{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RWFZO3VLTQG35PRNAK2ACVE5KV","short_pith_number":"pith:RWFZO3VL","canonical_record":{"source":{"id":"2412.02797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-03T20:00:11Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"2945e7a1bbf9288577c880115a114843d015ca9794f82e98bd57c75e70f850a5","abstract_canon_sha256":"9a0db65b49cc7bed37799b0a2020aad35eb38d900533669449674a6e098dba83"},"schema_version":"1.0"},"canonical_sha256":"8d8b976eab9c0dbebe2d02b401549d55638e4127d3239fbb22e4267399eb78b4","source":{"kind":"arxiv","id":"2412.02797","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.02797","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.02797v2","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.02797","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"RWFZO3VLTQG3","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"RWFZO3VLTQG35PRN","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"RWFZO3VL","created_at":"2026-07-05T11:10:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RWFZO3VLTQG35PRNAK2ACVE5KV","target":"record","payload":{"canonical_record":{"source":{"id":"2412.02797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-03T20:00:11Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"2945e7a1bbf9288577c880115a114843d015ca9794f82e98bd57c75e70f850a5","abstract_canon_sha256":"9a0db65b49cc7bed37799b0a2020aad35eb38d900533669449674a6e098dba83"},"schema_version":"1.0"},"canonical_sha256":"8d8b976eab9c0dbebe2d02b401549d55638e4127d3239fbb22e4267399eb78b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:49.324299Z","signature_b64":"GbZRxplPZ8unqLt/R7AIzjzBv6v4OHwVrhs2vjEFo8Q5KZyi/5s3VET2FCefZkTWenu6O6XUPhUeovPOpu60DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8b976eab9c0dbebe2d02b401549d55638e4127d3239fbb22e4267399eb78b4","last_reissued_at":"2026-07-05T11:10:49.323799Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:49.323799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.02797","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":"2026-07-05T11:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1viTm5OHnrV44KJA69PeSilvav2OqH1/96oq+bHxIYyoGiyL5eKTVvqVi+dSvqZ/o/LfQiruozGvuaBfKGvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:52:51.096568Z"},"content_sha256":"b41f336ca827fb9b84f798d22620c15270637f004258a313fa3f9d604a800707","schema_version":"1.0","event_id":"sha256:b41f336ca827fb9b84f798d22620c15270637f004258a313fa3f9d604a800707"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RWFZO3VLTQG35PRNAK2ACVE5KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some lower bounds for optimal sampling recovery of functions with mixed smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"A. Gasnikov, V. Temlyakov","submitted_at":"2024-12-03T20:00:11Z","abstract_excerpt":"Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes optimal upper bounds for both linear sampling recovery and for nonlinear sampling recovery. In this paper we address the problem of lower bounds for the optimal rates of nonlinear sampling recovery.\n  In the case of linear recovery one can use the well developed theory of estimating the Kolmogorov and linear widths for establishing some lower bounds for the optimal rates. In the case of nonlinear recovery we cannot use t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02797","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.02797/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5JA4AW9MCNoaJgTxcdwIDzCefBL0bArYZamI+zV/9yZ8LAooe9QOZptqqT7lyMNj6YGVq6Wf98itlSlwSK0pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T04:52:51.097164Z"},"content_sha256":"a287b648770e60a9fdb51d8470ebe0843f96d7e1fa4603a4a5b387406152d3b8","schema_version":"1.0","event_id":"sha256:a287b648770e60a9fdb51d8470ebe0843f96d7e1fa4603a4a5b387406152d3b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/bundle.json","state_url":"https://pith.science/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/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":"2026-08-17T04:52:51Z","links":{"resolver":"https://pith.science/pith/RWFZO3VLTQG35PRNAK2ACVE5KV","bundle":"https://pith.science/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/bundle.json","state":"https://pith.science/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWFZO3VLTQG35PRNAK2ACVE5KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RWFZO3VLTQG35PRNAK2ACVE5KV","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":"9a0db65b49cc7bed37799b0a2020aad35eb38d900533669449674a6e098dba83","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-03T20:00:11Z","title_canon_sha256":"2945e7a1bbf9288577c880115a114843d015ca9794f82e98bd57c75e70f850a5"},"schema_version":"1.0","source":{"id":"2412.02797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.02797","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.02797v2","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.02797","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"RWFZO3VLTQG3","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"RWFZO3VLTQG35PRN","created_at":"2026-07-05T11:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"RWFZO3VL","created_at":"2026-07-05T11:10:49Z"}],"graph_snapshots":[{"event_id":"sha256:a287b648770e60a9fdb51d8470ebe0843f96d7e1fa4603a4a5b387406152d3b8","target":"graph","created_at":"2026-07-05T11:10:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.02797/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes optimal upper bounds for both linear sampling recovery and for nonlinear sampling recovery. In this paper we address the problem of lower bounds for the optimal rates of nonlinear sampling recovery.\n  In the case of linear recovery one can use the well developed theory of estimating the Kolmogorov and linear widths for establishing some lower bounds for the optimal rates. In the case of nonlinear recovery we cannot use t","authors_text":"A. Gasnikov, V. Temlyakov","cross_cats":["cs.NA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-03T20:00:11Z","title":"Some lower bounds for optimal sampling recovery of functions with mixed smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02797","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:b41f336ca827fb9b84f798d22620c15270637f004258a313fa3f9d604a800707","target":"record","created_at":"2026-07-05T11:10:49Z","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":"9a0db65b49cc7bed37799b0a2020aad35eb38d900533669449674a6e098dba83","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-03T20:00:11Z","title_canon_sha256":"2945e7a1bbf9288577c880115a114843d015ca9794f82e98bd57c75e70f850a5"},"schema_version":"1.0","source":{"id":"2412.02797","kind":"arxiv","version":2}},"canonical_sha256":"8d8b976eab9c0dbebe2d02b401549d55638e4127d3239fbb22e4267399eb78b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8b976eab9c0dbebe2d02b401549d55638e4127d3239fbb22e4267399eb78b4","first_computed_at":"2026-07-05T11:10:49.323799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:49.323799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GbZRxplPZ8unqLt/R7AIzjzBv6v4OHwVrhs2vjEFo8Q5KZyi/5s3VET2FCefZkTWenu6O6XUPhUeovPOpu60DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:49.324299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.02797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b41f336ca827fb9b84f798d22620c15270637f004258a313fa3f9d604a800707","sha256:a287b648770e60a9fdb51d8470ebe0843f96d7e1fa4603a4a5b387406152d3b8"],"state_sha256":"7f2996a564eb765ce7497425503c99698997febf2af88eeead5cab315cf41653"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Reh7MzPY1dJiSMtOlGHtTaG4XaHasltFYXopAfLVambQfluEiSpK/kcOf0FpjBbe04yjAvBh1zB2e2uNQCfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T04:52:51.103032Z","bundle_sha256":"9ddbb2f52cf5cab49c1d21ab357d2087bef786304cd46f316bf3f0ebbca9f6b9"}}