{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UKZY3J2J5WNIK5X437SACOB56C","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":"18e47d557d7ffc0a859d0a447bdfecf8b7ce0b2203ed4a0c694159663234c402","cross_cats_sorted":["cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T13:37:49Z","title_canon_sha256":"0ce7aee0fd2cc462d1021fe8c0c7bbf9c4e80a9a8046c2bf72a0eb2c532aa86a"},"schema_version":"1.0","source":{"id":"1206.5986","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5986","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5986v3","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5986","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"UKZY3J2J5WNI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UKZY3J2J5WNIK5X4","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UKZY3J2J","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:eca8381bb1df0e7337fd13d2b9e341eff26537eedf7e30f50ec7f7a86340c612","target":"graph","created_at":"2026-05-18T03:21:54Z","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":"We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements (with high probability) is known to be $m\\gtrsim s(\\ln s)^3\\ln N$. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of $m\\times N$-matrices, by considering what we call \\emph{low entropy}. We also present an improved condition on the so-called restricted iso","authors_text":"Jan-Olov Str\\\"omberg, Joel Andersson","cross_cats":["cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T13:37:49Z","title":"On the Theorem of Uniform Recovery of Random Sampling Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5986","kind":"arxiv","version":3},"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:e4873adb39e7d02a65acec000345fbdcd2cc8dd8527a6005e5c6b7c3e44c6694","target":"record","created_at":"2026-05-18T03:21:54Z","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":"18e47d557d7ffc0a859d0a447bdfecf8b7ce0b2203ed4a0c694159663234c402","cross_cats_sorted":["cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-26T13:37:49Z","title_canon_sha256":"0ce7aee0fd2cc462d1021fe8c0c7bbf9c4e80a9a8046c2bf72a0eb2c532aa86a"},"schema_version":"1.0","source":{"id":"1206.5986","kind":"arxiv","version":3}},"canonical_sha256":"a2b38da749ed9a8576fcdfe401383df0a57e8a803955c50585a45f424b641b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b38da749ed9a8576fcdfe401383df0a57e8a803955c50585a45f424b641b2a","first_computed_at":"2026-05-18T03:21:54.125708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:54.125708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8mrUPTGjZAHGJ9l1Z9aNfADwtZ3zPKtnlei35/54kj60sxna1FAAIC96UQpWNgnY9Y6+TmZIBFVezml8aboBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:54.126096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5986","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4873adb39e7d02a65acec000345fbdcd2cc8dd8527a6005e5c6b7c3e44c6694","sha256:eca8381bb1df0e7337fd13d2b9e341eff26537eedf7e30f50ec7f7a86340c612"],"state_sha256":"2f27bd163b5048adb8b1583f2b82dde037916ba3e5bd4f95acb2dfaf132f7d10"}