{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GT5D7ZYB32AIYVNCZCGAZLFJ7E","short_pith_number":"pith:GT5D7ZYB","canonical_record":{"source":{"id":"1211.5822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-25T23:46:01Z","cross_cats_sorted":[],"title_canon_sha256":"f5d4092d5833430bc87a38fe5e268d2273e471697ee99bb321f074594845fc6d","abstract_canon_sha256":"1ffe05c387c41550cb1375575cef5c206a4ff3c4e9f8db3f7d3b99e3f9fa6438"},"schema_version":"1.0"},"canonical_sha256":"34fa3fe701de808c55a2c88c0caca9f93074e1400c71d6b1d6702a32d18cf1f4","source":{"kind":"arxiv","id":"1211.5822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5822","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5822v1","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5822","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"GT5D7ZYB32AI","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GT5D7ZYB32AIYVNC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GT5D7ZYB","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GT5D7ZYB32AIYVNCZCGAZLFJ7E","target":"record","payload":{"canonical_record":{"source":{"id":"1211.5822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-25T23:46:01Z","cross_cats_sorted":[],"title_canon_sha256":"f5d4092d5833430bc87a38fe5e268d2273e471697ee99bb321f074594845fc6d","abstract_canon_sha256":"1ffe05c387c41550cb1375575cef5c206a4ff3c4e9f8db3f7d3b99e3f9fa6438"},"schema_version":"1.0"},"canonical_sha256":"34fa3fe701de808c55a2c88c0caca9f93074e1400c71d6b1d6702a32d18cf1f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:01.867082Z","signature_b64":"DUbsuZdB/3uUQupA2K2clWaIKK5pTpJz1DYpiW7agCm0lZ8yOihdBxYoUUdUELEl4OI8X00zYV6HRkBJDn/CCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34fa3fe701de808c55a2c88c0caca9f93074e1400c71d6b1d6702a32d18cf1f4","last_reissued_at":"2026-05-18T03:40:01.866570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:01.866570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.5822","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":"2026-05-18T03:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vasIdsGgzHRkUBuYOdYpeFLxOpouMPpcfmkjdvsmFih+AyrFV1Xr0v9yNCBYdNMjmjkQLCNxGZNvQVk88AwWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:14:52.298292Z"},"content_sha256":"5f26ee05acf7e0e5c80a30f587f13b4c2109f30e2946b28986bf871415dfb48b","schema_version":"1.0","event_id":"sha256:5f26ee05acf7e0e5c80a30f587f13b4c2109f30e2946b28986bf871415dfb48b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GT5D7ZYB32AIYVNCZCGAZLFJ7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of analytic functions in Korobov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Friedrich Pillichshammer, Henryk Wo\\'zniakowski, Josef Dick, Peter Kritzer","submitted_at":"2012-11-25T23:46:01Z","abstract_excerpt":"We study multivariate $L_2$-approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences $\\boldsymbol{a} =\\{a_j\\}$ and $\\boldsymbol{b} =\\{b_j\\}$ of numbers no less than one. Let $e^{L_2-\\mathrm{app},\\Lambda}(n,s)$ be the minimal worst-case error of all algorithms that use $n$ information functionals from the class $\\Lambda$ in the $s$-variate case. We consider two classes $\\Lambda$: the class $\\Lambda^{{\\rm all}}$ consists of all linear functionals and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5822","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":"2026-05-18T03:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yoU65AfbD04/tG+5uOWPpCYGtf122m5RbGdhlKyjMBLkiaFBeeynf+ukTQk9uXOXO+w9cQgFN9289YH6d2rwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:14:52.298946Z"},"content_sha256":"6f5e0bb2ee31dc41866e469cc350b6e3faa225481c8062c4cedcb094b8cd25d0","schema_version":"1.0","event_id":"sha256:6f5e0bb2ee31dc41866e469cc350b6e3faa225481c8062c4cedcb094b8cd25d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/bundle.json","state_url":"https://pith.science/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/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":"2026-05-27T12:14:52Z","links":{"resolver":"https://pith.science/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E","bundle":"https://pith.science/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/bundle.json","state":"https://pith.science/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GT5D7ZYB32AIYVNCZCGAZLFJ7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GT5D7ZYB32AIYVNCZCGAZLFJ7E","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":"1ffe05c387c41550cb1375575cef5c206a4ff3c4e9f8db3f7d3b99e3f9fa6438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-25T23:46:01Z","title_canon_sha256":"f5d4092d5833430bc87a38fe5e268d2273e471697ee99bb321f074594845fc6d"},"schema_version":"1.0","source":{"id":"1211.5822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5822","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5822v1","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5822","created_at":"2026-05-18T03:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"GT5D7ZYB32AI","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GT5D7ZYB32AIYVNC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GT5D7ZYB","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:6f5e0bb2ee31dc41866e469cc350b6e3faa225481c8062c4cedcb094b8cd25d0","target":"graph","created_at":"2026-05-18T03:40:01Z","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 study multivariate $L_2$-approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences $\\boldsymbol{a} =\\{a_j\\}$ and $\\boldsymbol{b} =\\{b_j\\}$ of numbers no less than one. Let $e^{L_2-\\mathrm{app},\\Lambda}(n,s)$ be the minimal worst-case error of all algorithms that use $n$ information functionals from the class $\\Lambda$ in the $s$-variate case. We consider two classes $\\Lambda$: the class $\\Lambda^{{\\rm all}}$ consists of all linear functionals and the","authors_text":"Friedrich Pillichshammer, Henryk Wo\\'zniakowski, Josef Dick, Peter Kritzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-25T23:46:01Z","title":"Approximation of analytic functions in Korobov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5822","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":"sha256:5f26ee05acf7e0e5c80a30f587f13b4c2109f30e2946b28986bf871415dfb48b","target":"record","created_at":"2026-05-18T03:40:01Z","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":"1ffe05c387c41550cb1375575cef5c206a4ff3c4e9f8db3f7d3b99e3f9fa6438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-25T23:46:01Z","title_canon_sha256":"f5d4092d5833430bc87a38fe5e268d2273e471697ee99bb321f074594845fc6d"},"schema_version":"1.0","source":{"id":"1211.5822","kind":"arxiv","version":1}},"canonical_sha256":"34fa3fe701de808c55a2c88c0caca9f93074e1400c71d6b1d6702a32d18cf1f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34fa3fe701de808c55a2c88c0caca9f93074e1400c71d6b1d6702a32d18cf1f4","first_computed_at":"2026-05-18T03:40:01.866570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:01.866570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DUbsuZdB/3uUQupA2K2clWaIKK5pTpJz1DYpiW7agCm0lZ8yOihdBxYoUUdUELEl4OI8X00zYV6HRkBJDn/CCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:01.867082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f26ee05acf7e0e5c80a30f587f13b4c2109f30e2946b28986bf871415dfb48b","sha256:6f5e0bb2ee31dc41866e469cc350b6e3faa225481c8062c4cedcb094b8cd25d0"],"state_sha256":"9086a19081eb7ce8cd231008d1ca147ca78e67fb2fa7bf4f985b0dd142e9ebd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLz6mwLVmJutbku55Yhx2UBeRJQUgeXAZ4gfw0aEyz6nz7tin8ZZbrNO3a4FHFAplIv+mwZ87lWW5nrLDDvBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:14:52.302156Z","bundle_sha256":"3878e3ff9a0037c8bd3b9db7d4fef630525c638febba1024db708d38725a8f6d"}}