{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CSLPCC6HZQIGA3DHFVRQIA7JSU","short_pith_number":"pith:CSLPCC6H","schema_version":"1.0","canonical_sha256":"1496f10bc7cc10606c672d630403e9952f758573350d29c7f0d0348fbeb6ec1d","source":{"kind":"arxiv","id":"1212.1134","version":1},"attestation_state":"computed","paper":{"title":"On the relation between Darboux transformations and polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.CA","authors_text":"Maxim Derevyagin","submitted_at":"2012-12-05T19:30:44Z","abstract_excerpt":"Let d\\mu(t) be a probability measure on [0,+\\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d\\mu(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present paper, we consider a matrix interpretation of the unwrapping transformation from S(\\lambda) to \\lambda S(\\lambda^2), which is intimately related to the simplest case of polynomial mappings. More precisely, it is shown that this transformation is essentially a Darboux transformation of the underlying Jacobi matrix. Moreover, in this scheme, the Chihara construc"},"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":"1212.1134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-05T19:30:44Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"71ae94e66ade71ab1f703a4f06e860f4455fae0713defe4d3eaf6c7ff722d61c","abstract_canon_sha256":"68c1c4ec8801966d01d137325495bcc431e404cb7ae7542af021808c04f4f5cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:05.746565Z","signature_b64":"PnEOAedDJ/mQPXwDFmWEHRc+QkEYOg2BHjwePPyPSKR2XrVb/U75RnrAhyCeJztJ1+C0JL5sxSLOFD57SOsoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1496f10bc7cc10606c672d630403e9952f758573350d29c7f0d0348fbeb6ec1d","last_reissued_at":"2026-05-18T03:39:05.745859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:05.745859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the relation between Darboux transformations and polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.CA","authors_text":"Maxim Derevyagin","submitted_at":"2012-12-05T19:30:44Z","abstract_excerpt":"Let d\\mu(t) be a probability measure on [0,+\\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d\\mu(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present paper, we consider a matrix interpretation of the unwrapping transformation from S(\\lambda) to \\lambda S(\\lambda^2), which is intimately related to the simplest case of polynomial mappings. More precisely, it is shown that this transformation is essentially a Darboux transformation of the underlying Jacobi matrix. Moreover, in this scheme, the Chihara construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1134","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":"1212.1134","created_at":"2026-05-18T03:39:05.745968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1134v1","created_at":"2026-05-18T03:39:05.745968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1134","created_at":"2026-05-18T03:39:05.745968+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSLPCC6HZQIG","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSLPCC6HZQIGA3DH","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSLPCC6H","created_at":"2026-05-18T12:27:01.376967+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/CSLPCC6HZQIGA3DHFVRQIA7JSU","json":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU.json","graph_json":"https://pith.science/api/pith-number/CSLPCC6HZQIGA3DHFVRQIA7JSU/graph.json","events_json":"https://pith.science/api/pith-number/CSLPCC6HZQIGA3DHFVRQIA7JSU/events.json","paper":"https://pith.science/paper/CSLPCC6H"},"agent_actions":{"view_html":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU","download_json":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU.json","view_paper":"https://pith.science/paper/CSLPCC6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1134&json=true","fetch_graph":"https://pith.science/api/pith-number/CSLPCC6HZQIGA3DHFVRQIA7JSU/graph.json","fetch_events":"https://pith.science/api/pith-number/CSLPCC6HZQIGA3DHFVRQIA7JSU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU/action/storage_attestation","attest_author":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU/action/author_attestation","sign_citation":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU/action/citation_signature","submit_replication":"https://pith.science/pith/CSLPCC6HZQIGA3DHFVRQIA7JSU/action/replication_record"}},"created_at":"2026-05-18T03:39:05.745968+00:00","updated_at":"2026-05-18T03:39:05.745968+00:00"}