{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5OYRL3RT45423OH2JXYISPOHBV","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":"b6729345266bc47eb72c92d5ba71c76954bf48e578fd9799e75616a0971459a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-29T13:10:25Z","title_canon_sha256":"bd2ae70021a36ed0078ae4e8af44a9a5a874a5676831d23fe0ae099c2537ee70"},"schema_version":"1.0","source":{"id":"1512.08673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08673","created_at":"2026-05-18T01:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08673v1","created_at":"2026-05-18T01:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08673","created_at":"2026-05-18T01:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"5OYRL3RT4542","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OYRL3RT45423OH2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OYRL3RT","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:ab62305e395f908de77df007af795e8429242c7c14c428978742e4b4173c2176","target":"graph","created_at":"2026-05-18T01:23:35Z","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 compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\\ell_1$-norm minimization. Upper bounds for the $\\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\\ell_1$-norm are given in [3]. When the unknown vector is not conventionally sparse but is \"group sparse\" instead, a variety of alternatives to the $\\ell_1$-norm have been proposed in the literature, including the group LASSO, sparse group LASSO, and group LASSO with tree structured o","authors_text":"M. Eren Ahsen, M. Vidyasagar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-29T13:10:25Z","title":"Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08673","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":"sha256:81b4dece45ee54f455a4d180b0e4bed6433b0475aab237d0f4e9f13eca7f66c1","target":"record","created_at":"2026-05-18T01:23:35Z","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":"b6729345266bc47eb72c92d5ba71c76954bf48e578fd9799e75616a0971459a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-29T13:10:25Z","title_canon_sha256":"bd2ae70021a36ed0078ae4e8af44a9a5a874a5676831d23fe0ae099c2537ee70"},"schema_version":"1.0","source":{"id":"1512.08673","kind":"arxiv","version":1}},"canonical_sha256":"ebb115ee33e779adb8fa4df0893dc70d7597ae2571d05fdea01ebaab5655c777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebb115ee33e779adb8fa4df0893dc70d7597ae2571d05fdea01ebaab5655c777","first_computed_at":"2026-05-18T01:23:35.138695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:35.138695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9eS2MzZ8XK5MoM4QiZcT5fFmb85Xb2S6qjFKfJ3K0vqkNFoPZRDH3abf6lXUQ9bb4xitcdEEXV2PeD1twBeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:35.139238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81b4dece45ee54f455a4d180b0e4bed6433b0475aab237d0f4e9f13eca7f66c1","sha256:ab62305e395f908de77df007af795e8429242c7c14c428978742e4b4173c2176"],"state_sha256":"b558324d90dcfe2ccb176b4464b8eba45cd66855e6dad6cdc6bb07edb60212be"}