{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:G2HX6ASXB7EP5UELUD7HS4ZJ7R","short_pith_number":"pith:G2HX6ASX","schema_version":"1.0","canonical_sha256":"368f7f02570fc8fed08ba0fe797329fc55c08ec7353eebd18c0e0d6cb1aab8a6","source":{"kind":"arxiv","id":"1005.3721","version":2},"attestation_state":"computed","paper":{"title":"The Jacobi matrices approach to Nevanlinna-Pick problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.SP"],"primary_cat":"math.CA","authors_text":"Maxim Derevyagin","submitted_at":"2010-05-20T14:52:39Z","abstract_excerpt":"A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\\bR_0$-functions gives rise to a linear pencil $H-\\lambda J$, where $H$ and $J$ are Hermitian tridiagonal matrices. First, we show that $J$ is a positive operator. Then it is proved that the corresponding Nevanlinna-Pick problem has a unique solution iff the densely defined symmetric operator $J^{-1/2}HJ^{-1/2}$ is self-adjoint and some criteria for this operator to be self-adjoint are presented. Finally, by means of the operator technique, we obtain that multipoint diagonal Pad\\'e appro"},"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":"1005.3721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-05-20T14:52:39Z","cross_cats_sorted":["math.CV","math.SP"],"title_canon_sha256":"305193728cb4317546c93aa8124883691ecc108b74b6f7b5afdec68da234af06","abstract_canon_sha256":"2e12835cc0e3ce5a26475bc0fd39fc66cde8aa80ebb5c242c8b5cf920c9d4eb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:55.780088Z","signature_b64":"AqTImQ//IbR8Rh6WcEVZNkhagnDwPFkOyXibsTAH3P7nhOR1EGi8U/xKeLZa6JJ4uIheSzq4XZFmo+ZBil3RBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"368f7f02570fc8fed08ba0fe797329fc55c08ec7353eebd18c0e0d6cb1aab8a6","last_reissued_at":"2026-05-18T04:41:55.779676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:55.779676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Jacobi matrices approach to Nevanlinna-Pick problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.SP"],"primary_cat":"math.CA","authors_text":"Maxim Derevyagin","submitted_at":"2010-05-20T14:52:39Z","abstract_excerpt":"A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\\bR_0$-functions gives rise to a linear pencil $H-\\lambda J$, where $H$ and $J$ are Hermitian tridiagonal matrices. First, we show that $J$ is a positive operator. Then it is proved that the corresponding Nevanlinna-Pick problem has a unique solution iff the densely defined symmetric operator $J^{-1/2}HJ^{-1/2}$ is self-adjoint and some criteria for this operator to be self-adjoint are presented. Finally, by means of the operator technique, we obtain that multipoint diagonal Pad\\'e appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3721","kind":"arxiv","version":2},"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":"1005.3721","created_at":"2026-05-18T04:41:55.779735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.3721v2","created_at":"2026-05-18T04:41:55.779735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3721","created_at":"2026-05-18T04:41:55.779735+00:00"},{"alias_kind":"pith_short_12","alias_value":"G2HX6ASXB7EP","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"G2HX6ASXB7EP5UEL","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"G2HX6ASX","created_at":"2026-05-18T12:26:07.630475+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/G2HX6ASXB7EP5UELUD7HS4ZJ7R","json":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R.json","graph_json":"https://pith.science/api/pith-number/G2HX6ASXB7EP5UELUD7HS4ZJ7R/graph.json","events_json":"https://pith.science/api/pith-number/G2HX6ASXB7EP5UELUD7HS4ZJ7R/events.json","paper":"https://pith.science/paper/G2HX6ASX"},"agent_actions":{"view_html":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R","download_json":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R.json","view_paper":"https://pith.science/paper/G2HX6ASX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.3721&json=true","fetch_graph":"https://pith.science/api/pith-number/G2HX6ASXB7EP5UELUD7HS4ZJ7R/graph.json","fetch_events":"https://pith.science/api/pith-number/G2HX6ASXB7EP5UELUD7HS4ZJ7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R/action/storage_attestation","attest_author":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R/action/author_attestation","sign_citation":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R/action/citation_signature","submit_replication":"https://pith.science/pith/G2HX6ASXB7EP5UELUD7HS4ZJ7R/action/replication_record"}},"created_at":"2026-05-18T04:41:55.779735+00:00","updated_at":"2026-05-18T04:41:55.779735+00:00"}