{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7PUN7IAWMP236WRBI3RQGXSD7S","short_pith_number":"pith:7PUN7IAW","schema_version":"1.0","canonical_sha256":"fbe8dfa01663f5bf5a2146e3035e43fc9ae5515c6d06f97a041fa7322cd41f25","source":{"kind":"arxiv","id":"2608.01658","version":1},"attestation_state":"computed","paper":{"title":"Non-KKT Accumulation in Entropic Mirror Descent","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","math.DS"],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Kuangyu Ding","submitted_at":"2026-08-03T03:47:30Z","abstract_excerpt":"For mirror descent generated by a Legendre kernel, perhaps one of the most basic question in optimization is this: must every accumulation point of a bounded mirror descent sequence be Karush--Kuhn--Tucker (KKT) stationary under proper stepsizes? We show that the answer is no. A longstanding obstacle to resolving this question is the boundary blow-up of the Legendre gradient: it keeps every mirror step in the interior, while at a boundary limit, the inverse entropy metric vanishes on active coordinates and can erase the dual-feasibility in the KKT system. We construct $C^\\infty$ objectives and"},"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":"2608.01658","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-03T03:47:30Z","cross_cats_sorted":["cs.LG","math.DS"],"title_canon_sha256":"f7d529f2dae438fe5632e055664126c90b1428f9c01db22116353c95c2506df2","abstract_canon_sha256":"8eb123b6f6e273415f6715b6102f413346e571b4f7144a75c61e31607ff3a070"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:06:21.337413Z","signature_b64":"eYTSp7TaoEryB46Lq3excnL0XEK9Nv/JTCmmmmGopr0AFq/5RxIoV+jNbykIowe+BeXNjeU4KIr8M/wsxDqOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbe8dfa01663f5bf5a2146e3035e43fc9ae5515c6d06f97a041fa7322cd41f25","last_reissued_at":"2026-08-04T02:06:21.335861Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:06:21.335861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-KKT Accumulation in Entropic Mirror Descent","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","math.DS"],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Kuangyu Ding","submitted_at":"2026-08-03T03:47:30Z","abstract_excerpt":"For mirror descent generated by a Legendre kernel, perhaps one of the most basic question in optimization is this: must every accumulation point of a bounded mirror descent sequence be Karush--Kuhn--Tucker (KKT) stationary under proper stepsizes? We show that the answer is no. A longstanding obstacle to resolving this question is the boundary blow-up of the Legendre gradient: it keeps every mirror step in the interior, while at a boundary limit, the inverse entropy metric vanishes on active coordinates and can erase the dual-feasibility in the KKT system. We construct $C^\\infty$ objectives and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01658","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/2608.01658/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":"2608.01658","created_at":"2026-08-04T02:06:21.337366+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.01658v1","created_at":"2026-08-04T02:06:21.337366+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01658","created_at":"2026-08-04T02:06:21.337366+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PUN7IAWMP23","created_at":"2026-08-04T02:06:21.337366+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PUN7IAWMP236WRB","created_at":"2026-08-04T02:06:21.337366+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PUN7IAW","created_at":"2026-08-04T02:06:21.337366+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.05536","citing_title":"A Unified Framework for Iterate Convergence of Bregman Proximal Methods","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S","json":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S.json","graph_json":"https://pith.science/api/pith-number/7PUN7IAWMP236WRBI3RQGXSD7S/graph.json","events_json":"https://pith.science/api/pith-number/7PUN7IAWMP236WRBI3RQGXSD7S/events.json","paper":"https://pith.science/paper/7PUN7IAW"},"agent_actions":{"view_html":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S","download_json":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S.json","view_paper":"https://pith.science/paper/7PUN7IAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.01658&json=true","fetch_graph":"https://pith.science/api/pith-number/7PUN7IAWMP236WRBI3RQGXSD7S/graph.json","fetch_events":"https://pith.science/api/pith-number/7PUN7IAWMP236WRBI3RQGXSD7S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S/action/storage_attestation","attest_author":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S/action/author_attestation","sign_citation":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S/action/citation_signature","submit_replication":"https://pith.science/pith/7PUN7IAWMP236WRBI3RQGXSD7S/action/replication_record"}},"created_at":"2026-08-04T02:06:21.337366+00:00","updated_at":"2026-08-04T02:06:21.337366+00:00"}