{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QR4QCSZSGQH2HT2EMHUDPWRDA3","short_pith_number":"pith:QR4QCSZS","canonical_record":{"source":{"id":"1709.03321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T10:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"5a010e82f4775d3938f720610eb544398fda2bacf12ee946d47440267047a14a","abstract_canon_sha256":"d8ca49a40428a133c027f4cfa6b998fdd2a93c5a7f6c1cb8e4f495f94d805d69"},"schema_version":"1.0"},"canonical_sha256":"8479014b32340fa3cf4461e837da2306fbfc2c79b0165882f22ff4f30b185e60","source":{"kind":"arxiv","id":"1709.03321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03321","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03321v1","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03321","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"QR4QCSZSGQH2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QR4QCSZSGQH2HT2E","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QR4QCSZS","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QR4QCSZSGQH2HT2EMHUDPWRDA3","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T10:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"5a010e82f4775d3938f720610eb544398fda2bacf12ee946d47440267047a14a","abstract_canon_sha256":"d8ca49a40428a133c027f4cfa6b998fdd2a93c5a7f6c1cb8e4f495f94d805d69"},"schema_version":"1.0"},"canonical_sha256":"8479014b32340fa3cf4461e837da2306fbfc2c79b0165882f22ff4f30b185e60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:15.997638Z","signature_b64":"wvRqe7lSljXRavoESqZMULct/SjTBNAQ9IwG9kcPgXAUnwKwfVz2DUn31zszNfo9yo/I7E/TJ9wsa4AZ4geGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8479014b32340fa3cf4461e837da2306fbfc2c79b0165882f22ff4f30b185e60","last_reissued_at":"2026-05-18T00:22:15.997123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:15.997123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03321","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vx5xhEvneoftT7NvuuO+zw+2QeWi8/O4ofAzylGVe8eGbcNXjYb5mv/MP+WUaFKzvGf3irrmn3GYm6Wm/imgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:27:34.691945Z"},"content_sha256":"b31cb9d606be4865cf8a10f25eca0c425d9e5a038936942caa388f48328fb86d","schema_version":"1.0","event_id":"sha256:b31cb9d606be4865cf8a10f25eca0c425d9e5a038936942caa388f48328fb86d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QR4QCSZSGQH2HT2EMHUDPWRDA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen","submitted_at":"2017-09-11T10:18:16Z","abstract_excerpt":"We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\\mathbb{T}^d$ into the space $L_{\\infty}(\\mathbb{T}^d)$ via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to $1/2$ in the main rate compared to the worst case approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03321","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2yCz7dWIpyN6Lk9rEfaTVtycav1dwRePw0E20V361mJlS8vkb3n69JfHVpoXU+buabQedAM4tHoxMpdPYGcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:27:34.692580Z"},"content_sha256":"bb599b260e41e4b6301081c05afb91fa0074b3d07c99d063678b34823a62ee38","schema_version":"1.0","event_id":"sha256:bb599b260e41e4b6301081c05afb91fa0074b3d07c99d063678b34823a62ee38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/bundle.json","state_url":"https://pith.science/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/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":"2026-05-26T04:27:34Z","links":{"resolver":"https://pith.science/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3","bundle":"https://pith.science/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/bundle.json","state":"https://pith.science/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QR4QCSZSGQH2HT2EMHUDPWRDA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QR4QCSZSGQH2HT2EMHUDPWRDA3","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":"d8ca49a40428a133c027f4cfa6b998fdd2a93c5a7f6c1cb8e4f495f94d805d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T10:18:16Z","title_canon_sha256":"5a010e82f4775d3938f720610eb544398fda2bacf12ee946d47440267047a14a"},"schema_version":"1.0","source":{"id":"1709.03321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03321","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03321v1","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03321","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"QR4QCSZSGQH2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QR4QCSZSGQH2HT2E","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QR4QCSZS","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:bb599b260e41e4b6301081c05afb91fa0074b3d07c99d063678b34823a62ee38","target":"graph","created_at":"2026-05-18T00:22:15Z","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 order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\\mathbb{T}^d$ into the space $L_{\\infty}(\\mathbb{T}^d)$ via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to $1/2$ in the main rate compared to the worst case approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan.","authors_text":"Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T10:18:16Z","title":"Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03321","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:b31cb9d606be4865cf8a10f25eca0c425d9e5a038936942caa388f48328fb86d","target":"record","created_at":"2026-05-18T00:22:15Z","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":"d8ca49a40428a133c027f4cfa6b998fdd2a93c5a7f6c1cb8e4f495f94d805d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-11T10:18:16Z","title_canon_sha256":"5a010e82f4775d3938f720610eb544398fda2bacf12ee946d47440267047a14a"},"schema_version":"1.0","source":{"id":"1709.03321","kind":"arxiv","version":1}},"canonical_sha256":"8479014b32340fa3cf4461e837da2306fbfc2c79b0165882f22ff4f30b185e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8479014b32340fa3cf4461e837da2306fbfc2c79b0165882f22ff4f30b185e60","first_computed_at":"2026-05-18T00:22:15.997123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:15.997123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wvRqe7lSljXRavoESqZMULct/SjTBNAQ9IwG9kcPgXAUnwKwfVz2DUn31zszNfo9yo/I7E/TJ9wsa4AZ4geGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:15.997638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b31cb9d606be4865cf8a10f25eca0c425d9e5a038936942caa388f48328fb86d","sha256:bb599b260e41e4b6301081c05afb91fa0074b3d07c99d063678b34823a62ee38"],"state_sha256":"3413f9269fe978b264dd405bae483905c24dcb3233d57f22f6dee431ab8fcd41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qZHBUqVgh97eLs6p3H5HYW48SMZRswt5ibpFF5fR60W3CODLV7wnLcqKHthfjnyRBI5bY8H3vvNsy5O5Yd3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:27:34.696066Z","bundle_sha256":"a6de1917157ed324a277263a44a7fd743070563fe01d84a71401c7f7b2c4252e"}}