{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VGCBAWI3JKUKBZGRXGOAQYOJVB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e9866100568b54adf9d003c69c401a8da6ead8c4f42f157ffaf8e26f158c295f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T13:24:11Z","title_canon_sha256":"5191c20796a22c247921d59d13340af090848ed5cf80e18533aa938ded4fb7a9"},"schema_version":"1.0","source":{"id":"1803.06211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06211","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06211v1","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06211","created_at":"2026-05-18T00:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"VGCBAWI3JKUK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VGCBAWI3JKUKBZGR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VGCBAWI3","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:7e0b753eed0c3843ee0815dd3c2fc19b288ff861204f853b866d557e62712c37","target":"graph","created_at":"2026-05-18T00:20:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present a numerical model for determining a finite Blaschke product of degree $n+1$ having $n$ preassigned distinct critical points $z_1,\\dots,z_n$ in the complex (open) unit disk $\\mathbb{D}$. The Blaschke product is uniquely determined up to postcomposition with conformal automorphisms of $\\mathbb{D}$. The proposed method is based on the construction of a sparse nonlinear system where the data dependency is isolated to two vectors and on a certain transformation of the critical points. The efficiency and accuracy of the method is illustrated in several examples.","authors_text":"Christer Glader, Ray P\\\"orn","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T13:24:11Z","title":"A Numerical Model for the Construction of Finite Blaschke Products with Preassigned Distinct Critical Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06211","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:95e61d01b7a61e066beb65cfd50f850e33af246d7648497a247d6b2184caa95a","target":"record","created_at":"2026-05-18T00:20:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e9866100568b54adf9d003c69c401a8da6ead8c4f42f157ffaf8e26f158c295f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-16T13:24:11Z","title_canon_sha256":"5191c20796a22c247921d59d13340af090848ed5cf80e18533aa938ded4fb7a9"},"schema_version":"1.0","source":{"id":"1803.06211","kind":"arxiv","version":1}},"canonical_sha256":"a98410591b4aa8a0e4d1b99c0861c9a8435997168b3a2078cc2cb57d93ec8cbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a98410591b4aa8a0e4d1b99c0861c9a8435997168b3a2078cc2cb57d93ec8cbd","first_computed_at":"2026-05-18T00:20:50.285187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:50.285187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSPIV7UduA0CH5qXeGpPzi/P3KWHgt4+MXBqgLLuabaBsa+8FL2aIfcGdbETqcQQWSPh2nlbQvjH6zHdBKzDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:50.285704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95e61d01b7a61e066beb65cfd50f850e33af246d7648497a247d6b2184caa95a","sha256:7e0b753eed0c3843ee0815dd3c2fc19b288ff861204f853b866d557e62712c37"],"state_sha256":"0ed7784b78ca3b00eefd1811874b59fe5787340e195b9326d4ac2de9daf9fff2"}