{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QXZ5GGTMANRY2DRLI53KUYWQ6R","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":"7baa5f3407c33d746d57b9ac1010611b61b6f671860e35fb135a09913cda9d1c","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T21:10:25Z","title_canon_sha256":"1148b6e075cbec471b207217e6ce25525f1ad77d599242d78bcc06dedd0650f2"},"schema_version":"1.0","source":{"id":"1906.09329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09329","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09329v1","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09329","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"QXZ5GGTMANRY","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QXZ5GGTMANRY2DRL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QXZ5GGTM","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:132347e193cb124206764822732601cb9b4682f3dda677f67aa5a66595d64688","target":"graph","created_at":"2026-05-17T23:42:38Z","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":"We consider an important problem in signal processing, which consists in finding the sparsest solution of a linear system $\\Phi x=b$. This problem has applications in several areas, but is NP-hard in general. Usually an alternative convex problem is considered, based on minimizing the (weighted) $\\ell_{1}$ norm. For this alternative to be useful, weights should be chosen as to obtain a solution of the original NP-hard problem. A well known algorithm for this is the Re-Weighted $\\ell_{1}$, proposed by Cand\\`es, Wakin and Boyd. In this article we introduce a new methodology for updating the weig","authors_text":"Marcelo Fiori, Mat\\'ias Vald\\'es","cross_cats":["cs.LG","cs.NA","eess.SP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T21:10:25Z","title":"Re-Weighted $\\ell_1$ Algorithms within the Lagrange Duality Framework: Bringing Interpretability to Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09329","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":"sha256:160e62347e861b424b6716a4b124331033d28e5a750888098185b07ef42b772d","target":"record","created_at":"2026-05-17T23:42:38Z","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":"7baa5f3407c33d746d57b9ac1010611b61b6f671860e35fb135a09913cda9d1c","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T21:10:25Z","title_canon_sha256":"1148b6e075cbec471b207217e6ce25525f1ad77d599242d78bcc06dedd0650f2"},"schema_version":"1.0","source":{"id":"1906.09329","kind":"arxiv","version":1}},"canonical_sha256":"85f3d31a6c03638d0e2b4776aa62d0f47630c2b8dd02c9201c8b3456dc01308c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f3d31a6c03638d0e2b4776aa62d0f47630c2b8dd02c9201c8b3456dc01308c","first_computed_at":"2026-05-17T23:42:38.477972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:38.477972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZEscJaHeh8PYPjiOtOWM2D6ZGxW9tca82NuH7Jlo7a3UHsXXI8s6agL89BVEXOziL5VzthLks1k/6x1nCpWgCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:38.478558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:160e62347e861b424b6716a4b124331033d28e5a750888098185b07ef42b772d","sha256:132347e193cb124206764822732601cb9b4682f3dda677f67aa5a66595d64688"],"state_sha256":"f1e188415dd5746f1d20309a6c5bf8f9dd07150c7ef0d4a5c0923df0aa528f7d"}