{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LZY3OM7ZDNKM3V6JE3CRR2DBTG","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":"d7e93d6d0b7a03f59e94d9248e12754a2d669f6eb72d23b443544cda0be520c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-08T11:10:25Z","title_canon_sha256":"439070f5275fd705b7d12aee8c36ce3282051153e646846fee6e5e54bb418b97"},"schema_version":"1.0","source":{"id":"1406.1972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1972","created_at":"2026-05-18T02:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1972v1","created_at":"2026-05-18T02:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1972","created_at":"2026-05-18T02:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"LZY3OM7ZDNKM","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LZY3OM7ZDNKM3V6J","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LZY3OM7Z","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:caae40f91b31f97abe74b203bb13bf79b00dcb81213671326d21c42de07ab3b7","target":"graph","created_at":"2026-05-18T02:50:12Z","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":"Below we discuss the existence of a motherbody measure for the exterior inverse problem in potential theory in the complex plane. More exactly, we study the question of representability almost everywhere (a.e.) in C of (a branch of) an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points.\n  Firstly, we present a large class of algebraic functions for which there (conjecturally) always exists a positive measure with the above properties. This class was discovered in our earl","authors_text":"Boris Shapiro, Rikard B{\\oe}gvad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-08T11:10:25Z","title":"On mother body measures with algebraic Cauchy transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1972","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:abc2fbc5cd6f0c5cfc234a389d0ae22622e26a74e725995a2dc1e5eeda0e0300","target":"record","created_at":"2026-05-18T02:50:12Z","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":"d7e93d6d0b7a03f59e94d9248e12754a2d669f6eb72d23b443544cda0be520c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-08T11:10:25Z","title_canon_sha256":"439070f5275fd705b7d12aee8c36ce3282051153e646846fee6e5e54bb418b97"},"schema_version":"1.0","source":{"id":"1406.1972","kind":"arxiv","version":1}},"canonical_sha256":"5e71b733f91b54cdd7c926c518e861998e2903aee8991efe4abe1cb568884ed2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e71b733f91b54cdd7c926c518e861998e2903aee8991efe4abe1cb568884ed2","first_computed_at":"2026-05-18T02:50:12.085526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:12.085526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tS/JDhI0uqmAQYVwvmS2RWu6sejS9SYDF6Dwk7Q3Cce5THHSrrm4a95HlOQQTvbB/qgmTu+tlVvIPYaGR6OFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:12.086221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abc2fbc5cd6f0c5cfc234a389d0ae22622e26a74e725995a2dc1e5eeda0e0300","sha256:caae40f91b31f97abe74b203bb13bf79b00dcb81213671326d21c42de07ab3b7"],"state_sha256":"0525c95eee235b1a46b18f2546c95bc382a21df325412895a0ca72ccb95064be"}