{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3JV2J5E66IA5GTAB6BBJDSWEOQ","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":"41cf220c2a3627f5a3873e7867515e1991f98599c5f187b53a8ffc3fa1e3e8f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-21T14:31:24Z","title_canon_sha256":"3bdf542bc0fd4dfcb8b41dc29100e05152aa89d2f13a75a86fbad952011ada26"},"schema_version":"1.0","source":{"id":"1309.5483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5483","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5483v3","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5483","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"3JV2J5E66IA5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3JV2J5E66IA5GTAB","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3JV2J5E6","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:1ea625ba60f86b40fb94b732ae03886b35f97c61ee3a7d8cf44aefb8a088a7c0","target":"graph","created_at":"2026-05-18T03:06:54Z","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":"Let u be the equilibrium potential of a compact set K. An electrostatic skeleton of K is a positive measure whose closed support has connected complement and no interior, and whose potential is equal to u near infinity. We prove the existence of an electrostatic skeleton for any simplex.","authors_text":"Alexandre Eremenko, Erik Lundberg, Koushik Ramachandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-21T14:31:24Z","title":"Electrostatic skeletons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5483","kind":"arxiv","version":3},"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:cb64b3f39fc3b550f3108e176fe70898fd5e992d3f24d0b957e4edf56501d657","target":"record","created_at":"2026-05-18T03:06:54Z","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":"41cf220c2a3627f5a3873e7867515e1991f98599c5f187b53a8ffc3fa1e3e8f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-21T14:31:24Z","title_canon_sha256":"3bdf542bc0fd4dfcb8b41dc29100e05152aa89d2f13a75a86fbad952011ada26"},"schema_version":"1.0","source":{"id":"1309.5483","kind":"arxiv","version":3}},"canonical_sha256":"da6ba4f49ef201d34c01f04291cac474265230047f6ce221e194a14b8ed008fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da6ba4f49ef201d34c01f04291cac474265230047f6ce221e194a14b8ed008fe","first_computed_at":"2026-05-18T03:06:54.323793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.323793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WyKOTMTnSqAYBT+N45VJTKbETE+IqIWsV9nsLzOXkW5DGU1PUgsvhnLsQV+Nn4tBTwm68A0GCcDj8qRCCKN/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.324558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb64b3f39fc3b550f3108e176fe70898fd5e992d3f24d0b957e4edf56501d657","sha256:1ea625ba60f86b40fb94b732ae03886b35f97c61ee3a7d8cf44aefb8a088a7c0"],"state_sha256":"da60da99aaf76e173400121269dbddaa9a34223407d10e7d10eeaffa53913b50"}