{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TGH6WD2MGSPBWTBZTZOMFUYNI6","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":"df4d033344a19483a09c0678b556fd6f48319e9a5fda3fd37cd632899696fcbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-08T17:28:10Z","title_canon_sha256":"c94b7568f3620f4b5c58653741c2cce491e3d292c89c6c310ffa3875fca92741"},"schema_version":"1.0","source":{"id":"1806.03284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03284","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03284v1","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03284","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"TGH6WD2MGSPB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TGH6WD2MGSPBWTBZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TGH6WD2M","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:fcb4c7578c0d2a8156c532c2563e220e162b7aeea66a3da6de2cb532ee6c0297","target":"graph","created_at":"2026-05-18T00:13:48Z","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 prove the H\\\"older continuity of the Lyapunov exponent for quasi-periodic Schr\\\"odinger cocycles with a $C^2$ cos-type potential and any fixed Liouvillean frequency, provided the coupling constant is sufficiently large. Moreover, the H\\\"older exponent is independent of the frequency and the coupling constant.","authors_text":"Jiangong You, Jinhao Liang, Yiqian Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-08T17:28:10Z","title":"H\\\"older continuity of Lyapunov exponent for a family of smooth Schr\\\"odinger cocycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03284","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:c0dc8b6c8947bf901313b5a09df185bbaffaea99eb5aedd6808e8afd804e83c0","target":"record","created_at":"2026-05-18T00:13:48Z","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":"df4d033344a19483a09c0678b556fd6f48319e9a5fda3fd37cd632899696fcbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-08T17:28:10Z","title_canon_sha256":"c94b7568f3620f4b5c58653741c2cce491e3d292c89c6c310ffa3875fca92741"},"schema_version":"1.0","source":{"id":"1806.03284","kind":"arxiv","version":1}},"canonical_sha256":"998feb0f4c349e1b4c399e5cc2d30d478b7e6b6c432a73f89bc5e2f39b8fad29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998feb0f4c349e1b4c399e5cc2d30d478b7e6b6c432a73f89bc5e2f39b8fad29","first_computed_at":"2026-05-18T00:13:48.884935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:48.884935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ja+ksRo+NWG26ZyDfcUNAoaZpMeE4a/vCxY4FmW8QTbLRV6H87FnpjyC/vjVOsaZc+pvEjs/aw9OsmBAIJQjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:48.885452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0dc8b6c8947bf901313b5a09df185bbaffaea99eb5aedd6808e8afd804e83c0","sha256:fcb4c7578c0d2a8156c532c2563e220e162b7aeea66a3da6de2cb532ee6c0297"],"state_sha256":"fdf442b87fe74d3da0cc4205586aa2fa9c6dab8c3c54fae1ab76e5f53fa84e75"}