{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P7PSWCZVAELZMGZVM5VGR7AIXJ","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":"3c9e36a20cf154eaf3f0be976eb554a87c0325951ff340e4b9e2e819f0e7523f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-05T14:13:47Z","title_canon_sha256":"609cf7f34e33e83b0f476877c5c6d286ce33ada4f4b0590b118b08796c6777eb"},"schema_version":"1.0","source":{"id":"1510.01163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01163","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01163v2","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01163","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"P7PSWCZVAELZ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P7PSWCZVAELZMGZV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P7PSWCZV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:3783392435eaf2c20e34df06962fe1899aa07d0c1f1013dff4daefb98f375c84","target":"graph","created_at":"2026-05-18T01:19:18Z","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 consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator ${r} \\in \\mathbb{N}$. It was shown in [De Klerk, E., Laurent, M., Sun, Z.: An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution. {\\em SIAM J. Optim.} 25(3) 1498--1514 (2015)] that the relative accuracy of this approximation depends on $r$ as $O(1/r^2)$ if there exists a rational global minimizer. In this note we show that the rational minimizer condition i","authors_text":"Etienne de Klerk, Juan C. Vera, Monique Laurent, Zhao Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-05T14:13:47Z","title":"On the convergence rate of grid search for polynomial optimization over the simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01163","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:edb0d9e470f7f31cd6684eb226f1c76831c4fac9078c9e8bd2aa7271068e4698","target":"record","created_at":"2026-05-18T01:19:18Z","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":"3c9e36a20cf154eaf3f0be976eb554a87c0325951ff340e4b9e2e819f0e7523f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-05T14:13:47Z","title_canon_sha256":"609cf7f34e33e83b0f476877c5c6d286ce33ada4f4b0590b118b08796c6777eb"},"schema_version":"1.0","source":{"id":"1510.01163","kind":"arxiv","version":2}},"canonical_sha256":"7fdf2b0b350117961b35676a68fc08ba660a8621c786b5f537048c9b97c2e52e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fdf2b0b350117961b35676a68fc08ba660a8621c786b5f537048c9b97c2e52e","first_computed_at":"2026-05-18T01:19:18.462770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:18.462770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nHyNV2V1LQymh7XYt5qHn+Uvu2tQW+CvrmyCu8CN4w+sSnLkFe6t6XSVaVpG8HhJbWQeFZp0pxXRHmKdWUSCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:18.463266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edb0d9e470f7f31cd6684eb226f1c76831c4fac9078c9e8bd2aa7271068e4698","sha256:3783392435eaf2c20e34df06962fe1899aa07d0c1f1013dff4daefb98f375c84"],"state_sha256":"9bc9fce5dfe8461ea85b45c3a9ebef9e0000de67964dba7cacc95fe0f222775a"}