{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3L5VCJZSKFO3TMX2RD4IC4SNS3","short_pith_number":"pith:3L5VCJZS","schema_version":"1.0","canonical_sha256":"dafb512732515db9b2fa88f881724d96f3edf56daa3c774d7be26d0e639f12a9","source":{"kind":"arxiv","id":"1312.4376","version":1},"attestation_state":"computed","paper":{"title":"Zero distribution of complex orthogonal polynomials with respect to exponential weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arno Kuijlaars, Daan Huybrechs, Nele Lejon","submitted_at":"2013-12-16T14:28:06Z","abstract_excerpt":"We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of the orthogonal polynomials accumulate on a single analytic arc (one cut case), and in which cases they do not. In a family of cubic polynomial potentials V(z) = - iz^3/3 + iKz, we determine the precise values of K for which we have the one cut case. We also prove the one cut case for a monomial quintic V(z) = - iz^5/5 on a contour that is symmetri"},"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":"1312.4376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-16T14:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"50f3704bfa96fab8af75a6d73be3e5db90f8a2eed5efc5850c2868f5a8d6e703","abstract_canon_sha256":"31c142f68ddb9aa5826fd6eafd7066c7d0068a23406976aa54ff145e491a0929"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:11.224123Z","signature_b64":"SokycMkme/2MSAyKN0eLV13M5Z13+TXwjNg0XHL3O20yHQuUS/XCwIzup2HMUOweUneT77CIlEoNUFpWGTnvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dafb512732515db9b2fa88f881724d96f3edf56daa3c774d7be26d0e639f12a9","last_reissued_at":"2026-05-18T02:29:11.223467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:11.223467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero distribution of complex orthogonal polynomials with respect to exponential weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arno Kuijlaars, Daan Huybrechs, Nele Lejon","submitted_at":"2013-12-16T14:28:06Z","abstract_excerpt":"We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of the orthogonal polynomials accumulate on a single analytic arc (one cut case), and in which cases they do not. In a family of cubic polynomial potentials V(z) = - iz^3/3 + iKz, we determine the precise values of K for which we have the one cut case. We also prove the one cut case for a monomial quintic V(z) = - iz^5/5 on a contour that is symmetri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4376","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":"1312.4376","created_at":"2026-05-18T02:29:11.223569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4376v1","created_at":"2026-05-18T02:29:11.223569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4376","created_at":"2026-05-18T02:29:11.223569+00:00"},{"alias_kind":"pith_short_12","alias_value":"3L5VCJZSKFO3","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3L5VCJZSKFO3TMX2","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3L5VCJZS","created_at":"2026-05-18T12:27:32.513160+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/3L5VCJZSKFO3TMX2RD4IC4SNS3","json":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3.json","graph_json":"https://pith.science/api/pith-number/3L5VCJZSKFO3TMX2RD4IC4SNS3/graph.json","events_json":"https://pith.science/api/pith-number/3L5VCJZSKFO3TMX2RD4IC4SNS3/events.json","paper":"https://pith.science/paper/3L5VCJZS"},"agent_actions":{"view_html":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3","download_json":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3.json","view_paper":"https://pith.science/paper/3L5VCJZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4376&json=true","fetch_graph":"https://pith.science/api/pith-number/3L5VCJZSKFO3TMX2RD4IC4SNS3/graph.json","fetch_events":"https://pith.science/api/pith-number/3L5VCJZSKFO3TMX2RD4IC4SNS3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3/action/storage_attestation","attest_author":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3/action/author_attestation","sign_citation":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3/action/citation_signature","submit_replication":"https://pith.science/pith/3L5VCJZSKFO3TMX2RD4IC4SNS3/action/replication_record"}},"created_at":"2026-05-18T02:29:11.223569+00:00","updated_at":"2026-05-18T02:29:11.223569+00:00"}