{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:4GV6DRJRNS3F63AO7P4BQNC6Z3","short_pith_number":"pith:4GV6DRJR","schema_version":"1.0","canonical_sha256":"e1abe1c5316cb65f6c0efbf818345ecee020b12da2efcd78b9fc5ef46bafab2e","source":{"kind":"arxiv","id":"math/0610087","version":3},"attestation_state":"computed","paper":{"title":"Indefinite Sturm-Liouville operators $ (\\sgn x) (- \\frac{d^2}{dx^2} +q(x))$ with finite-zone potentials","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"I. M. Karabash, M. M. Malamud","submitted_at":"2006-10-02T19:23:26Z","abstract_excerpt":"The indefinite Sturm-Liouville operator $A = (\\sgn x)(-d^2/dx^2+q(x))$ is studied. It is proved that similarity of $A$ to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components $\\Aess$ and $\\Adisc$ of $A$ corresponding to essential and discrete spectrums, respectively, are considered. A criterion of similarity of $\\Aess$ to a selfadjoint operator is given in terms of Weyl functions for the Sturm-Liouville operator $-d^2/dx^2+q(x)$ with a finite-zo"},"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":"math/0610087","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2006-10-02T19:23:26Z","cross_cats_sorted":[],"title_canon_sha256":"acf42fbdf1678523a5a9879fbfe7cff3ab976260c8c77cb2ff579e2766b46029","abstract_canon_sha256":"06932c72edbf04ee7676b1d2a08d0c88598de9df610b07937d4acac9b34d7d3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:10.308261Z","signature_b64":"2PU0lWQ8l47HgocbzJ6ifuFnxJlLPNUZs3WkD9nNS6U2zb+4CB3j/+3K0fBw+ePScKCpKeX/cFwaMmvyqSPpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1abe1c5316cb65f6c0efbf818345ecee020b12da2efcd78b9fc5ef46bafab2e","last_reissued_at":"2026-05-18T04:34:10.307743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:10.307743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Indefinite Sturm-Liouville operators $ (\\sgn x) (- \\frac{d^2}{dx^2} +q(x))$ with finite-zone potentials","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"I. M. Karabash, M. M. Malamud","submitted_at":"2006-10-02T19:23:26Z","abstract_excerpt":"The indefinite Sturm-Liouville operator $A = (\\sgn x)(-d^2/dx^2+q(x))$ is studied. It is proved that similarity of $A$ to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components $\\Aess$ and $\\Adisc$ of $A$ corresponding to essential and discrete spectrums, respectively, are considered. A criterion of similarity of $\\Aess$ to a selfadjoint operator is given in terms of Weyl functions for the Sturm-Liouville operator $-d^2/dx^2+q(x)$ with a finite-zo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610087","kind":"arxiv","version":3},"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":"math/0610087","created_at":"2026-05-18T04:34:10.307806+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0610087v3","created_at":"2026-05-18T04:34:10.307806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610087","created_at":"2026-05-18T04:34:10.307806+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GV6DRJRNS3F","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GV6DRJRNS3F63AO","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GV6DRJR","created_at":"2026-05-18T12:25:53.939244+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/4GV6DRJRNS3F63AO7P4BQNC6Z3","json":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3.json","graph_json":"https://pith.science/api/pith-number/4GV6DRJRNS3F63AO7P4BQNC6Z3/graph.json","events_json":"https://pith.science/api/pith-number/4GV6DRJRNS3F63AO7P4BQNC6Z3/events.json","paper":"https://pith.science/paper/4GV6DRJR"},"agent_actions":{"view_html":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3","download_json":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3.json","view_paper":"https://pith.science/paper/4GV6DRJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0610087&json=true","fetch_graph":"https://pith.science/api/pith-number/4GV6DRJRNS3F63AO7P4BQNC6Z3/graph.json","fetch_events":"https://pith.science/api/pith-number/4GV6DRJRNS3F63AO7P4BQNC6Z3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3/action/storage_attestation","attest_author":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3/action/author_attestation","sign_citation":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3/action/citation_signature","submit_replication":"https://pith.science/pith/4GV6DRJRNS3F63AO7P4BQNC6Z3/action/replication_record"}},"created_at":"2026-05-18T04:34:10.307806+00:00","updated_at":"2026-05-18T04:34:10.307806+00:00"}