{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BGG5SDGKTZJWPKGNNPWQO5NOQ3","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":"2e05d1f16079ad017b23a2dcdaafb59815dc5d463a5228f75db422617f901dbe","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-01T18:10:21Z","title_canon_sha256":"590b1c4f7d668abe934be7c8b52a84b00c8c5e8dcf01b8977477463034265062"},"schema_version":"1.0","source":{"id":"2403.00719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.00719","created_at":"2026-07-05T10:37:24Z"},{"alias_kind":"arxiv_version","alias_value":"2403.00719v2","created_at":"2026-07-05T10:37:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.00719","created_at":"2026-07-05T10:37:24Z"},{"alias_kind":"pith_short_12","alias_value":"BGG5SDGKTZJW","created_at":"2026-07-05T10:37:24Z"},{"alias_kind":"pith_short_16","alias_value":"BGG5SDGKTZJWPKGN","created_at":"2026-07-05T10:37:24Z"},{"alias_kind":"pith_short_8","alias_value":"BGG5SDGK","created_at":"2026-07-05T10:37:24Z"}],"graph_snapshots":[{"event_id":"sha256:2602ec01aa50228e7ff64b9eba6ab3ebdd7ac5065cea85079c83266549cbf631","target":"graph","created_at":"2026-07-05T10:37:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.00719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical P\\'olya-Tchebotarev problem, commonly stated as a max-min logarithmic energy problem, asks for finding a compact of minimal capacity in the complex plane which connects a prescribed collection of fixed points. Variants of this problem have found ramifications and applications in the theory of non-hermitian orthogonal polynomials, random matrices, approximation theory, among others. Here we consider an extension of this classical problem, including a semiclassical external field, and enforcing finitely many prescribed collections of points to be connected, possibly also to infinit","authors_text":"Guilherme Silva, Victor Alves","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-01T18:10:21Z","title":"The P\\'olya-Tchebotarev problem with semiclassical external fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00719","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":"sha256:72544d2c9d614fe5a2c00f6f8154d310cc51457ed1daf9353f33ef6137b04fa3","target":"record","created_at":"2026-07-05T10:37:24Z","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":"2e05d1f16079ad017b23a2dcdaafb59815dc5d463a5228f75db422617f901dbe","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-01T18:10:21Z","title_canon_sha256":"590b1c4f7d668abe934be7c8b52a84b00c8c5e8dcf01b8977477463034265062"},"schema_version":"1.0","source":{"id":"2403.00719","kind":"arxiv","version":2}},"canonical_sha256":"098dd90cca9e5367a8cd6bed0775ae86e681511d42de899c763d49a0dfb93bbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"098dd90cca9e5367a8cd6bed0775ae86e681511d42de899c763d49a0dfb93bbf","first_computed_at":"2026-07-05T10:37:24.541077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:37:24.541077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m0aN1z41ZeKW5cvE378wiRdhyz9iDXmhgr/mqJisGOLgoNxi6bSzdlhUzAxQcYH9xhAMZob7tYUAUAYGDcRXBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:37:24.541688Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.00719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72544d2c9d614fe5a2c00f6f8154d310cc51457ed1daf9353f33ef6137b04fa3","sha256:2602ec01aa50228e7ff64b9eba6ab3ebdd7ac5065cea85079c83266549cbf631"],"state_sha256":"79e7e47161ab181f4715c14983ba00fc36f9f0149c84b733f46ce76e9700fc85"}