{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BEPHGTPJV4Y7NXWHDAQOHQ6JZC","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":"8cefbe3779adddeb16e308c6119730828e8711df1f70c21e6ac345a24dc0cc16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T00:22:30Z","title_canon_sha256":"1cab3cd7739f9557af51b9c98d2bc6dd600913fea4453bd974cba2a46e69b718"},"schema_version":"1.0","source":{"id":"1805.11756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11756","created_at":"2026-05-17T23:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11756v2","created_at":"2026-05-17T23:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11756","created_at":"2026-05-17T23:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"BEPHGTPJV4Y7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BEPHGTPJV4Y7NXWH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BEPHGTPJ","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:1c49c29c343724b9c6380a7f3b26ce4b9aacd73afe734428a005b73a529ba9e7","target":"graph","created_at":"2026-05-17T23:52:27Z","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":"We study the density of polynomials in $H^2(\\Omega,e^{-\\varphi})$, the space of square integrable holomorphic functions in a bounded domain $\\Omega$ in $\\mathbb{C}$, where $\\varphi$ is a subharmonic function. In particular, we prove that the density holds in Carath\\'{e}odory domains for any subharmonic function $\\varphi$ in a neighborhood of $\\overline{\\Omega}$. In non-Carath\\'{e}odory domains, we prove that the density depends on the weight function, giving examples.","authors_text":"John Erik Forn{\\ae}ss, Jujie Wu, S\\'everine Biard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T00:22:30Z","title":"Weighted-$L^2$ polynomial approximation in $\\mathbb{C}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11756","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:fa909b704e3896da4f85ee0f1fe8b1ede6901c8ae99d9c52c23b61e16107e6e3","target":"record","created_at":"2026-05-17T23:52:27Z","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":"8cefbe3779adddeb16e308c6119730828e8711df1f70c21e6ac345a24dc0cc16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T00:22:30Z","title_canon_sha256":"1cab3cd7739f9557af51b9c98d2bc6dd600913fea4453bd974cba2a46e69b718"},"schema_version":"1.0","source":{"id":"1805.11756","kind":"arxiv","version":2}},"canonical_sha256":"091e734de9af31f6dec71820e3c3c9c8abedacf4864f5a11f5c1cc65064f4333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"091e734de9af31f6dec71820e3c3c9c8abedacf4864f5a11f5c1cc65064f4333","first_computed_at":"2026-05-17T23:52:27.358184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:27.358184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gc332yUdJFQknYeEHuyjvfnRnUpRDnPw7Oz6mD0j6CNn1nIPZUq42lLy7KOYzmc87sGCXXSu40TydKMFUwMDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:27.358967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa909b704e3896da4f85ee0f1fe8b1ede6901c8ae99d9c52c23b61e16107e6e3","sha256:1c49c29c343724b9c6380a7f3b26ce4b9aacd73afe734428a005b73a529ba9e7"],"state_sha256":"3b1084551ae0a7bbfbbc48fdf057ee35f8c0f01f155e50e2cf6b11137caeedeb"}