{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FADQQDGTZLFBKKV6DUO4PQOD2Y","short_pith_number":"pith:FADQQDGT","canonical_record":{"source":{"id":"1610.01365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-05T11:29:27Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"d02b70edc72c3f1515531b81fa6857f0b2b9820d859f62ab92d694ffe74bebaa","abstract_canon_sha256":"17daa4971b820ec827da6059881335b9e4d64ae89d2bbde0358117f0e6bb5867"},"schema_version":"1.0"},"canonical_sha256":"2807080cd3caca152abe1d1dc7c1c3d604ae1fb1f3a75a6dd83e36d5f604fee7","source":{"kind":"arxiv","id":"1610.01365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01365","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01365v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01365","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"FADQQDGTZLFB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FADQQDGTZLFBKKV6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FADQQDGT","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FADQQDGTZLFBKKV6DUO4PQOD2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-05T11:29:27Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"d02b70edc72c3f1515531b81fa6857f0b2b9820d859f62ab92d694ffe74bebaa","abstract_canon_sha256":"17daa4971b820ec827da6059881335b9e4d64ae89d2bbde0358117f0e6bb5867"},"schema_version":"1.0"},"canonical_sha256":"2807080cd3caca152abe1d1dc7c1c3d604ae1fb1f3a75a6dd83e36d5f604fee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.044665Z","signature_b64":"PpKcQ3mI1LBDiAlAhrNnaefAmUWH3LJc7lrp1JIjK0h7C5n9q4JBEDbzuSSrhb/vne6sq7v37VaHQUeku2DZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2807080cd3caca152abe1d1dc7c1c3d604ae1fb1f3a75a6dd83e36d5f604fee7","last_reissued_at":"2026-05-18T01:03:11.044160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.044160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01365","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNp5rqx44TPkBNR475vmhZEF6X7oIbXH7Z/aTy1rpMNnADEqmjh8P/CaT6T+NyKWrSs81D006W6c8Ct6egKBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:56:26.857792Z"},"content_sha256":"6c7a882a878b276af87a4c458c02d1804742bc5e4c682248423bbf2f7011d694","schema_version":"1.0","event_id":"sha256:6c7a882a878b276af87a4c458c02d1804742bc5e4c682248423bbf2f7011d694"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FADQQDGTZLFBKKV6DUO4PQOD2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One valued primitives and the F. and M. Riesz theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"V. Nestoridis","submitted_at":"2016-10-05T11:29:27Z","abstract_excerpt":"For a non-simply connected domain Omega in C and f a holomorphic function on Omega we prove that f admits one-valued primitives of any order in Omega, if and only if, it extends holomorphically in the simply connected envelope of Omega . This leads to a generalization of the F. and M. Riesz theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01365","kind":"arxiv","version":1},"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":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CjdE2WAfMcs6FO7n9MEp7hVc1hRNYv2zf75FhCGXDh3LtD+w9x++BSeVPTWenk2515i1QZOHTBCwatTcE3fFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:56:26.858126Z"},"content_sha256":"7d8be7c6fbfc594f8bc4deea701ca88a90de5fdb3fe590fed6c0853adf2ae326","schema_version":"1.0","event_id":"sha256:7d8be7c6fbfc594f8bc4deea701ca88a90de5fdb3fe590fed6c0853adf2ae326"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/bundle.json","state_url":"https://pith.science/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/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":"2026-06-29T15:56:26Z","links":{"resolver":"https://pith.science/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y","bundle":"https://pith.science/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/bundle.json","state":"https://pith.science/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FADQQDGTZLFBKKV6DUO4PQOD2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FADQQDGTZLFBKKV6DUO4PQOD2Y","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":"17daa4971b820ec827da6059881335b9e4d64ae89d2bbde0358117f0e6bb5867","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-05T11:29:27Z","title_canon_sha256":"d02b70edc72c3f1515531b81fa6857f0b2b9820d859f62ab92d694ffe74bebaa"},"schema_version":"1.0","source":{"id":"1610.01365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01365","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01365v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01365","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"FADQQDGTZLFB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FADQQDGTZLFBKKV6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FADQQDGT","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:7d8be7c6fbfc594f8bc4deea701ca88a90de5fdb3fe590fed6c0853adf2ae326","target":"graph","created_at":"2026-05-18T01:03:11Z","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 a non-simply connected domain Omega in C and f a holomorphic function on Omega we prove that f admits one-valued primitives of any order in Omega, if and only if, it extends holomorphically in the simply connected envelope of Omega . This leads to a generalization of the F. and M. Riesz theorem.","authors_text":"V. Nestoridis","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-05T11:29:27Z","title":"One valued primitives and the F. and M. Riesz theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01365","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":"sha256:6c7a882a878b276af87a4c458c02d1804742bc5e4c682248423bbf2f7011d694","target":"record","created_at":"2026-05-18T01:03:11Z","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":"17daa4971b820ec827da6059881335b9e4d64ae89d2bbde0358117f0e6bb5867","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-05T11:29:27Z","title_canon_sha256":"d02b70edc72c3f1515531b81fa6857f0b2b9820d859f62ab92d694ffe74bebaa"},"schema_version":"1.0","source":{"id":"1610.01365","kind":"arxiv","version":1}},"canonical_sha256":"2807080cd3caca152abe1d1dc7c1c3d604ae1fb1f3a75a6dd83e36d5f604fee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2807080cd3caca152abe1d1dc7c1c3d604ae1fb1f3a75a6dd83e36d5f604fee7","first_computed_at":"2026-05-18T01:03:11.044160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:11.044160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PpKcQ3mI1LBDiAlAhrNnaefAmUWH3LJc7lrp1JIjK0h7C5n9q4JBEDbzuSSrhb/vne6sq7v37VaHQUeku2DZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:11.044665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c7a882a878b276af87a4c458c02d1804742bc5e4c682248423bbf2f7011d694","sha256:7d8be7c6fbfc594f8bc4deea701ca88a90de5fdb3fe590fed6c0853adf2ae326"],"state_sha256":"21a66f15e35c5f3748e5db9b78ae7110f3c8e345289359480a62a6736f328bf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qjcm/mKrwYLgoFu9SjHOwpdsMzutRiLaMAZnVui8kwmGTi77JcJUT+CeqZmco47jqdZTeI93mQ3dgxtMti49DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:56:26.860027Z","bundle_sha256":"cc05a1634f3c7c09f166fee0f5c0c73dc9b06a38547513d21798ced4e81f5fa8"}}