{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5AEGOHOXJO56RBPIBT3M5HDMFL","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":"a48789c608e05e1a8f36d2a3a59ab8445f342807a4c16ea3d74d23c6fd80db5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-01T17:08:03Z","title_canon_sha256":"b8b454cc1920516dcd592262966136204deb1e83aa5fe7508d2399466c97e2c2"},"schema_version":"1.0","source":{"id":"1407.0321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0321","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0321v1","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0321","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"5AEGOHOXJO56","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5AEGOHOXJO56RBPI","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5AEGOHOX","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:18dc8f9f604a9cfa102ef06a6e46587ee48724ebe3ccd9024929347f3b0b0ec4","target":"graph","created_at":"2026-05-18T02:48:34Z","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":"Approximation properties of the expansions $\\sum_{k\\in{\\mathbb z}^d}c_k\\phi(M^jx+k)$, where $M$ is a matrix dilation, $c_k$ is either the sampled value of a signal $f$ at $M^{-j}k$ or the integral average of $f$ near $M^{-j}k$ (falsified sampled value), are studied. Error estimations in $L_p$-norm, $2\\le p\\le\\infty$, are given in terms of the Fourier transform of $f$. The approximation order depends on how smooth is $f$, on the order of Strang-Fix condition for $\\phi$ and on $M$. Some special properties of $\\phi$ are\n  required. To estimate the approximation order of falsified sampling expansi","authors_text":"A. Krivoshein, M. Skopina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-01T17:08:03Z","title":"Multivariate exact and falsified sampling approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0321","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:a7a6a50fad5d3fafa85cc21e35663159a93d531a57be3fd29ba1706c242ac212","target":"record","created_at":"2026-05-18T02:48:34Z","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":"a48789c608e05e1a8f36d2a3a59ab8445f342807a4c16ea3d74d23c6fd80db5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-01T17:08:03Z","title_canon_sha256":"b8b454cc1920516dcd592262966136204deb1e83aa5fe7508d2399466c97e2c2"},"schema_version":"1.0","source":{"id":"1407.0321","kind":"arxiv","version":1}},"canonical_sha256":"e808671dd74bbbe885e80cf6ce9c6c2af3a7dbe6b3023413ac282620de9f09b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e808671dd74bbbe885e80cf6ce9c6c2af3a7dbe6b3023413ac282620de9f09b7","first_computed_at":"2026-05-18T02:48:34.345110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:34.345110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ov6rt+DtBZwyq77UD3TloSAT4AQpngHAw9drv+sjKbesA9dw7W4c8MlFQjZLMz9cwZCHpqrrJnFl1Y4wGbXEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:34.345881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7a6a50fad5d3fafa85cc21e35663159a93d531a57be3fd29ba1706c242ac212","sha256:18dc8f9f604a9cfa102ef06a6e46587ee48724ebe3ccd9024929347f3b0b0ec4"],"state_sha256":"a550ef600e61a0a8c642da34bf07c073f304e65b75075c63f03770d78d2a1894"}