{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EMCK5QAFXI6IGRCL5LZ4UQLEZM","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":"5bbb0f1e1664b7d97b7478b9d694aa60f580ab340ca6257d8d89484466eee771","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-27T16:16:15Z","title_canon_sha256":"c5e47be51a2c51300bcc7746680fc16ab3bf20c3a74578b1374a5bfde49a7ad8"},"schema_version":"1.0","source":{"id":"1311.7026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7026","created_at":"2026-05-18T02:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7026v2","created_at":"2026-05-18T02:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7026","created_at":"2026-05-18T02:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"EMCK5QAFXI6I","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EMCK5QAFXI6IGRCL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EMCK5QAF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:3d325e70a801a717013e52d38b0a9aa7f0b0406f7ad93fea4e16232ffa0e5802","target":"graph","created_at":"2026-05-18T02:55:10Z","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":"Curves in the complex plane that satisfy the S-property were first introduced by Stahl and they were further studied by Gonchar and Rakhmanov in the 1980s. Rakhmanov recently showed the existence of curves with the S-property in a harmonic external field by means of a max-min variational problem in logarithmic potential theory. This is done in a fairly general setting, which however does not include the important special case of an external field given by the real part of a polynomial of degree greater than or equal to 2. In this paper we give a detailed proof of the existence of a curve with ","authors_text":"Arno Kuijlaars, Guilherme Silva","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-27T16:16:15Z","title":"S-curves in Polynomial External Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7026","kind":"arxiv","version":2},"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":"sha256:7845cd900abd3a1f3d3b210c4f30bfd7ca08fd3d301d5040de08d030c5afaebb","target":"record","created_at":"2026-05-18T02:55:10Z","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":"5bbb0f1e1664b7d97b7478b9d694aa60f580ab340ca6257d8d89484466eee771","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-27T16:16:15Z","title_canon_sha256":"c5e47be51a2c51300bcc7746680fc16ab3bf20c3a74578b1374a5bfde49a7ad8"},"schema_version":"1.0","source":{"id":"1311.7026","kind":"arxiv","version":2}},"canonical_sha256":"2304aec005ba3c83444beaf3ca4164cb3a70188d132e2fb0e2b6221eaddbe5f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2304aec005ba3c83444beaf3ca4164cb3a70188d132e2fb0e2b6221eaddbe5f9","first_computed_at":"2026-05-18T02:55:10.771763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:10.771763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4ZQgW3E77UDTqyNH2T78lQZoM/Wl3mtB0RjfVkPJEOIWPhxqCdR9MdUlb2HFDn7BspC+kMwc5PPGPH1QnK5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:10.772244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7845cd900abd3a1f3d3b210c4f30bfd7ca08fd3d301d5040de08d030c5afaebb","sha256:3d325e70a801a717013e52d38b0a9aa7f0b0406f7ad93fea4e16232ffa0e5802"],"state_sha256":"21ea6431fec97b6bbf79da80680a47317276021218657a0c699d5eaf65cf8263"}