{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C7ZYFSS5N6CV6VGMXYYEIALF6G","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":"f9b6cfbfb8783d789e4d27745b7d495ff0c8638d23411a7b8c9e8584739ec7f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-21T02:01:14Z","title_canon_sha256":"4c4bfd11a3c51fea9a2f258159e28c1a5e9b7d9b7a3f7f1016589058fcba8dc6"},"schema_version":"1.0","source":{"id":"1708.06055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06055","created_at":"2026-05-18T00:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06055v1","created_at":"2026-05-18T00:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06055","created_at":"2026-05-18T00:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"C7ZYFSS5N6CV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"C7ZYFSS5N6CV6VGM","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"C7ZYFSS5","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:d605d4d3c934fda5176e0917b7640522806a2c3775eb15f0eac72b09892773ba","target":"graph","created_at":"2026-05-18T00:37:43Z","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":"Motivated by $\\ell_p$-optimization arising from sparse optimization, high dimensional data analytics and statistics, this paper studies sparse properties of a wide range of $p$-norm based optimization problems with $p > 1$, including generalized basis pursuit, basis pursuit denoising, ridge regression, and elastic net. It is well known that when $p > 1$, these optimization problems lead to less sparse solutions. However, the quantitative characterization of the adverse sparse properties is not available. In this paper, by exploiting optimization and matrix analysis techniques, we give a system","authors_text":"Jinglai Shen, Seyedahmad Mousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-21T02:01:14Z","title":"Least Sparsity of $p$-norm based Optimization Problems with $p > 1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06055","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":"sha256:4258635bf750c84cdd40abd5f83f87909094c30180a3e75a422fff32d78bb019","target":"record","created_at":"2026-05-18T00:37:43Z","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":"f9b6cfbfb8783d789e4d27745b7d495ff0c8638d23411a7b8c9e8584739ec7f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-21T02:01:14Z","title_canon_sha256":"4c4bfd11a3c51fea9a2f258159e28c1a5e9b7d9b7a3f7f1016589058fcba8dc6"},"schema_version":"1.0","source":{"id":"1708.06055","kind":"arxiv","version":1}},"canonical_sha256":"17f382ca5d6f855f54ccbe30440165f1832104b32ec4cc1e163061406df27627","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17f382ca5d6f855f54ccbe30440165f1832104b32ec4cc1e163061406df27627","first_computed_at":"2026-05-18T00:37:43.413475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:43.413475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPsYBrOmblTFSzHsU1nG0qnPvxnFvIPQxPlzT6LQLCs4u9qqIlhnNVxI9lNZU51qSm28PNzQQLPSAGW0t461DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:43.414097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4258635bf750c84cdd40abd5f83f87909094c30180a3e75a422fff32d78bb019","sha256:d605d4d3c934fda5176e0917b7640522806a2c3775eb15f0eac72b09892773ba"],"state_sha256":"c13b880ee2a88cbf046cc6d13da8b2d06fc9e8da41a951bee08514e8eed46574"}