{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GKU3MHPG5V2JMYVWOBDQI2YOZT","short_pith_number":"pith:GKU3MHPG","schema_version":"1.0","canonical_sha256":"32a9b61de6ed749662b67047046b0eccd8f113503d8b8a0b9bf0e7ae7d6010e5","source":{"kind":"arxiv","id":"1202.4735","version":5},"attestation_state":"computed","paper":{"title":"Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"O. A. Veliev","submitted_at":"2012-02-21T19:36:02Z","abstract_excerpt":"We obtain uniform, with respect to t asymptotic formulas for the eigenvalues of the operators generated in (0,1) by the Mathieu-Hill equation with a complex-valued potential and by the t-periodic boundary conditions. Then using it we investigate the non-self-adjoint Mathieu-Hill operator H generated in the allreal line by the same equation and establish the necessary and sufficient conditions for the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.4735","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-21T19:36:02Z","cross_cats_sorted":[],"title_canon_sha256":"98d25194e922ac418ccc4f12ccbef0a1c71c1b941e3cb8b8dd03671d03601cf8","abstract_canon_sha256":"c50c1df9bdb2b8df68d2345f63eb8320917c25c81c77f70a589fe77e3f75fd02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:31.814636Z","signature_b64":"zkfJBqh6LJS4RMaxBnPstyPIYKbhOq7QJtOIn8l48hJHJxEauCeNnVjOn3qPnkHrka1FsjKQDNql2w08EQXKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a9b61de6ed749662b67047046b0eccd8f113503d8b8a0b9bf0e7ae7d6010e5","last_reissued_at":"2026-05-18T00:47:31.814118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:31.814118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"O. A. Veliev","submitted_at":"2012-02-21T19:36:02Z","abstract_excerpt":"We obtain uniform, with respect to t asymptotic formulas for the eigenvalues of the operators generated in (0,1) by the Mathieu-Hill equation with a complex-valued potential and by the t-periodic boundary conditions. Then using it we investigate the non-self-adjoint Mathieu-Hill operator H generated in the allreal line by the same equation and establish the necessary and sufficient conditions for the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4735","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.4735","created_at":"2026-05-18T00:47:31.814193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4735v5","created_at":"2026-05-18T00:47:31.814193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4735","created_at":"2026-05-18T00:47:31.814193+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKU3MHPG5V2J","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKU3MHPG5V2JMYVW","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKU3MHPG","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT","json":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT.json","graph_json":"https://pith.science/api/pith-number/GKU3MHPG5V2JMYVWOBDQI2YOZT/graph.json","events_json":"https://pith.science/api/pith-number/GKU3MHPG5V2JMYVWOBDQI2YOZT/events.json","paper":"https://pith.science/paper/GKU3MHPG"},"agent_actions":{"view_html":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT","download_json":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT.json","view_paper":"https://pith.science/paper/GKU3MHPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4735&json=true","fetch_graph":"https://pith.science/api/pith-number/GKU3MHPG5V2JMYVWOBDQI2YOZT/graph.json","fetch_events":"https://pith.science/api/pith-number/GKU3MHPG5V2JMYVWOBDQI2YOZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT/action/storage_attestation","attest_author":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT/action/author_attestation","sign_citation":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT/action/citation_signature","submit_replication":"https://pith.science/pith/GKU3MHPG5V2JMYVWOBDQI2YOZT/action/replication_record"}},"created_at":"2026-05-18T00:47:31.814193+00:00","updated_at":"2026-05-18T00:47:31.814193+00:00"}