{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RNN7EKSKYRBZPA3QTWAO2IM37N","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":"05052e2a92d4a07e2fbf3fdd9ee941f99339f4ab9ce9c01ec14b93d081133815","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-19T19:28:05Z","title_canon_sha256":"ffddf5bc49e9cc301dc007e4177857eac6c725f08fc1219619f78ddf8ebc2e88"},"schema_version":"1.0","source":{"id":"1304.5511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5511","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5511v1","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5511","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"pith_short_12","alias_value":"RNN7EKSKYRBZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RNN7EKSKYRBZPA3Q","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RNN7EKSK","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:fd8b8ef40511b62901af64a5f05ddd377e1356749262eab7876d9144a323ad30","target":"graph","created_at":"2026-05-18T03:27:33Z","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 investigate the sets of uniform limits $A(\\bar{B}_n)$, $A(\\bar{D}^I)$ of polynomials on the closed unit ball $\\bar{B}_n$ of $\\mathbb{C}^n$ and on the cartesian product $\\bar{D}^I$ where $I$ is an arbitrary set and $\\bar{D}$ is the closed unit disc in $\\mathbb{C}$. We introduce the notion of set of uniqueness for $A(\\bar{D}^I)$ (respectively for $A(\\bar{B}_n)$) for compact subsets $K$ of $T^I$ (respectively of $\\partial \\bar{B}_n$) where $T=\\partial D$ is the unit circle. Our main result is that if $K$ has positive measure then $K$ is a set of uniqueness. The converse does not hold. Finally,","authors_text":"K. Makridis, V. Nestoridis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-19T19:28:05Z","title":"Sets of uniqueness for uniform limits of polynomials in several complex variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5511","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":"sha256:8bc0fcc3ec1f671e0c461018563890be7eb29ee6dc01112eb21c5a077b900111","target":"record","created_at":"2026-05-18T03:27:33Z","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":"05052e2a92d4a07e2fbf3fdd9ee941f99339f4ab9ce9c01ec14b93d081133815","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-19T19:28:05Z","title_canon_sha256":"ffddf5bc49e9cc301dc007e4177857eac6c725f08fc1219619f78ddf8ebc2e88"},"schema_version":"1.0","source":{"id":"1304.5511","kind":"arxiv","version":1}},"canonical_sha256":"8b5bf22a4ac4439783709d80ed219bfb6516efe000f2aa7171023325b0615907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b5bf22a4ac4439783709d80ed219bfb6516efe000f2aa7171023325b0615907","first_computed_at":"2026-05-18T03:27:33.350719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:33.350719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I62CaozSNUc6pvOPqLwh5olWMs/ITk7UQK9A2nk4NjW6SU/1na9RzZS80ZWfIxq74QQok+r2wlb7u5dcsWA5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:33.351162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bc0fcc3ec1f671e0c461018563890be7eb29ee6dc01112eb21c5a077b900111","sha256:fd8b8ef40511b62901af64a5f05ddd377e1356749262eab7876d9144a323ad30"],"state_sha256":"700ee014a953689456c3af2cef44028ef50d6b436d96d4d0ac41a1850097da6f"}