{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CTY45M2WGCOODVEV5BBZPGGZOS","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":"5ec9ce133cd02c760f3db87494c0fc6cb252b9cd0b26a5a9334bd6f21258efac","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-27T02:15:25Z","title_canon_sha256":"82e5836e8f19415fd230e00895962fa261ac97ac08bb929ad8d5c54d670a0a02"},"schema_version":"1.0","source":{"id":"1008.4632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4632","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4632v1","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4632","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"CTY45M2WGCOO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CTY45M2WGCOODVEV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CTY45M2W","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:122fe8a1b44088c0713c77871d75ef6d299eace44f36064d6f26b01d072f1f15","target":"graph","created_at":"2026-05-18T04:41:44Z","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 study Schr\\\"{o}dinger operator $H=-\\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i\\langle \\vec k,\\vec x\\rangle }$ at the high energy region. Second, the isoenergetic curves in the space of momenta $\\vec k$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corre","authors_text":"Young-Ran Lee, Yulia Karpeshina","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-27T02:15:25Z","title":"Spectral properties of a limit-periodic Schr\\\"odinger operator in dimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4632","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:e296450495392811fd13d07ee58b55059330686bc09e2b3231d9b1b55c6a4177","target":"record","created_at":"2026-05-18T04:41:44Z","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":"5ec9ce133cd02c760f3db87494c0fc6cb252b9cd0b26a5a9334bd6f21258efac","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-27T02:15:25Z","title_canon_sha256":"82e5836e8f19415fd230e00895962fa261ac97ac08bb929ad8d5c54d670a0a02"},"schema_version":"1.0","source":{"id":"1008.4632","kind":"arxiv","version":1}},"canonical_sha256":"14f1ceb356309ce1d495e8439798d974938a5572deb239abf17443f47ac38c98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f1ceb356309ce1d495e8439798d974938a5572deb239abf17443f47ac38c98","first_computed_at":"2026-05-18T04:41:44.578311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:44.578311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zZ5la0w36XB5tOi6zPPc4PZvDgbOHt6MHDnz0DdWwxmOPy9VfjeA5HWfvfB0NI0AIYO+Euf97yEn1ie76B7+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:44.578701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e296450495392811fd13d07ee58b55059330686bc09e2b3231d9b1b55c6a4177","sha256:122fe8a1b44088c0713c77871d75ef6d299eace44f36064d6f26b01d072f1f15"],"state_sha256":"80db480f1a39dce53805e6c0c7ae0cbbb26f6f74027fe354114d5e34947a5d8f"}