{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FTU2EBB4CKSN5X5ZCRIZTLKEID","short_pith_number":"pith:FTU2EBB4","schema_version":"1.0","canonical_sha256":"2ce9a2043c12a4dedfb9145199ad4440ee82943ceb960ce80cd70fc310bf31cd","source":{"kind":"arxiv","id":"1101.4840","version":2},"attestation_state":"computed","paper":{"title":"Uniform algebras and approximation on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Erlend Forn{\\ae}ss Wold, H{\\aa}kan Samuelsson","submitted_at":"2011-01-25T15:07:15Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{C}^n$ be a bounded domain and let $\\mathcal{A} \\subset \\mathcal{C}(\\bar{\\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\\Omega$ and $F$ we show that the only obstruction to $\\mathcal{A} = \\mathcal{C}(\\bar{\\Omega})$ is that there is a holomorphic disk $D \\subset \\bar{\\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguish"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.4840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-25T15:07:15Z","cross_cats_sorted":[],"title_canon_sha256":"0ecf5c00bbe8c84710466e2b0351ca1b0949524adc4a17ac2936ed1afd0477e5","abstract_canon_sha256":"4202c051f8e3997559abc82f081d22724a76b61aeb7fadcc10c0e80b75038d1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:25.843783Z","signature_b64":"/yCpmS+IRDOklT1Wo1RzQb5zP13nbQmlvSrKgus0cFo0ChpZwIyuDVRq1D0lPRn5+KUkCMfBZ5sBtA/bVUOjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ce9a2043c12a4dedfb9145199ad4440ee82943ceb960ce80cd70fc310bf31cd","last_reissued_at":"2026-05-18T01:09:25.843285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:25.843285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform algebras and approximation on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Erlend Forn{\\ae}ss Wold, H{\\aa}kan Samuelsson","submitted_at":"2011-01-25T15:07:15Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{C}^n$ be a bounded domain and let $\\mathcal{A} \\subset \\mathcal{C}(\\bar{\\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\\Omega$ and $F$ we show that the only obstruction to $\\mathcal{A} = \\mathcal{C}(\\bar{\\Omega})$ is that there is a holomorphic disk $D \\subset \\bar{\\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4840","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.4840","created_at":"2026-05-18T01:09:25.843380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4840v2","created_at":"2026-05-18T01:09:25.843380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4840","created_at":"2026-05-18T01:09:25.843380+00:00"},{"alias_kind":"pith_short_12","alias_value":"FTU2EBB4CKSN","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FTU2EBB4CKSN5X5Z","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FTU2EBB4","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID","json":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID.json","graph_json":"https://pith.science/api/pith-number/FTU2EBB4CKSN5X5ZCRIZTLKEID/graph.json","events_json":"https://pith.science/api/pith-number/FTU2EBB4CKSN5X5ZCRIZTLKEID/events.json","paper":"https://pith.science/paper/FTU2EBB4"},"agent_actions":{"view_html":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID","download_json":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID.json","view_paper":"https://pith.science/paper/FTU2EBB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4840&json=true","fetch_graph":"https://pith.science/api/pith-number/FTU2EBB4CKSN5X5ZCRIZTLKEID/graph.json","fetch_events":"https://pith.science/api/pith-number/FTU2EBB4CKSN5X5ZCRIZTLKEID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID/action/storage_attestation","attest_author":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID/action/author_attestation","sign_citation":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID/action/citation_signature","submit_replication":"https://pith.science/pith/FTU2EBB4CKSN5X5ZCRIZTLKEID/action/replication_record"}},"created_at":"2026-05-18T01:09:25.843380+00:00","updated_at":"2026-05-18T01:09:25.843380+00:00"}