{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CROP3TOZBPOMF4ALLTRL5WMEXK","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":"03a4f5b7ae1feb5b1c8ff3e8aa40abccd82c9e1dc13c3c469740304b788ef249","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-21T07:38:24Z","title_canon_sha256":"d9dc559848f18fe63958232e9b81a4fb92e6453bef3ac6b47ba8ee855bed518f"},"schema_version":"1.0","source":{"id":"1110.4716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4716","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4716v1","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4716","created_at":"2026-05-18T04:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"CROP3TOZBPOM","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CROP3TOZBPOMF4AL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CROP3TOZ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:ad14af191b5b85e112a41ae44418683e5f64ff0204c14adb909e6eb4a3ab9458","target":"graph","created_at":"2026-05-18T04:10:35Z","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 consider the Schr\\\"odinger operator with a periodic potential $p$ on the real line. We assume that $p$ belongs to the Sobolev space $\\mH_m$ on the circle for some $m\\ge -1$, and we determine the asymptotics of the quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high energy.","authors_text":"Evgeny L. Korotyaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-21T07:38:24Z","title":"Sharp asymptotics of the quasimomentum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4716","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":"sha256:9e3c1bea6f2f5f4297b7c7d1f720b998ec020cfc8e444745a4970197beaa6da1","target":"record","created_at":"2026-05-18T04:10:35Z","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":"03a4f5b7ae1feb5b1c8ff3e8aa40abccd82c9e1dc13c3c469740304b788ef249","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-21T07:38:24Z","title_canon_sha256":"d9dc559848f18fe63958232e9b81a4fb92e6453bef3ac6b47ba8ee855bed518f"},"schema_version":"1.0","source":{"id":"1110.4716","kind":"arxiv","version":1}},"canonical_sha256":"145cfdcdd90bdcc2f00b5ce2bed984bab9a09eda563214151e6dcde6f8473b48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"145cfdcdd90bdcc2f00b5ce2bed984bab9a09eda563214151e6dcde6f8473b48","first_computed_at":"2026-05-18T04:10:35.221367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:35.221367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9aaniWbTxoKBQV0V6DxyW5s1XRjtawPytAX3DYgYFge0ZW2wBkRo2IdRW/qHC3wxRMG+ytP0gr1kPUQZyUqRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:35.222086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e3c1bea6f2f5f4297b7c7d1f720b998ec020cfc8e444745a4970197beaa6da1","sha256:ad14af191b5b85e112a41ae44418683e5f64ff0204c14adb909e6eb4a3ab9458"],"state_sha256":"2d1745d8a7e0393a99227d8c7e675e73e2f65edc99a67a99cb101247c3d00604"}