{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UE27WZ7OLVGHQX7CUD2WGKYCN2","short_pith_number":"pith:UE27WZ7O","canonical_record":{"source":{"id":"1805.06220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-16T10:03:31Z","cross_cats_sorted":[],"title_canon_sha256":"5b00704a3b1671294020d94d27a4bddacf1fc8f1959a7dd647a243a81ef043a1","abstract_canon_sha256":"17623d4e5ad25bf5d54f65a1598a7e9a923d2e6ed65010f5b473e9df3a1c2961"},"schema_version":"1.0"},"canonical_sha256":"a135fb67ee5d4c785fe2a0f5632b026e85113af7de7018d5e4189e9bc6ba91ce","source":{"kind":"arxiv","id":"1805.06220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06220","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06220v2","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06220","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"UE27WZ7OLVGH","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UE27WZ7OLVGHQX7C","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UE27WZ7O","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UE27WZ7OLVGHQX7CUD2WGKYCN2","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-16T10:03:31Z","cross_cats_sorted":[],"title_canon_sha256":"5b00704a3b1671294020d94d27a4bddacf1fc8f1959a7dd647a243a81ef043a1","abstract_canon_sha256":"17623d4e5ad25bf5d54f65a1598a7e9a923d2e6ed65010f5b473e9df3a1c2961"},"schema_version":"1.0"},"canonical_sha256":"a135fb67ee5d4c785fe2a0f5632b026e85113af7de7018d5e4189e9bc6ba91ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:55.956713Z","signature_b64":"z0KkuNmNwsj7n6QWAT67h0ggI3IiP33AuAaoI95WOSTSRTjNvt4yqfXTsaKfHqGOhdXPi65RHcd62M8Sk0d2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a135fb67ee5d4c785fe2a0f5632b026e85113af7de7018d5e4189e9bc6ba91ce","last_reissued_at":"2026-05-18T00:03:55.956013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:55.956013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06220","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P05dV3gunkgOkqLHl3k36OhDwICc4cWkXz1KiVCa5P0cJ78bA4z6ts2dD1+Li0dhJMl9RyNDaWM0cYqbCL/iDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:37:14.393083Z"},"content_sha256":"0fcda92f51d0d75bb4a24253e98b5c51903ee2f3f638e669ad790137836ff7e3","schema_version":"1.0","event_id":"sha256:0fcda92f51d0d75bb4a24253e98b5c51903ee2f3f638e669ad790137836ff7e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UE27WZ7OLVGHQX7CUD2WGKYCN2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform recovery of high-dimensional $C^r$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David Krieg","submitted_at":"2018-05-16T10:03:31Z","abstract_excerpt":"We consider functions on the $d$-dimensional unit cube whose partial derivatives up to order $r$ are bounded by one. It is known that the minimal number of function values that is needed to approximate the integral of such functions up to the error $\\varepsilon$ is of order $(d/ \\varepsilon)^{d/r}$. Among other things, we show that the minimal number of function values that is needed to approximate such functions in the uniform norm is of order $(d^{r/2} /\\varepsilon)^{d/r}$ whenever $r$ is even."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06220","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJTpRQFTK2P58xpQZQcC3zstKIWSLTcot0E/tLrF03xIq4kcnZA/bocrFVbAtZF5PJJ+G4K8TAZwQvcleEoKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:37:14.393437Z"},"content_sha256":"5291eac227a7520b6f9e657b5a5f978af06ef74020cb153637dfec3b5a1d7a37","schema_version":"1.0","event_id":"sha256:5291eac227a7520b6f9e657b5a5f978af06ef74020cb153637dfec3b5a1d7a37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/bundle.json","state_url":"https://pith.science/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T02:37:14Z","links":{"resolver":"https://pith.science/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2","bundle":"https://pith.science/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/bundle.json","state":"https://pith.science/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UE27WZ7OLVGHQX7CUD2WGKYCN2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UE27WZ7OLVGHQX7CUD2WGKYCN2","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":"17623d4e5ad25bf5d54f65a1598a7e9a923d2e6ed65010f5b473e9df3a1c2961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-16T10:03:31Z","title_canon_sha256":"5b00704a3b1671294020d94d27a4bddacf1fc8f1959a7dd647a243a81ef043a1"},"schema_version":"1.0","source":{"id":"1805.06220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06220","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06220v2","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06220","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"UE27WZ7OLVGH","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UE27WZ7OLVGHQX7C","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UE27WZ7O","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:5291eac227a7520b6f9e657b5a5f978af06ef74020cb153637dfec3b5a1d7a37","target":"graph","created_at":"2026-05-18T00:03:55Z","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 functions on the $d$-dimensional unit cube whose partial derivatives up to order $r$ are bounded by one. It is known that the minimal number of function values that is needed to approximate the integral of such functions up to the error $\\varepsilon$ is of order $(d/ \\varepsilon)^{d/r}$. Among other things, we show that the minimal number of function values that is needed to approximate such functions in the uniform norm is of order $(d^{r/2} /\\varepsilon)^{d/r}$ whenever $r$ is even.","authors_text":"David Krieg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-16T10:03:31Z","title":"Uniform recovery of high-dimensional $C^r$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06220","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":"sha256:0fcda92f51d0d75bb4a24253e98b5c51903ee2f3f638e669ad790137836ff7e3","target":"record","created_at":"2026-05-18T00:03:55Z","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":"17623d4e5ad25bf5d54f65a1598a7e9a923d2e6ed65010f5b473e9df3a1c2961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-16T10:03:31Z","title_canon_sha256":"5b00704a3b1671294020d94d27a4bddacf1fc8f1959a7dd647a243a81ef043a1"},"schema_version":"1.0","source":{"id":"1805.06220","kind":"arxiv","version":2}},"canonical_sha256":"a135fb67ee5d4c785fe2a0f5632b026e85113af7de7018d5e4189e9bc6ba91ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a135fb67ee5d4c785fe2a0f5632b026e85113af7de7018d5e4189e9bc6ba91ce","first_computed_at":"2026-05-18T00:03:55.956013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:55.956013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0KkuNmNwsj7n6QWAT67h0ggI3IiP33AuAaoI95WOSTSRTjNvt4yqfXTsaKfHqGOhdXPi65RHcd62M8Sk0d2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:55.956713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fcda92f51d0d75bb4a24253e98b5c51903ee2f3f638e669ad790137836ff7e3","sha256:5291eac227a7520b6f9e657b5a5f978af06ef74020cb153637dfec3b5a1d7a37"],"state_sha256":"740a39e681527f484f98e0bbd9a75e83a596e4e76a1a97fbbe72f9b6c6ecf65f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUU6nwRc8+HIis9gV8LxuUBzB9SGOUdtKTU26G+nd08OHmaZvit5BoxeHUgJo4TKfoAf6vkLF4We+lX8KrQnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:37:14.395385Z","bundle_sha256":"602e33beb7e8a9fadd4da2db1d25642f814bd9f31104e0f158440d398d22aa82"}}