{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MACZFXMCXE37LKRLWQ6HYNQCCS","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":"f37c0eaa607070f7aa5cd6cf6d7f9192d482f8368f284aea10b6ebce9531deed","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-09T09:35:32Z","title_canon_sha256":"837f0bfbc34bbeb56ff657b3cab0aa92969e83cbce0f9fc71dd24d79e428b318"},"schema_version":"1.0","source":{"id":"1310.2410","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2410","created_at":"2026-05-18T01:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2410v2","created_at":"2026-05-18T01:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2410","created_at":"2026-05-18T01:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"MACZFXMCXE37","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"MACZFXMCXE37LKRL","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"MACZFXMC","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:f7ee5b1333ed28fb5a281ef2b04c149acf7ea70fe8a5853f16f652f1ea60f289","target":"graph","created_at":"2026-05-18T01:47:07Z","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":"In the context of compressed sensing, the nonconvex $\\ell_q$ minimization with $0<q<1$ has been studied in recent years. In this paper, by generalizing the sharp bound for $\\ell_1$ minimization of Cai and Zhang, we show that the condition $\\delta_{(s^q+1)k}<\\dfrac{1}{\\sqrt{s^{q-2}+1}}$ in terms of \\emph{restricted isometry constant (RIC)} can guarantee the exact recovery of $k$-sparse signals in noiseless case and the stable recovery of approximately $k$-sparse signals in noisy case by $\\ell_q$ minimization. This result is more general than the sharp bound for $\\ell_1$ minimization when the or","authors_text":"Chao-Bing Song, Shu-Tao Xia","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-09T09:35:32Z","title":"Sparse signal recovery by $\\ell_q$ minimization under restricted isometry property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2410","kind":"arxiv","version":2},"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:ff4e0e4eaae5efef064bc28b3e6e3cfdb466786d84e38c1e6520e8d1dcde7846","target":"record","created_at":"2026-05-18T01:47:07Z","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":"f37c0eaa607070f7aa5cd6cf6d7f9192d482f8368f284aea10b6ebce9531deed","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-09T09:35:32Z","title_canon_sha256":"837f0bfbc34bbeb56ff657b3cab0aa92969e83cbce0f9fc71dd24d79e428b318"},"schema_version":"1.0","source":{"id":"1310.2410","kind":"arxiv","version":2}},"canonical_sha256":"600592dd82b937f5aa2bb43c7c3602148b084df1dd83b18822e9642bb56cbdd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"600592dd82b937f5aa2bb43c7c3602148b084df1dd83b18822e9642bb56cbdd5","first_computed_at":"2026-05-18T01:47:07.623155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:07.623155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jl5szPI4mPu3H7Y7akVyMxGNT+jsR3anjNBPFVqBw2QPeuWLGdwzCcHIKImTfWFW/x/tQs9IqVjIBAtCuGnyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:07.623764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2410","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff4e0e4eaae5efef064bc28b3e6e3cfdb466786d84e38c1e6520e8d1dcde7846","sha256:f7ee5b1333ed28fb5a281ef2b04c149acf7ea70fe8a5853f16f652f1ea60f289"],"state_sha256":"8a741563422aed7254589eab1ed46e140c0ee5580198e97cb920ac6165862f8f"}