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Given the efficacy of random constructions in generating useful RIP matrices, the problem of certifying the RIP parameters of a matrix has become important.\n  In this paper, we prove"},"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":"1406.5791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-06-23T02:08:08Z","cross_cats_sorted":[],"title_canon_sha256":"bb8c4790a350423b6bce3b8ec1781b8fedfd9c506943426d3a86cbd59566bc21","abstract_canon_sha256":"eac8f37e21b04ed7c9b7896c5d561b4080989b634a57dd2e055183cef6c40e37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.747536Z","signature_b64":"pv433wTqnHi+z0TN8x60zqol5JUXrMwi0JAni3YrAc1xvrMberIT5MaCr0jyrmeHhtOP5vscIbORXI3d00KHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df57809dbbd06754209ff70482a5f6bfd36829a7d0e3f90b9f51c5f234678201","last_reissued_at":"2026-05-18T02:49:10.747032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.747032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational Complexity of Certifying Restricted Isometry Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abhiram Natarajan, Yi Wu","submitted_at":"2014-06-23T02:08:08Z","abstract_excerpt":"Given a matrix $A$ with $n$ rows, a number $k<n$, and $0<\\delta < 1$, $A$ is $(k,\\delta)$-RIP (Restricted Isometry Property) if, for any vector $x \\in \\mathbb{R}^n$, with at most $k$ non-zero co-ordinates, $$(1-\\delta) \\|x\\|_2 \\leq \\|A x\\|_2 \\leq (1+\\delta)\\|x\\|_2$$ In many applications, such as compressed sensing and sparse recovery, it is desirable to construct RIP matrices with a large $k$ and a small $\\delta$. 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