{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GTZMTCSF2H3JY32CPBKIP36UGB","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":"8a1eba11049159b41d2603ccdcb351263f5e29991b9cd3ef4cdd7f6aac18922e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:14:28Z","title_canon_sha256":"27a55928aa031c65ddc2b330750326919356fd7952108c7bf5e4fe167fd07106"},"schema_version":"1.0","source":{"id":"1807.04643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04643","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04643v1","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04643","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"pith_short_12","alias_value":"GTZMTCSF2H3J","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GTZMTCSF2H3JY32C","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GTZMTCSF","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:dd3aa842caf49ca528ee038656e785873debcafa85b3f39c8b5ec33f2db587ea","target":"graph","created_at":"2026-05-18T00:10:52Z","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":"Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied in the literature. In this paper, we show that for any $K$-sparse signal $\\x$, if the sensing matrix $\\A$ satisfies the restricted isometry property (RIP) of order $K + 1$ with restricted isometry constant (RIC) $\\delta_{K+1} < 1/\\sqrt {K+1}$, then under some constraint on the minimum magnitude of the nonzero elements of $\\x$, the OMP algorithm exactly recovers the support of $\\x$ from the measurements $\\y=\\A\\x+\\v$ in $K$ iterations, where $\\v$ is the noise vector. Thi","authors_text":"Jian Wang, Jinming Wen, Qun Mo, Xiaohu Tang, Zhengchun Zhou","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:14:28Z","title":"A Sharp Condition for Exact Support Recovery of Sparse Signals With Orthogonal Matching Pursuit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04643","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":"sha256:441e95cc22119eaa88e107b5332d05799ca1bdba155537e01047df097e77ab3c","target":"record","created_at":"2026-05-18T00:10:52Z","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":"8a1eba11049159b41d2603ccdcb351263f5e29991b9cd3ef4cdd7f6aac18922e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T21:14:28Z","title_canon_sha256":"27a55928aa031c65ddc2b330750326919356fd7952108c7bf5e4fe167fd07106"},"schema_version":"1.0","source":{"id":"1807.04643","kind":"arxiv","version":1}},"canonical_sha256":"34f2c98a45d1f69c6f42785487efd43070c551f1273d5db934c9e4cce1c6c1a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34f2c98a45d1f69c6f42785487efd43070c551f1273d5db934c9e4cce1c6c1a7","first_computed_at":"2026-05-18T00:10:52.912437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:52.912437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R6ZwdluQ1Ta/XheaGTkIvJ7sTw1BUDRYJrUANu/+cFvB2obv4eG1MyV+dBFQbtAl48PVUpBeyd3ufetfLWhlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:52.913085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:441e95cc22119eaa88e107b5332d05799ca1bdba155537e01047df097e77ab3c","sha256:dd3aa842caf49ca528ee038656e785873debcafa85b3f39c8b5ec33f2db587ea"],"state_sha256":"85bd622b3153e415c6fc6d5cf2e04956d3431caeff0a0edc6db791a66eb60e7f"}