{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:RNMZTBNEC5IHTUPB37LCWAGMP3","short_pith_number":"pith:RNMZTBNE","schema_version":"1.0","canonical_sha256":"8b599985a4175079d1e1dfd62b00cc7ece1d176646114c9156b818df268939ff","source":{"kind":"arxiv","id":"2304.01400","version":1},"attestation_state":"computed","paper":{"title":"Revisiting mean-square approximation by polynomials in the unit disk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Bartosz Malman","submitted_at":"2023-04-03T22:33:38Z","abstract_excerpt":"For a positive finite Borel measure $\\mu$ compactly supported in the complex plane, the space $\\mathcal{P}^2(\\mu)$ is the closure of the analytic polynomials in the Lebesgue space $L^2(\\mu)$. According to Thomson's famous result, any space $\\mathcal{P}^2(\\mu)$ decomposes as an orthogonal sum of pieces which are essentially analytic, and a residual $L^2$-space. We study the structure of this decomposition for a class of Borel measures $\\mu$ supported on the closed unit disk for which the part $\\mu_\\mathbb{D}$, living in the open disk $\\mathbb{D}$, is radial and decreases at least exponentially "},"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":"2304.01400","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-04-03T22:33:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"114260c0966671b73edc0bd1552543f10c1032a13403a34ecd7d82f8bb08aef6","abstract_canon_sha256":"fa5225961483213036637bd7c581ba14f25e5bd87265bf4ed5f44aa8895cb21e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:39.766190Z","signature_b64":"2Z9r8I8jqDn6TCMRz6tYm4hv9KPHbx4R8DSs4QuazRMyvsJHLBeDeQJBi8rN+2S5eLVSI7luK95z1A/HIk92Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b599985a4175079d1e1dfd62b00cc7ece1d176646114c9156b818df268939ff","last_reissued_at":"2026-07-05T05:57:39.765749Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:39.765749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting mean-square approximation by polynomials in the unit disk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Bartosz Malman","submitted_at":"2023-04-03T22:33:38Z","abstract_excerpt":"For a positive finite Borel measure $\\mu$ compactly supported in the complex plane, the space $\\mathcal{P}^2(\\mu)$ is the closure of the analytic polynomials in the Lebesgue space $L^2(\\mu)$. According to Thomson's famous result, any space $\\mathcal{P}^2(\\mu)$ decomposes as an orthogonal sum of pieces which are essentially analytic, and a residual $L^2$-space. We study the structure of this decomposition for a class of Borel measures $\\mu$ supported on the closed unit disk for which the part $\\mu_\\mathbb{D}$, living in the open disk $\\mathbb{D}$, is radial and decreases at least exponentially "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01400","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.01400/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2304.01400","created_at":"2026-07-05T05:57:39.765817+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.01400v1","created_at":"2026-07-05T05:57:39.765817+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.01400","created_at":"2026-07-05T05:57:39.765817+00:00"},{"alias_kind":"pith_short_12","alias_value":"RNMZTBNEC5IH","created_at":"2026-07-05T05:57:39.765817+00:00"},{"alias_kind":"pith_short_16","alias_value":"RNMZTBNEC5IHTUPB","created_at":"2026-07-05T05:57:39.765817+00:00"},{"alias_kind":"pith_short_8","alias_value":"RNMZTBNE","created_at":"2026-07-05T05:57:39.765817+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.06911","citing_title":"A critical majorant for the Khinchin-Ostrowski property","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3","json":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3.json","graph_json":"https://pith.science/api/pith-number/RNMZTBNEC5IHTUPB37LCWAGMP3/graph.json","events_json":"https://pith.science/api/pith-number/RNMZTBNEC5IHTUPB37LCWAGMP3/events.json","paper":"https://pith.science/paper/RNMZTBNE"},"agent_actions":{"view_html":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3","download_json":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3.json","view_paper":"https://pith.science/paper/RNMZTBNE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.01400&json=true","fetch_graph":"https://pith.science/api/pith-number/RNMZTBNEC5IHTUPB37LCWAGMP3/graph.json","fetch_events":"https://pith.science/api/pith-number/RNMZTBNEC5IHTUPB37LCWAGMP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3/action/storage_attestation","attest_author":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3/action/author_attestation","sign_citation":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3/action/citation_signature","submit_replication":"https://pith.science/pith/RNMZTBNEC5IHTUPB37LCWAGMP3/action/replication_record"}},"created_at":"2026-07-05T05:57:39.765817+00:00","updated_at":"2026-07-05T05:57:39.765817+00:00"}