{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AHQ44AR5USIP2KA5TWZKJAJBHZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d59eb00d91a4af59ec0b406f1712c4dcb34d4a256715e0a6822b3073c5713643","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-16T21:28:04Z","title_canon_sha256":"a86def9df5f5faa37647c426a522ace1c63f3250c523e129f1ce32ded3f90e70"},"schema_version":"1.0","source":{"id":"0912.3246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3246","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3246v1","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3246","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"AHQ44AR5USIP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHQ44AR5USIP2KA5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHQ44AR5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9df0641e08065fbc932b7cf493b306d4558f18dc83f6593a47b974c569d5a6e1","target":"graph","created_at":"2026-05-18T02:10:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder continuity near almost reducible energies (an essential support of absolutely continuous spectrum). For non-perturbatively small potentials (and for the almost Mathieu operator with subcritical coupling), our results apply for all energies.","authors_text":"Artur Avila, Svetlana Jitomirskaya","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-16T21:28:04Z","title":"Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3246","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7891b911a91ea88fff5226bc1687af82399b9909ef2c261a61da1728b8dee266","target":"record","created_at":"2026-05-18T02:10:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d59eb00d91a4af59ec0b406f1712c4dcb34d4a256715e0a6822b3073c5713643","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-16T21:28:04Z","title_canon_sha256":"a86def9df5f5faa37647c426a522ace1c63f3250c523e129f1ce32ded3f90e70"},"schema_version":"1.0","source":{"id":"0912.3246","kind":"arxiv","version":1}},"canonical_sha256":"01e1ce023da490fd281d9db2a481213e42abb76ac0cc0ff49e91cac3c4ef6d4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e1ce023da490fd281d9db2a481213e42abb76ac0cc0ff49e91cac3c4ef6d4d","first_computed_at":"2026-05-18T02:10:16.285222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:16.285222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdAKCEFRRSiJ4TUk5+vYAOd+3jWYoTjPuspma85nxZ/dDcUh3SubMC9tQfBLjuuH8EQgsD9dQ44YZAbmwEaoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:16.285880Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7891b911a91ea88fff5226bc1687af82399b9909ef2c261a61da1728b8dee266","sha256:9df0641e08065fbc932b7cf493b306d4558f18dc83f6593a47b974c569d5a6e1"],"state_sha256":"b8d0ca820100eabf3deee31be851db114fba9d2686177d3a131f301050b3385a"}