{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:C4WR43ZSCAJ5FQ5ZDL2FVX67XN","short_pith_number":"pith:C4WR43ZS","schema_version":"1.0","canonical_sha256":"172d1e6f321013d2c3b91af45adfdfbb5e94921e688c0aa366a3fad0827ed40f","source":{"kind":"arxiv","id":"2608.05536","version":1},"attestation_state":"computed","paper":{"title":"A Unified Framework for Iterate Convergence of Bregman Proximal Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anthony Man-Cho So, He Chen, Jiaming Fan","submitted_at":"2026-08-06T02:30:16Z","abstract_excerpt":"Iterate convergence of Bregman proximal methods (BPMs) has long remained open, especially for nonconvex objectives. Recently, \\citet{chen2026skl} made progress by establishing iterate convergence for a BPM via the so-called scaled Kurdyka-\\L{}ojasiewicz (SK\\L{}) property, but only for the Shannon entropy kernel and linearly constrained problems. In this paper, we develop a unified iterate convergence framework that applies to a broad group of kernels and composite objective functions. Our approach extends the analytical tools in \\cite{chen2026skl}, in particular the SK\\L{} property, which play"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.05536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T02:30:16Z","cross_cats_sorted":[],"title_canon_sha256":"026d91e7d01de2532f40ebeeebe1317f25ec1dd5d9be791f83a9826dc266cc84","abstract_canon_sha256":"f6fdeb4e92c28e35df79aca0e3ca4c85ab0c20a7345081651b9f98a3f2bc276f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:48:15.825084Z","signature_b64":"klxwfgpEAmZwwrpE+rsLKx0FV98AarVr3jvct5LCrDgsyFlWzReVQBuCgr6eYo2DIHN74e2blEcUJsZ0q7fqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"172d1e6f321013d2c3b91af45adfdfbb5e94921e688c0aa366a3fad0827ed40f","last_reissued_at":"2026-08-07T00:48:15.823216Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:48:15.823216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Unified Framework for Iterate Convergence of Bregman Proximal Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anthony Man-Cho So, He Chen, Jiaming Fan","submitted_at":"2026-08-06T02:30:16Z","abstract_excerpt":"Iterate convergence of Bregman proximal methods (BPMs) has long remained open, especially for nonconvex objectives. Recently, \\citet{chen2026skl} made progress by establishing iterate convergence for a BPM via the so-called scaled Kurdyka-\\L{}ojasiewicz (SK\\L{}) property, but only for the Shannon entropy kernel and linearly constrained problems. In this paper, we develop a unified iterate convergence framework that applies to a broad group of kernels and composite objective functions. Our approach extends the analytical tools in \\cite{chen2026skl}, in particular the SK\\L{} property, which play"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05536","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05536/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.05536","created_at":"2026-08-07T00:48:15.824748+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.05536v1","created_at":"2026-08-07T00:48:15.824748+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05536","created_at":"2026-08-07T00:48:15.824748+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4WR43ZSCAJ5","created_at":"2026-08-07T00:48:15.824748+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4WR43ZSCAJ5FQ5Z","created_at":"2026-08-07T00:48:15.824748+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4WR43ZS","created_at":"2026-08-07T00:48:15.824748+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN","json":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN.json","graph_json":"https://pith.science/api/pith-number/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/graph.json","events_json":"https://pith.science/api/pith-number/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/events.json","paper":"https://pith.science/paper/C4WR43ZS"},"agent_actions":{"view_html":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN","download_json":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN.json","view_paper":"https://pith.science/paper/C4WR43ZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.05536&json=true","fetch_graph":"https://pith.science/api/pith-number/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/graph.json","fetch_events":"https://pith.science/api/pith-number/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/action/storage_attestation","attest_author":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/action/author_attestation","sign_citation":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/action/citation_signature","submit_replication":"https://pith.science/pith/C4WR43ZSCAJ5FQ5ZDL2FVX67XN/action/replication_record"}},"created_at":"2026-08-07T00:48:15.824748+00:00","updated_at":"2026-08-07T00:48:15.824748+00:00"}