{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I4Y7KHKA64NGCMVFMOBTS4XYA2","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":"1b06717d6aa4bfde70b4b02093d637ec01b1dd69377aea4e918a5f862f7f9e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-19T13:09:26Z","title_canon_sha256":"1022288ab807d43de0e404a23aa26274164d04bcd595c7f3ec86ac3e05d6512a"},"schema_version":"1.0","source":{"id":"1711.07017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07017","created_at":"2026-05-18T00:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07017v1","created_at":"2026-05-18T00:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07017","created_at":"2026-05-18T00:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"I4Y7KHKA64NG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I4Y7KHKA64NGCMVF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I4Y7KHKA","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:8a9d04be40bebe2fd175868e9596eaf7a7852faceb2ff663890353da32b99eda","target":"graph","created_at":"2026-05-18T00:30:14Z","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":"The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work in proving lower bounds for recently developed new type of discrepancy -- the smooth discrepancy.","authors_text":"V.N. Temlyakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-19T13:09:26Z","title":"Remarks on numerical integration, discrepancy, and diaphony"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07017","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:aba866491e902c776c8d98d0ddf578a95c4bc334b4c3427251557300cd5d1ec3","target":"record","created_at":"2026-05-18T00:30:14Z","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":"1b06717d6aa4bfde70b4b02093d637ec01b1dd69377aea4e918a5f862f7f9e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-19T13:09:26Z","title_canon_sha256":"1022288ab807d43de0e404a23aa26274164d04bcd595c7f3ec86ac3e05d6512a"},"schema_version":"1.0","source":{"id":"1711.07017","kind":"arxiv","version":1}},"canonical_sha256":"4731f51d40f71a6132a563833972f80686439767db565f36e8582b51ac9df240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4731f51d40f71a6132a563833972f80686439767db565f36e8582b51ac9df240","first_computed_at":"2026-05-18T00:30:14.814517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:14.814517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2g/EWY9WnbeAMfG/Hy8Bm0wxT8MiPzCi25gIzZT28HanDuxYDFtbYci+slci49NGht5y4bgBQgDLBVK/wcKaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:14.815277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aba866491e902c776c8d98d0ddf578a95c4bc334b4c3427251557300cd5d1ec3","sha256:8a9d04be40bebe2fd175868e9596eaf7a7852faceb2ff663890353da32b99eda"],"state_sha256":"ddbea74cdddc306b178c59a503f0d205f5465a5bcc9ad364d1dbb8214c76b3d6"}