{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VCN36TVKWFCV4CNI2S3KUVN7Y5","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":"7827af5bcfea1e56fb371a20d82a7ee36393fede8ad330e804bc91f2c6cf71d8","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-01T03:57:20Z","title_canon_sha256":"5d32837cdc8725ac1ecd0faded965d8e5ce5b6efb43be20b6b8d2cc07b33e5a0"},"schema_version":"1.0","source":{"id":"1410.0101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0101","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0101v1","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0101","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"VCN36TVKWFCV","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VCN36TVKWFCV4CNI","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VCN36TVK","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:654f67ac079f74ce070563aa9ba15b213442cc4e8d5930f6e8f73e923419a2ab","target":"graph","created_at":"2026-05-18T02:41:18Z","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 show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schr\\\"odinger operators is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general $\\mathrm{SL}(2,\\mathbb R)$ cocycles, and obtain that uniform hyperbolic systems form a open and dense set in some one-parameter family.","authors_text":"Yiqian Wang, Zhenghe Zhang","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-01T03:57:20Z","title":"Cantor spectrum for a class of $C^2$ quasiperiodic Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0101","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":"sha256:6f18a75966e6b99164ca4af1b4cf657f140bc954cb380ca9547d023b65200347","target":"record","created_at":"2026-05-18T02:41:18Z","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":"7827af5bcfea1e56fb371a20d82a7ee36393fede8ad330e804bc91f2c6cf71d8","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-01T03:57:20Z","title_canon_sha256":"5d32837cdc8725ac1ecd0faded965d8e5ce5b6efb43be20b6b8d2cc07b33e5a0"},"schema_version":"1.0","source":{"id":"1410.0101","kind":"arxiv","version":1}},"canonical_sha256":"a89bbf4eaab1455e09a8d4b6aa55bfc749a9557708c7908154e0db001f2a30da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a89bbf4eaab1455e09a8d4b6aa55bfc749a9557708c7908154e0db001f2a30da","first_computed_at":"2026-05-18T02:41:18.020991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.020991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ly5v/Myd7AVU/ctJgSgev4XmVOAU4xhMGyWZs4Bcn6xACjYT7J/WyY17Zs9RbbS4I6bX7iWy0h2vFCIFX1Q2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.021511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f18a75966e6b99164ca4af1b4cf657f140bc954cb380ca9547d023b65200347","sha256:654f67ac079f74ce070563aa9ba15b213442cc4e8d5930f6e8f73e923419a2ab"],"state_sha256":"438ccec48afaa6ea76f8e16486aa8f8388b8e3c19ac3a51dea755f9d92a99d18"}