{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:EMLNCHQDUM3JEJO2NQ3H63C3ZZ","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":"e78e4bf025691e177e796c3ee3e2cb7720a81d5dbf9e8f78dcd00e7af51c4c42","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-09-30T09:53:23Z","title_canon_sha256":"776cc9c07e648075823776f445bcd2e664823659c31807538cd8de8bbf3b5769"},"schema_version":"1.0","source":{"id":"0809.5153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.5153","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"0809.5153v1","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.5153","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"EMLNCHQDUM3J","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"EMLNCHQDUM3JEJO2","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"EMLNCHQD","created_at":"2026-06-03T22:06:10Z"}],"graph_snapshots":[{"event_id":"sha256:7f78fb0e843be1aaad5b8797a98885cd62a3845ce00b90fe8622337844c4f908","target":"graph","created_at":"2026-06-03T22:06:10Z","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/0809.5153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the monograph Kounchev, O. I., Multivariate Polysplines. Applications to Numerical and Wavelet Analysis, Academic Press, San Diego-London, 2001, and in the paper Kounchev O., Render, H., Cardinal interpolation with polysplines on annuli, Journal of Approximation Theory 137 (2005) 89--107, we have introduced and studied a new paradigm for cardinal interpolation which is related to the theory of multivariate polysplines. In the present paper we show that this is related to a new sampling paradigm in the multivariate case, whereas we obtain a Shannon type function $S(x) $ and the following Sha","authors_text":"Hermann Render, Ognyan Kounchev","cross_cats":["cs.IT","cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-09-30T09:53:23Z","title":"On a new multivariate sampling paradigm and a polyspline Shannon function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.5153","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":"sha256:6588a29c747ea654cb2249957e72dbe377643d8ae338a4aee10696caac2c7304","target":"record","created_at":"2026-06-03T22:06:10Z","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":"e78e4bf025691e177e796c3ee3e2cb7720a81d5dbf9e8f78dcd00e7af51c4c42","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-09-30T09:53:23Z","title_canon_sha256":"776cc9c07e648075823776f445bcd2e664823659c31807538cd8de8bbf3b5769"},"schema_version":"1.0","source":{"id":"0809.5153","kind":"arxiv","version":1}},"canonical_sha256":"2316d11e03a3369225da6c367f6c5bce4c28854dad1df5f28a06dbd9bea27a60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2316d11e03a3369225da6c367f6c5bce4c28854dad1df5f28a06dbd9bea27a60","first_computed_at":"2026-06-03T22:06:10.332877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:10.332877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKh06E01UbMqDeoDGzux//F7YJCVSLA7xp9ea8w0PGLCnquy2iTeJnFBUsYYITKcOroTyx3DZRXfr53cCraFDQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:10.333631Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.5153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6588a29c747ea654cb2249957e72dbe377643d8ae338a4aee10696caac2c7304","sha256:7f78fb0e843be1aaad5b8797a98885cd62a3845ce00b90fe8622337844c4f908"],"state_sha256":"1ca4aa84acdd2d126f2e40fc93cdae0d3b0c3b51ae2d62f7d83b84d3d32e37bd"}