{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MGCIXWQXU7UPMGX25YLWRU4FOU","short_pith_number":"pith:MGCIXWQX","canonical_record":{"source":{"id":"1107.0393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-02T16:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"8c78ef57f1dfefbaaa46e170506f72a19bb5e050e0bdc85dffd2fe8331323dab","abstract_canon_sha256":"29a3d33411c01b2a57344c7d873d9bd323aace04eaaec960ad6f4fcf057233fb"},"schema_version":"1.0"},"canonical_sha256":"61848bda17a7e8f61afaee1768d385753218eca68b41dc9760de496fd605b398","source":{"kind":"arxiv","id":"1107.0393","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0393","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0393v1","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0393","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"MGCIXWQXU7UP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MGCIXWQXU7UPMGX2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MGCIXWQX","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MGCIXWQXU7UPMGX25YLWRU4FOU","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-02T16:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"8c78ef57f1dfefbaaa46e170506f72a19bb5e050e0bdc85dffd2fe8331323dab","abstract_canon_sha256":"29a3d33411c01b2a57344c7d873d9bd323aace04eaaec960ad6f4fcf057233fb"},"schema_version":"1.0"},"canonical_sha256":"61848bda17a7e8f61afaee1768d385753218eca68b41dc9760de496fd605b398","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:54.053526Z","signature_b64":"KHJwGZxq9T17HenPct0zacQekxhBauC0uW02G569lmRn0ox7Ek30u6ZLptCvopF/2QbIU3oV8Fau7VPZ861RAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61848bda17a7e8f61afaee1768d385753218eca68b41dc9760de496fd605b398","last_reissued_at":"2026-05-18T04:18:54.053134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:54.053134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0393","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":"2026-05-18T04:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrIKTge5s7g5u2HJxVaBy9LyX77xvLaZOLNCz/Xx5unKbMAXBAuc4wi+BRCh1eoqzsVgGNTMvdKzEk8hPAhjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:12:58.330387Z"},"content_sha256":"9cd9b34a91c5b7f7cabbcb6e843635436f4686cae813157b4077efd4807e3ddc","schema_version":"1.0","event_id":"sha256:9cd9b34a91c5b7f7cabbcb6e843635436f4686cae813157b4077efd4807e3ddc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MGCIXWQXU7UPMGX25YLWRU4FOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a characterization of Arakelian sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"G. Fournodavlos","submitted_at":"2011-07-02T16:29:35Z","abstract_excerpt":"Let $K$ be a compact set in the complex plane $\\C$, such that its complement in the Riemann sphere, $(\\C\\cup\\{\\infty\\})\\sm K$, is connected. Also, let $U\\subseteq\\C$ be an open set which contains $K$. Then there exists a simply connected open set $V$ such that $K\\subseteq V\\subseteq U$. We show that if the set $K$ is replaced by a closed set $F$ in $\\C$, then the above lemma is equivalent to the fact that $F$ is an Arakelian set in $\\C$. This holds more generally, if $\\C$ is replaced by any simply connected open set $\\OO\\subseteq\\C$. In the case of an arbitrary open set $\\OO\\subseteq\\C$, the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0393","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":"2026-05-18T04:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eeaQW8vWvdC7JJoKCPqc3MA35MRJLJJJqTNZ4+wmIuVjCxuxFtCcJArdXViCOQ5AJHG+hBRSCHHVO1P3iJLODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:12:58.330738Z"},"content_sha256":"962b5686daabe205c2a5fe70136efd15f38e3d212937ff40502c8256197afc00","schema_version":"1.0","event_id":"sha256:962b5686daabe205c2a5fe70136efd15f38e3d212937ff40502c8256197afc00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/bundle.json","state_url":"https://pith.science/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/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":"2026-06-29T08:12:58Z","links":{"resolver":"https://pith.science/pith/MGCIXWQXU7UPMGX25YLWRU4FOU","bundle":"https://pith.science/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/bundle.json","state":"https://pith.science/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGCIXWQXU7UPMGX25YLWRU4FOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MGCIXWQXU7UPMGX25YLWRU4FOU","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":"29a3d33411c01b2a57344c7d873d9bd323aace04eaaec960ad6f4fcf057233fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-02T16:29:35Z","title_canon_sha256":"8c78ef57f1dfefbaaa46e170506f72a19bb5e050e0bdc85dffd2fe8331323dab"},"schema_version":"1.0","source":{"id":"1107.0393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0393","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0393v1","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0393","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"MGCIXWQXU7UP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MGCIXWQXU7UPMGX2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MGCIXWQX","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:962b5686daabe205c2a5fe70136efd15f38e3d212937ff40502c8256197afc00","target":"graph","created_at":"2026-05-18T04:18:54Z","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 $K$ be a compact set in the complex plane $\\C$, such that its complement in the Riemann sphere, $(\\C\\cup\\{\\infty\\})\\sm K$, is connected. Also, let $U\\subseteq\\C$ be an open set which contains $K$. Then there exists a simply connected open set $V$ such that $K\\subseteq V\\subseteq U$. We show that if the set $K$ is replaced by a closed set $F$ in $\\C$, then the above lemma is equivalent to the fact that $F$ is an Arakelian set in $\\C$. This holds more generally, if $\\C$ is replaced by any simply connected open set $\\OO\\subseteq\\C$. In the case of an arbitrary open set $\\OO\\subseteq\\C$, the a","authors_text":"G. Fournodavlos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-02T16:29:35Z","title":"On a characterization of Arakelian sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0393","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":"sha256:9cd9b34a91c5b7f7cabbcb6e843635436f4686cae813157b4077efd4807e3ddc","target":"record","created_at":"2026-05-18T04:18:54Z","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":"29a3d33411c01b2a57344c7d873d9bd323aace04eaaec960ad6f4fcf057233fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-07-02T16:29:35Z","title_canon_sha256":"8c78ef57f1dfefbaaa46e170506f72a19bb5e050e0bdc85dffd2fe8331323dab"},"schema_version":"1.0","source":{"id":"1107.0393","kind":"arxiv","version":1}},"canonical_sha256":"61848bda17a7e8f61afaee1768d385753218eca68b41dc9760de496fd605b398","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61848bda17a7e8f61afaee1768d385753218eca68b41dc9760de496fd605b398","first_computed_at":"2026-05-18T04:18:54.053134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:54.053134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHJwGZxq9T17HenPct0zacQekxhBauC0uW02G569lmRn0ox7Ek30u6ZLptCvopF/2QbIU3oV8Fau7VPZ861RAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:54.053526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd9b34a91c5b7f7cabbcb6e843635436f4686cae813157b4077efd4807e3ddc","sha256:962b5686daabe205c2a5fe70136efd15f38e3d212937ff40502c8256197afc00"],"state_sha256":"aed3254fe2e32be28e914e1191b7b032f0618a6f4b2e01609448c09313a4b448"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0mY6AalVtYggHYckHOuzPYP2ECT3poVMzK6bR667LgPpnWedMjcBQDA5tWvNHFeJDjOGzwiZNImUSIXPOpOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:12:58.332603Z","bundle_sha256":"41b2d270561fb160a10592c49cb220d8358c06709632d4b5e48cac66c002d222"}}