{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AN4OE4DLZFXQ6GFDQXHTQUDKSP","short_pith_number":"pith:AN4OE4DL","canonical_record":{"source":{"id":"1506.06543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-22T10:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"d38b7e960a82a08f259ed7ba2befbaf2a3db50bcd944cbf372a48620d4eb0a8e","abstract_canon_sha256":"a5f73b75c39a25e289d0e6aa4cc2ca365f4bd494c66094c98483fc09d8b1c5db"},"schema_version":"1.0"},"canonical_sha256":"0378e2706bc96f0f18a385cf38506a93f566910ef2b65e4993b951346ed2ab2d","source":{"kind":"arxiv","id":"1506.06543","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06543","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06543v2","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06543","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"AN4OE4DLZFXQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AN4OE4DLZFXQ6GFD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AN4OE4DL","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AN4OE4DLZFXQ6GFDQXHTQUDKSP","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-22T10:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"d38b7e960a82a08f259ed7ba2befbaf2a3db50bcd944cbf372a48620d4eb0a8e","abstract_canon_sha256":"a5f73b75c39a25e289d0e6aa4cc2ca365f4bd494c66094c98483fc09d8b1c5db"},"schema_version":"1.0"},"canonical_sha256":"0378e2706bc96f0f18a385cf38506a93f566910ef2b65e4993b951346ed2ab2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:19.071612Z","signature_b64":"BUFpIdEGJ69Ty+dfjplb75P0OjaX3tyUuWPKEYIgt8B0BsGP3DQabwRB7VY0BdCZkacoclJvK0fE0NESZL97AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0378e2706bc96f0f18a385cf38506a93f566910ef2b65e4993b951346ed2ab2d","last_reissued_at":"2026-05-18T01:20:19.071125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:19.071125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06543","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRQQpurZ2YL/Gm42Q25orcfWQyFMlN15/W++NgcErYgzNl7Pamsi75NRAAI9S6nvG1GJDnLl/4/E4uwix60UBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:34:13.126084Z"},"content_sha256":"2d5e9dc172a3ca66c4cd3a54f076c49636ee1db276c9479d5969ca7f48c853b8","schema_version":"1.0","event_id":"sha256:2d5e9dc172a3ca66c4cd3a54f076c49636ee1db276c9479d5969ca7f48c853b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AN4OE4DLZFXQ6GFDQXHTQUDKSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Faouzi Thabet, Mohamed Jalel Atia","submitted_at":"2015-06-22T10:39:02Z","abstract_excerpt":"In this paper, we discuss the representability almost everywhere (a.e.) in the plane 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. We discuss the existence of critical trajectories of a family of quadratic differentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06543","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UMq2AwllxfVQn9oKtwxB5rPtmZMVeJ60C508cgH166li8zyVAOTdSnXzwhkkp7ObL69kBao4qFhEja0fo29PAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:34:13.126604Z"},"content_sha256":"724bf01a781e69cea6903ea186d8214cee4ba97d85510914b290b6d13b57e32c","schema_version":"1.0","event_id":"sha256:724bf01a781e69cea6903ea186d8214cee4ba97d85510914b290b6d13b57e32c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/bundle.json","state_url":"https://pith.science/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T16:34:13Z","links":{"resolver":"https://pith.science/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP","bundle":"https://pith.science/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/bundle.json","state":"https://pith.science/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AN4OE4DLZFXQ6GFDQXHTQUDKSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AN4OE4DLZFXQ6GFDQXHTQUDKSP","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":"a5f73b75c39a25e289d0e6aa4cc2ca365f4bd494c66094c98483fc09d8b1c5db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-22T10:39:02Z","title_canon_sha256":"d38b7e960a82a08f259ed7ba2befbaf2a3db50bcd944cbf372a48620d4eb0a8e"},"schema_version":"1.0","source":{"id":"1506.06543","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06543","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06543v2","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06543","created_at":"2026-05-18T01:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"AN4OE4DLZFXQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AN4OE4DLZFXQ6GFD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AN4OE4DL","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:724bf01a781e69cea6903ea186d8214cee4ba97d85510914b290b6d13b57e32c","target":"graph","created_at":"2026-05-18T01:20:19Z","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":"In this paper, we discuss the representability almost everywhere (a.e.) in the plane 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. We discuss the existence of critical trajectories of a family of quadratic differentials.","authors_text":"Faouzi Thabet, Mohamed Jalel Atia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-22T10:39:02Z","title":"Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06543","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":"sha256:2d5e9dc172a3ca66c4cd3a54f076c49636ee1db276c9479d5969ca7f48c853b8","target":"record","created_at":"2026-05-18T01:20:19Z","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":"a5f73b75c39a25e289d0e6aa4cc2ca365f4bd494c66094c98483fc09d8b1c5db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-22T10:39:02Z","title_canon_sha256":"d38b7e960a82a08f259ed7ba2befbaf2a3db50bcd944cbf372a48620d4eb0a8e"},"schema_version":"1.0","source":{"id":"1506.06543","kind":"arxiv","version":2}},"canonical_sha256":"0378e2706bc96f0f18a385cf38506a93f566910ef2b65e4993b951346ed2ab2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0378e2706bc96f0f18a385cf38506a93f566910ef2b65e4993b951346ed2ab2d","first_computed_at":"2026-05-18T01:20:19.071125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:19.071125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUFpIdEGJ69Ty+dfjplb75P0OjaX3tyUuWPKEYIgt8B0BsGP3DQabwRB7VY0BdCZkacoclJvK0fE0NESZL97AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:19.071612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06543","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d5e9dc172a3ca66c4cd3a54f076c49636ee1db276c9479d5969ca7f48c853b8","sha256:724bf01a781e69cea6903ea186d8214cee4ba97d85510914b290b6d13b57e32c"],"state_sha256":"5d49ef87d10376910b34ab39fea1048d5a476c2f6f0b475e74c25509941b260e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rRHPFUhmmRnPfQeCVISgFHGLjpTTJJaHUxPOPyrzcNhF9tYvObdwb9L2UaeCGBoYwl1nXty+Z54VL4Pff/4iAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:34:13.129205Z","bundle_sha256":"d504e998654e8cfaf65124ea34bcad7b9a2331f9584df791a4adfcf04b819b57"}}