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Under certain conditions on $\\phi$, it is proved that if there exists a positive integer $\\nu$ such that $$\\delta_\\nu:=\\sup\\limits_{i\\in\\mathbb{Z}}(x_{i+\\nu}-x_i)<\\dfrac{\\nu}{2\\pi}\\left(\\dfrac{c_{k}^2}{M_{2k}}\\right)^{\\frac{1}{4k}},$$ then every function belonging to a shift-invariant space $V(\\phi)$ can be reconstructed stably from its nonuniform sample values $\\{f^{(j)}(x_i):j=0,1,\\dots, k-1, i\\in\\mathbb{Z}\\}$, where $c_k$ is a Wirtinger-Sobolev constant and $M_{2"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.00170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-01T09:19:16Z","cross_cats_sorted":[],"title_canon_sha256":"9710fd02f22eb0eb774802d8f39c8dc91f1bd6cb66907551d7058d1c34530958","abstract_canon_sha256":"c0ec6d7c01eb5194a3020d6c9204f096a6aa2026036a4ad52f094921637a6009"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:35.031789Z","signature_b64":"th6Rj2hmk3xUPotXY60ukQspIE1gc+BFGTsOplSVmybgvxH5XL57DbFWBPQMNt2Tq8BEqqC8m+3SZqCu7jy1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87581076ec60865221087db0dbd8013baef5b209b556bde459756e21a6d5633a","last_reissued_at":"2026-05-18T00:51:35.031409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:35.031409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new sampling density condition for shift-invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. 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