{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C3NCXRGM75VLZK5AYVTB2D4PUG","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":"41db24bef91ef0ef9faa312b0fa1ac0c013fd0c11a7e49e39bd01b8c2fd78a50","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-12T02:11:13Z","title_canon_sha256":"40add8d4a55a0c8fa9e8144e393ea2c8347923d9d63e9e875fbb184c3ce3f97f"},"schema_version":"1.0","source":{"id":"1201.2462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2462","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2462v1","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2462","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"C3NCXRGM75VL","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3NCXRGM75VLZK5A","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3NCXRGM","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:be6939b0b8c3b1a65982ddd4a6c48a3e520f1cd99be1637c689a469bfda09520","target":"graph","created_at":"2026-05-18T04:04:44Z","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 optimality of the minimax risk of truncated series estimators for symmetric convex polytopes. We show that the optimal truncated series estimator is within $O(\\log m)$ factor of the optimal if the polytope is defined by $m$ hyperplanes. This represents the first such bounds towards general convex bodies. In proving our result, we first define a geometric quantity, called the \\emph{approximation radius}, for lower bounding the minimax risk. We then derive our bounds by establishing a connection between the approximation radius and the Kolmogorov width, the quantity that provides up","authors_text":"Adel Javanmard, Li Zhang","cross_cats":["cs.IT","math.IT","math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-12T02:11:13Z","title":"The minimax risk of truncated series estimators for symmetric convex polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2462","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":"sha256:97c92a5f89fa94cdf67b7cdc217760c6a7c2dfb6ed3450be9a18373f986c0e29","target":"record","created_at":"2026-05-18T04:04:44Z","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":"41db24bef91ef0ef9faa312b0fa1ac0c013fd0c11a7e49e39bd01b8c2fd78a50","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-12T02:11:13Z","title_canon_sha256":"40add8d4a55a0c8fa9e8144e393ea2c8347923d9d63e9e875fbb184c3ce3f97f"},"schema_version":"1.0","source":{"id":"1201.2462","kind":"arxiv","version":1}},"canonical_sha256":"16da2bc4ccff6abcaba0c5661d0f8fa18bc0e6d9123bb44812896b7420257f47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16da2bc4ccff6abcaba0c5661d0f8fa18bc0e6d9123bb44812896b7420257f47","first_computed_at":"2026-05-18T04:04:44.368641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:44.368641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0S+pgCWEobBELTp6uk8qXQQdb65T8/Z3hJt31SUDkPd1NiMtvtw3Le+eNKzPaSQlu1qtlW2wsWwOcW2BJzuoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:44.369097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97c92a5f89fa94cdf67b7cdc217760c6a7c2dfb6ed3450be9a18373f986c0e29","sha256:be6939b0b8c3b1a65982ddd4a6c48a3e520f1cd99be1637c689a469bfda09520"],"state_sha256":"ce9f1aa3d26c630cb83f5a5190011b97e7cf54237cc25601201800ebda1f3b9c"}