{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GMJDNQ3FHDBWTA44QX6N6UIJVH","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":"b13b1f0ddf358c6a33fca1a2361224021bfcd687ec6839e7cf743590f3e57c53","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-23T11:08:01Z","title_canon_sha256":"6bb15278c5fe42a524bd477c484b2ed02f36df5156b3d9c5e79e1aa1655dfdd6"},"schema_version":"1.0","source":{"id":"2212.12256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12256","created_at":"2026-07-05T09:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12256v1","created_at":"2026-07-05T09:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12256","created_at":"2026-07-05T09:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"GMJDNQ3FHDBW","created_at":"2026-07-05T09:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"GMJDNQ3FHDBWTA44","created_at":"2026-07-05T09:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"GMJDNQ3F","created_at":"2026-07-05T09:15:05Z"}],"graph_snapshots":[{"event_id":"sha256:05439360c5833c446012f65d324936df6f5db78def792d17048891364aec16bb","target":"graph","created_at":"2026-07-05T09:15:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.12256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a penalty parameter. This so-called fixed-point continuation method allows one to approximate the problem's trade-off curve, i.e. to compute the minimizers of the cost function for a whole range of values of the penalty parameter at once. The algorithm is shown to converge, and a rate of convergence of the cost function is also derived. Furthermore, it is shown th","authors_text":"Gesa Sarnighausen, Ignace Loris, Jean-Baptiste Fest, Luca Ratti, S\\'egol\\`ene Martin, Simone Rebegoldi, Tommi Heikkil\\\"a","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-23T11:08:01Z","title":"On a fixed-point continuation method for a convex optimization problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12256","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":"sha256:4cb60fc0f2037394b41844630dc1e16e426db590d8203f0cc9fd4b30e28eb5b6","target":"record","created_at":"2026-07-05T09:15:05Z","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":"b13b1f0ddf358c6a33fca1a2361224021bfcd687ec6839e7cf743590f3e57c53","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-23T11:08:01Z","title_canon_sha256":"6bb15278c5fe42a524bd477c484b2ed02f36df5156b3d9c5e79e1aa1655dfdd6"},"schema_version":"1.0","source":{"id":"2212.12256","kind":"arxiv","version":1}},"canonical_sha256":"331236c36538c369839c85fcdf5109a9ed1c7650bc894ad678887fbb6dd951d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"331236c36538c369839c85fcdf5109a9ed1c7650bc894ad678887fbb6dd951d8","first_computed_at":"2026-07-05T09:15:05.699285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:15:05.699285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lcOnnAI/bLOpoyQ6XEQF/arT9CM4HTrssmdEFa3LOr30lPmIydF0tMQ7/3RwuXSS7xwHhK9O2/Ipdkoi497LBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:15:05.699781Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.12256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb60fc0f2037394b41844630dc1e16e426db590d8203f0cc9fd4b30e28eb5b6","sha256:05439360c5833c446012f65d324936df6f5db78def792d17048891364aec16bb"],"state_sha256":"78796596043d387c8b84ca18b4fce377150e1aea1f47eb1b9a560bda1e565569"}