{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GN2DPE4GRE77PGBH4AN7T6VRZJ","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":"de4e8f30cf186fb79750696da511f5446fc81090bd2d243f471de48d8bc350b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-22T15:19:55Z","title_canon_sha256":"15cc319f2350b4935a5cc5af3ad606551c3f2389f71c9334c699f2a25d46f5e0"},"schema_version":"1.0","source":{"id":"1505.06120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06120","created_at":"2026-05-18T02:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06120v1","created_at":"2026-05-18T02:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06120","created_at":"2026-05-18T02:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"GN2DPE4GRE77","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GN2DPE4GRE77PGBH","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GN2DPE4G","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:1e70b9f7591a3fa3667fda3cfb79fc0fc159ab14f18e40d47db39ecf2024523b","target":"graph","created_at":"2026-05-18T02:03:49Z","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":"For an interval $E=[a,b]$ on the real line, let $\\mu$ be either the equilibrium measure, or the normalized Lebesgue measure of $E$, and let $V^{\\mu}$ denote the associated logarithmic potential. In the present paper, we construct a function $f$ which is analytic on $E$ and possesses four branch points of second order outside of $E$ such that the family of the admissible compacta of $f$ has no minimizing elements with regard to the extremal theoretic-potential problem, in the external field equals $V^{-\\mu}$.","authors_text":"Sergey P. Suetin, Viktor I. Buslaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-22T15:19:55Z","title":"On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06120","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:b3831c80d2bd4fbd1cde8c20377e83cd549bf7da31916f10a62359bdb1ce1449","target":"record","created_at":"2026-05-18T02:03:49Z","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":"de4e8f30cf186fb79750696da511f5446fc81090bd2d243f471de48d8bc350b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-22T15:19:55Z","title_canon_sha256":"15cc319f2350b4935a5cc5af3ad606551c3f2389f71c9334c699f2a25d46f5e0"},"schema_version":"1.0","source":{"id":"1505.06120","kind":"arxiv","version":1}},"canonical_sha256":"3374379386893ff79827e01bf9fab1ca4c623351fe038a717549bbffd2f43423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3374379386893ff79827e01bf9fab1ca4c623351fe038a717549bbffd2f43423","first_computed_at":"2026-05-18T02:03:49.062819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:49.062819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RpMuG4EbozdnM8uSI7bGJ3B8Yv1FXdlYsPuFCjfX7urwfiXZM97w3n6emrgB/U96uIsAQZBObECLZdKzmZ6PAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:49.063442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3831c80d2bd4fbd1cde8c20377e83cd549bf7da31916f10a62359bdb1ce1449","sha256:1e70b9f7591a3fa3667fda3cfb79fc0fc159ab14f18e40d47db39ecf2024523b"],"state_sha256":"0b35ed3524fc6d0dec03c371f5530a32d2494b9b777b3802919a16409098e56c"}