{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2U3BP3KE6MMBODBWQTXS3VUEL2","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":"dece0369dc858cb3c6cd096096cb2f35f218b1e7d110ec6be43d1d69cbb8d79e","cross_cats_sorted":["cs.CV","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-15T14:22:34Z","title_canon_sha256":"66a5062075fbd60e09e120bbb65f3bb6df2f71250f4b128d2abef10983937848"},"schema_version":"1.0","source":{"id":"1409.4271","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4271","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4271v5","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4271","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"2U3BP3KE6MMB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2U3BP3KE6MMBODBW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2U3BP3KE","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:ef41e41dd699aace854f218e2318efcb3e3717d45772bd3571211fe80f86a1b4","target":"graph","created_at":"2026-05-18T02:19:08Z","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 ordered weighted $\\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\\it octagonal shrinkage and clustering algorithm for regression} (OSCAR), which has the ability to cluster/group regression variables that are highly correlated. This paper contains several contributions to the study and application of OWL regularization: the derivation of the atomic formulation of the OWL norm; the derivation of the dual of the OWL norm, based on its atomic formulation; ","authors_text":"M\\'ario A. T. Figueiredo, Xiangrong Zeng","cross_cats":["cs.CV","cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-15T14:22:34Z","title":"The Ordered Weighted $\\ell_1$ Norm: Atomic Formulation, Projections, and Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4271","kind":"arxiv","version":5},"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:ac847e74d67e9341e81727703346bfca86cfc13592092a13f8c59dd86a6069a4","target":"record","created_at":"2026-05-18T02:19:08Z","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":"dece0369dc858cb3c6cd096096cb2f35f218b1e7d110ec6be43d1d69cbb8d79e","cross_cats_sorted":["cs.CV","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-15T14:22:34Z","title_canon_sha256":"66a5062075fbd60e09e120bbb65f3bb6df2f71250f4b128d2abef10983937848"},"schema_version":"1.0","source":{"id":"1409.4271","kind":"arxiv","version":5}},"canonical_sha256":"d53617ed44f318170c3684ef2dd6845ea5d7df17f7e8db2bd7bde5d10d8c2efa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d53617ed44f318170c3684ef2dd6845ea5d7df17f7e8db2bd7bde5d10d8c2efa","first_computed_at":"2026-05-18T02:19:08.292614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:08.292614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ie58o+OiY0gFMwCFdfgG/NLWYCJ8aSmJQzvv7UP2JC/pXXn3HFqVmGpVlePzXgNfhHcQJg2zUMPLfuGfpPABg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:08.293239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4271","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac847e74d67e9341e81727703346bfca86cfc13592092a13f8c59dd86a6069a4","sha256:ef41e41dd699aace854f218e2318efcb3e3717d45772bd3571211fe80f86a1b4"],"state_sha256":"82ee905c4543f296f949ada301684075ad6922a802d767599ac9b1e26041a03c"}