{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WL55WX4XH4PLJZXRZP64VTSEOD","short_pith_number":"pith:WL55WX4X","schema_version":"1.0","canonical_sha256":"b2fbdb5f973f1eb4e6f1cbfdcace4470df85222fe78d29079d18a00e6e18f19d","source":{"kind":"arxiv","id":"1803.00099","version":1},"attestation_state":"computed","paper":{"title":"The Difficulty of Monte Carlo Approximation of Multivariate Monotone Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Robert J. Kunsch","submitted_at":"2018-02-28T21:40:44Z","abstract_excerpt":"We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number $n(\\varepsilon,d)$ of function evaluations needed in order to approximate an unknown monotone function within a given error threshold $\\varepsilon$ grows at least exponentially in $d$. This is not the case in the randomized setting (Monte Carlo setting) where the complexity $n(\\varepsilon,d)$ grows exponentially in $\\sqrt{d}$ (modulo logarithmic terms) only."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.00099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T21:40:44Z","cross_cats_sorted":[],"title_canon_sha256":"aa0912932edce1dfd800f6bb2633a81cd29930cc8789ec1b99528f0f113bc675","abstract_canon_sha256":"924608fd33bee9f245910e3b6b88a7b2e7fd4383140ed4c8d630abca8714066e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:13.350021Z","signature_b64":"KTa28RCvXc5mbwX8rQNz38htibRsMRR5tvhiMdQ6UsNpG2fD6Men6U033ZnxH2fuCeIBpH4xkPTSv12A2W5XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2fbdb5f973f1eb4e6f1cbfdcace4470df85222fe78d29079d18a00e6e18f19d","last_reissued_at":"2026-05-18T00:22:13.349518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:13.349518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Difficulty of Monte Carlo Approximation of Multivariate Monotone Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Robert J. Kunsch","submitted_at":"2018-02-28T21:40:44Z","abstract_excerpt":"We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number $n(\\varepsilon,d)$ of function evaluations needed in order to approximate an unknown monotone function within a given error threshold $\\varepsilon$ grows at least exponentially in $d$. This is not the case in the randomized setting (Monte Carlo setting) where the complexity $n(\\varepsilon,d)$ grows exponentially in $\\sqrt{d}$ (modulo logarithmic terms) only."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.00099","created_at":"2026-05-18T00:22:13.349584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.00099v1","created_at":"2026-05-18T00:22:13.349584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00099","created_at":"2026-05-18T00:22:13.349584+00:00"},{"alias_kind":"pith_short_12","alias_value":"WL55WX4XH4PL","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WL55WX4XH4PLJZXR","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WL55WX4X","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD","json":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD.json","graph_json":"https://pith.science/api/pith-number/WL55WX4XH4PLJZXRZP64VTSEOD/graph.json","events_json":"https://pith.science/api/pith-number/WL55WX4XH4PLJZXRZP64VTSEOD/events.json","paper":"https://pith.science/paper/WL55WX4X"},"agent_actions":{"view_html":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD","download_json":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD.json","view_paper":"https://pith.science/paper/WL55WX4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.00099&json=true","fetch_graph":"https://pith.science/api/pith-number/WL55WX4XH4PLJZXRZP64VTSEOD/graph.json","fetch_events":"https://pith.science/api/pith-number/WL55WX4XH4PLJZXRZP64VTSEOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD/action/storage_attestation","attest_author":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD/action/author_attestation","sign_citation":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD/action/citation_signature","submit_replication":"https://pith.science/pith/WL55WX4XH4PLJZXRZP64VTSEOD/action/replication_record"}},"created_at":"2026-05-18T00:22:13.349584+00:00","updated_at":"2026-05-18T00:22:13.349584+00:00"}