{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LIT3KZIVWJKSNZI6JHJG2YYSNM","short_pith_number":"pith:LIT3KZIV","canonical_record":{"source":{"id":"1402.5489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-22T07:00:40Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"68783de716b8e06161c4e9d004fce904e251083d088af99a1293056a4216c08f","abstract_canon_sha256":"00dd3e8318734af1283645f8e5e31a2fc8dd0a359e3f8be74165a28a77def0f9"},"schema_version":"1.0"},"canonical_sha256":"5a27b56515b25526e51e49d26d63126b0054a14fcc61c2cd49bc7c348778a5f5","source":{"kind":"arxiv","id":"1402.5489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5489","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5489v1","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5489","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LIT3KZIVWJKS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LIT3KZIVWJKSNZI6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LIT3KZIV","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LIT3KZIVWJKSNZI6JHJG2YYSNM","target":"record","payload":{"canonical_record":{"source":{"id":"1402.5489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-22T07:00:40Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"68783de716b8e06161c4e9d004fce904e251083d088af99a1293056a4216c08f","abstract_canon_sha256":"00dd3e8318734af1283645f8e5e31a2fc8dd0a359e3f8be74165a28a77def0f9"},"schema_version":"1.0"},"canonical_sha256":"5a27b56515b25526e51e49d26d63126b0054a14fcc61c2cd49bc7c348778a5f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:37.694122Z","signature_b64":"QuPfVfTTHSfE3tOJr7w1WvCkElNuaByzs9ZktWonSB4RPfaUNFkLqYl8LaX9qZ4lbOb1G+DdhJReqPyDyatuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a27b56515b25526e51e49d26d63126b0054a14fcc61c2cd49bc7c348778a5f5","last_reissued_at":"2026-05-17T23:41:37.693341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:37.693341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.5489","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":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ym0XytCGzhtFvpWFC7bQc3OqkTnrxLWstygFqa46CgDWuil8t9lpo3Qk6LcUA1msGkFQly5ITTPNtoDum9UyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:14:39.458257Z"},"content_sha256":"8110ba36c053362c5ab0cc39e8c9fc2eeb034dd841be7a92490f366d3d05f712","schema_version":"1.0","event_id":"sha256:8110ba36c053362c5ab0cc39e8c9fc2eeb034dd841be7a92490f366d3d05f712"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LIT3KZIVWJKSNZI6JHJG2YYSNM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of additive random fields based on standard information: average case and probabilistic settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Marguerite Zani, Mikhail Lifshits","submitted_at":"2014-02-22T07:00:40Z","abstract_excerpt":"We consider approximation problems for tensor product and additive random fields based on standard information in the average case setting. We also study the probabilistic setting of the mentioned problem for tensor products. The main question we are concerned with in this paper is ``How much do we loose by considering standard information algorithms against those using general linear information?'' For both types of the fields, the error of linear algorithms has been studied in great detail. However, the power of standard information for them was not addressed so far, which we do here. Our ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5489","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":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qqg03xK5hl6FSrenFAPMkeTvTD4+aDLKET/uMtdaV6n7iStPGVZ2KHd72ST0MmG9R9C7+moo2RdsiuWpwqlqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:14:39.458790Z"},"content_sha256":"cf39ceb8ed88594648498cba45afd7972965384db0c65703dbe2e7e00c577506","schema_version":"1.0","event_id":"sha256:cf39ceb8ed88594648498cba45afd7972965384db0c65703dbe2e7e00c577506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/bundle.json","state_url":"https://pith.science/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/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":"2026-05-27T20:14:39Z","links":{"resolver":"https://pith.science/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM","bundle":"https://pith.science/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/bundle.json","state":"https://pith.science/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIT3KZIVWJKSNZI6JHJG2YYSNM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LIT3KZIVWJKSNZI6JHJG2YYSNM","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":"00dd3e8318734af1283645f8e5e31a2fc8dd0a359e3f8be74165a28a77def0f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-22T07:00:40Z","title_canon_sha256":"68783de716b8e06161c4e9d004fce904e251083d088af99a1293056a4216c08f"},"schema_version":"1.0","source":{"id":"1402.5489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5489","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5489v1","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5489","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LIT3KZIVWJKS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LIT3KZIVWJKSNZI6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LIT3KZIV","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:cf39ceb8ed88594648498cba45afd7972965384db0c65703dbe2e7e00c577506","target":"graph","created_at":"2026-05-17T23:41:37Z","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 approximation problems for tensor product and additive random fields based on standard information in the average case setting. We also study the probabilistic setting of the mentioned problem for tensor products. The main question we are concerned with in this paper is ``How much do we loose by considering standard information algorithms against those using general linear information?'' For both types of the fields, the error of linear algorithms has been studied in great detail. However, the power of standard information for them was not addressed so far, which we do here. Our ma","authors_text":"Marguerite Zani, Mikhail Lifshits","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-22T07:00:40Z","title":"Approximation of additive random fields based on standard information: average case and probabilistic settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5489","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":"sha256:8110ba36c053362c5ab0cc39e8c9fc2eeb034dd841be7a92490f366d3d05f712","target":"record","created_at":"2026-05-17T23:41:37Z","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":"00dd3e8318734af1283645f8e5e31a2fc8dd0a359e3f8be74165a28a77def0f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-22T07:00:40Z","title_canon_sha256":"68783de716b8e06161c4e9d004fce904e251083d088af99a1293056a4216c08f"},"schema_version":"1.0","source":{"id":"1402.5489","kind":"arxiv","version":1}},"canonical_sha256":"5a27b56515b25526e51e49d26d63126b0054a14fcc61c2cd49bc7c348778a5f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a27b56515b25526e51e49d26d63126b0054a14fcc61c2cd49bc7c348778a5f5","first_computed_at":"2026-05-17T23:41:37.693341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:37.693341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuPfVfTTHSfE3tOJr7w1WvCkElNuaByzs9ZktWonSB4RPfaUNFkLqYl8LaX9qZ4lbOb1G+DdhJReqPyDyatuDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:37.694122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8110ba36c053362c5ab0cc39e8c9fc2eeb034dd841be7a92490f366d3d05f712","sha256:cf39ceb8ed88594648498cba45afd7972965384db0c65703dbe2e7e00c577506"],"state_sha256":"bb4422da60ee5f71adcf5eb63b8ab93bb3314e6bdd969476f069b0f266c30b26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aK3ZMss7LwywTGrCq8tyxCX6yvYkWbejMARztnbwG6xjNGUYJxhy1NzMtnYsOHHF1IfLFGHFXBc3SHvREtbsDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:14:39.461900Z","bundle_sha256":"3afbeace786c55023f4d67ce02af67baf3cd50ae41bb1223e7dd18cf64972936"}}