{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3SJ3TLNWH76OJ4GWPJAM6FC535","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":"9e784730a797962aa5505cfabc18eb985983b7e811dc08a07bebd9981c744550","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-04-22T19:24:26Z","title_canon_sha256":"d61bcdd0eb849000836d430aedf244f44aa3cbee3bfbd89e083f564819ac680f"},"schema_version":"1.0","source":{"id":"1004.3991","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3991","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3991v3","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3991","created_at":"2026-05-18T04:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"3SJ3TLNWH76O","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3SJ3TLNWH76OJ4GW","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3SJ3TLNW","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:14ed6f691b2dc198ee480974b7713778b7a76c817e9b44e1069dd6db36d3862a","target":"graph","created_at":"2026-05-18T04:05:16Z","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 investigate the problem of similarity to a self-adjoint operator for $J$-positive Sturm-Liouville operators $L=\\frac{1}{\\omega}(-\\frac{d^2}{dx^2}+q)$ with $2\\pi$-periodic coefficients $q$ and $\\omega$. It is shown that if 0 is a critical point of the operator $L$, then it is a singular critical point. This gives us a new class of $J$-positive differential operators with the singular critical point 0. Also, we extend the Beals and Parfenov regularity conditions for the critical point $\\infty$ to the case of operators with periodic coefficients.","authors_text":"Aleksey Kostenko","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-04-22T19:24:26Z","title":"The similarity problem for indefinite Sturm-Liouville operators with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3991","kind":"arxiv","version":3},"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":"sha256:0bc54b7caf01bdc19bf20337b7b362606ddd60f63720741a33ae2d1c806054c2","target":"record","created_at":"2026-05-18T04:05:16Z","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":"9e784730a797962aa5505cfabc18eb985983b7e811dc08a07bebd9981c744550","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-04-22T19:24:26Z","title_canon_sha256":"d61bcdd0eb849000836d430aedf244f44aa3cbee3bfbd89e083f564819ac680f"},"schema_version":"1.0","source":{"id":"1004.3991","kind":"arxiv","version":3}},"canonical_sha256":"dc93b9adb63ffce4f0d67a40cf145ddf7cb281b702b4b9bffcaa4f24c2203be7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc93b9adb63ffce4f0d67a40cf145ddf7cb281b702b4b9bffcaa4f24c2203be7","first_computed_at":"2026-05-18T04:05:16.049493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:16.049493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tP/6BQgVp+4SJhAteypS0nBlteUk7D7IjjvlP/KJoaiXNLI1B9Hyos3G+1ZN57Niv8rfIjJQTzERhTNt7SXUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:16.050035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3991","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bc54b7caf01bdc19bf20337b7b362606ddd60f63720741a33ae2d1c806054c2","sha256:14ed6f691b2dc198ee480974b7713778b7a76c817e9b44e1069dd6db36d3862a"],"state_sha256":"69851d949f79e2010af78527a956de27690836c212dd3b1c2f2b8d594c970deb"}