3K3BCYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV/action/storage_attestation","attest_author":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV/action/author_attestation","sign_citation":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV/action/citation_signature","submit_replication":"https://pith.science/pith/2CD7MQFJTCMPE53TARK3K3BCYV/action/replication_record"}},"created_at":"2026-07-04T14:33:40.571220+00:00","updated_at":"2026-07-04T14:33:40.571220+00:00"}