{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H6NSYMBSOK7PLPUPWIVBY33RX2","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":"f48e77efc38aec3ffb6054d8b4b4faf06609f73d1f559a35c90165e815b3e23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-07T02:17:19Z","title_canon_sha256":"70020b7a110823ddcae42de2d9cf2c60c37ad94b8ffb76a9c0a4987a32fb73c5"},"schema_version":"1.0","source":{"id":"1610.02125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02125","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02125v1","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02125","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"pith_short_12","alias_value":"H6NSYMBSOK7P","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H6NSYMBSOK7PLPUP","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H6NSYMBS","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:aa1e4faf80e636511f0dbfcea502f3351eacf89dda7d5b363c12be1904a52c36","target":"graph","created_at":"2026-05-18T00:51:43Z","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":"The constrained $\\ell_0$ regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the connections between global minimizers of the constrained $\\ell_0$ problem and its penalty problem have never been studied in a systematic way. This work provides a comprehensive investigation on optimal solutions of these two problems and their connections. We give detailed descriptions of optimal solutions of the two problems, including existence, stability with","authors_text":"Na Zhang, Qia Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-07T02:17:19Z","title":"On optimal solutions of the constrained $\\ell_0$ regularization and its penalty problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02125","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":"sha256:3adfd82f13d0a0e44225ac84f7a52d5cb4b335e19a03de51f420c5f93b98c7f7","target":"record","created_at":"2026-05-18T00:51:43Z","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":"f48e77efc38aec3ffb6054d8b4b4faf06609f73d1f559a35c90165e815b3e23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-07T02:17:19Z","title_canon_sha256":"70020b7a110823ddcae42de2d9cf2c60c37ad94b8ffb76a9c0a4987a32fb73c5"},"schema_version":"1.0","source":{"id":"1610.02125","kind":"arxiv","version":1}},"canonical_sha256":"3f9b2c303272bef5be8fb22a1c6f71be8c346577b8c3b83e4e33080b67476b92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f9b2c303272bef5be8fb22a1c6f71be8c346577b8c3b83e4e33080b67476b92","first_computed_at":"2026-05-18T00:51:43.612856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:43.612856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJ7xZTNKHV9SNdRy1J68sUHtnl7znqFNGhdV37+oOmiwD74uDSSkezoD4e6GtOZ1tugTAEOOPpQHkAWtSJbECg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:43.613492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3adfd82f13d0a0e44225ac84f7a52d5cb4b335e19a03de51f420c5f93b98c7f7","sha256:aa1e4faf80e636511f0dbfcea502f3351eacf89dda7d5b363c12be1904a52c36"],"state_sha256":"0d987859637b6730f87b82fc31f397d64d860c964e507e46922a789865d6f8d1"}