{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:W3WFMBFBAPJ73IV7U67GXQVB3L","short_pith_number":"pith:W3WFMBFB","schema_version":"1.0","canonical_sha256":"b6ec5604a103d3fda2bfa7be6bc2a1daef761a67c3b1085a380ee4f73c877b15","source":{"kind":"arxiv","id":"1306.1473","version":1},"attestation_state":"computed","paper":{"title":"On the Non-Self-adjoint Sturm-Liouville Operators in the Space of Vector-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fulya Seref, O. A. Veliev","submitted_at":"2013-06-06T16:52:56Z","abstract_excerpt":"In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operator generated in space of vector-functions by the Sturm-Liouville equation with m by m matrix potential and the boundary conditions whose scalar case (m=1) are strongly regular. Using these asymptotic formulas, we find a condition on the potential for which the root functions of this operator form a Riesz basis."},"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":"1306.1473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-06-06T16:52:56Z","cross_cats_sorted":[],"title_canon_sha256":"85ca7b9eed2b4f8dc513a5458387ba4e9e534766bc5e63389c85308c96e8814c","abstract_canon_sha256":"c2a290adfae9849d422cdae835790863a9f8d7c622ac7b3015cdeda253069a08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:34.098130Z","signature_b64":"k/E9d6LSN2Y8F7QgE25/596q1lAc2RtQ0Nlbl+RDuD7r6N1Z78vhQc8ZEk99HsE6Hd3OFVjIfQ6lKp1UHHlSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6ec5604a103d3fda2bfa7be6bc2a1daef761a67c3b1085a380ee4f73c877b15","last_reissued_at":"2026-05-18T03:21:34.097259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:34.097259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Non-Self-adjoint Sturm-Liouville Operators in the Space of Vector-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fulya Seref, O. A. Veliev","submitted_at":"2013-06-06T16:52:56Z","abstract_excerpt":"In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operator generated in space of vector-functions by the Sturm-Liouville equation with m by m matrix potential and the boundary conditions whose scalar case (m=1) are strongly regular. Using these asymptotic formulas, we find a condition on the potential for which the root functions of this operator form a Riesz basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1473","kind":"arxiv","version":1},"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":"1306.1473","created_at":"2026-05-18T03:21:34.097429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1473v1","created_at":"2026-05-18T03:21:34.097429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1473","created_at":"2026-05-18T03:21:34.097429+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3WFMBFBAPJ7","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3WFMBFBAPJ73IV7","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3WFMBFB","created_at":"2026-05-18T12:28:04.890932+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/W3WFMBFBAPJ73IV7U67GXQVB3L","json":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L.json","graph_json":"https://pith.science/api/pith-number/W3WFMBFBAPJ73IV7U67GXQVB3L/graph.json","events_json":"https://pith.science/api/pith-number/W3WFMBFBAPJ73IV7U67GXQVB3L/events.json","paper":"https://pith.science/paper/W3WFMBFB"},"agent_actions":{"view_html":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L","download_json":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L.json","view_paper":"https://pith.science/paper/W3WFMBFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1473&json=true","fetch_graph":"https://pith.science/api/pith-number/W3WFMBFBAPJ73IV7U67GXQVB3L/graph.json","fetch_events":"https://pith.science/api/pith-number/W3WFMBFBAPJ73IV7U67GXQVB3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L/action/storage_attestation","attest_author":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L/action/author_attestation","sign_citation":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L/action/citation_signature","submit_replication":"https://pith.science/pith/W3WFMBFBAPJ73IV7U67GXQVB3L/action/replication_record"}},"created_at":"2026-05-18T03:21:34.097429+00:00","updated_at":"2026-05-18T03:21:34.097429+00:00"}