{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VVISH4NX5VDOCS6MEAYCSZSBFQ","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":"5f301a77b4611d8e40742d8d93e0727a261a32046076854e4ca8edf198ce1da1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-12T13:46:35Z","title_canon_sha256":"3515e08f4c5f3a2dc115b360ea3c52e66b458265ce46423577a611d6d3a12fdd"},"schema_version":"1.0","source":{"id":"1705.04567","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04567","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04567v3","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04567","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"VVISH4NX5VDO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VVISH4NX5VDOCS6M","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VVISH4NX","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:98b7e9c32e38be0d161ea760267c3939c84865e88e220f5c74f34b57c2e8ef36","target":"graph","created_at":"2026-05-18T00:20:56Z","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 construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling $n$ pieces of arbitrary linear information, including function values.","authors_text":"David Krieg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-12T13:46:35Z","title":"Optimal Monte Carlo Methods for $L^2$-Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04567","kind":"arxiv","version":3},"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":"sha256:62b67f19cf4431e2d260e59735c88c904ffe6b7e3781c7dbedbf324fa6d6e22a","target":"record","created_at":"2026-05-18T00:20:56Z","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":"5f301a77b4611d8e40742d8d93e0727a261a32046076854e4ca8edf198ce1da1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-12T13:46:35Z","title_canon_sha256":"3515e08f4c5f3a2dc115b360ea3c52e66b458265ce46423577a611d6d3a12fdd"},"schema_version":"1.0","source":{"id":"1705.04567","kind":"arxiv","version":3}},"canonical_sha256":"ad5123f1b7ed46e14bcc20302966412c17cd75e8581f7f2a508c85a440e80534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad5123f1b7ed46e14bcc20302966412c17cd75e8581f7f2a508c85a440e80534","first_computed_at":"2026-05-18T00:20:56.443355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.443355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BqAK6QmUPMqgqGXmN+e6z4mBpe1ekzyXYcZSfidvHMy5CUt105EV6XEtiLX65mdeCWZrmMX8b3CUI/793GVfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.443798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04567","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b67f19cf4431e2d260e59735c88c904ffe6b7e3781c7dbedbf324fa6d6e22a","sha256:98b7e9c32e38be0d161ea760267c3939c84865e88e220f5c74f34b57c2e8ef36"],"state_sha256":"f25af87910d25a960c900e6cc36e417ea36782ae74fb8089ecf54b1ee98c9124"}