{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IJOUTAHCZ6MDOFRAMRGOACAS3P","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":"55c9cba25a6e350ae890dec7c1e4e950efc1f425289b59316f4d710baa6fb547","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-20T08:38:04Z","title_canon_sha256":"0dd5e2862d6c59c48da2277f774be034f4567a15c01c137b3068172466166fee"},"schema_version":"1.0","source":{"id":"2605.20898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20898","created_at":"2026-05-21T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20898v1","created_at":"2026-05-21T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20898","created_at":"2026-05-21T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"IJOUTAHCZ6MD","created_at":"2026-05-21T01:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"IJOUTAHCZ6MDOFRA","created_at":"2026-05-21T01:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"IJOUTAHC","created_at":"2026-05-21T01:05:26Z"}],"graph_snapshots":[{"event_id":"sha256:eaa4ccdc52c1fec4420a3117615b911b9b48c68bf904628d9385fde168713845","target":"graph","created_at":"2026-05-21T01:05:26Z","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/2605.20898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study single-loop gradient-flow dynamics for nested optimization, where the outer variable evolves while auxiliary variables track the inner solution map. While existing analyses typically rely on problem- and condition-specific Lyapunov constructions, we propose, to our knowledge, the first unified Lyapunov template for continuous-time analysis that covers minimax, bilevel via a lifted penalty formulation, and min--min--max. Our proof is modular, built from reusable lemmas that yield a unified characterization of time-scale separation. This characterization bridges regimes from strong conv","authors_text":"Dohyun Kwon, Hyunwoo Lee, Jeongyeol Kwon","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-20T08:38:04Z","title":"Continuous-Time Analysis for Minimax and Bilevel Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20898","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":"sha256:3c135723c0c211dcbc043005a2b1dab5e5db8b2773bad2ee091d0efd71594178","target":"record","created_at":"2026-05-21T01:05:26Z","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":"55c9cba25a6e350ae890dec7c1e4e950efc1f425289b59316f4d710baa6fb547","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-20T08:38:04Z","title_canon_sha256":"0dd5e2862d6c59c48da2277f774be034f4567a15c01c137b3068172466166fee"},"schema_version":"1.0","source":{"id":"2605.20898","kind":"arxiv","version":1}},"canonical_sha256":"425d4980e2cf98371620644ce00812dbc498654f1abccad66041d31ca8456c87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"425d4980e2cf98371620644ce00812dbc498654f1abccad66041d31ca8456c87","first_computed_at":"2026-05-21T01:05:26.953179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:26.953179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUPBs79/vavYXWHJPGPZ6b4T+nCX9mWGBgkUvIGeGf+ps97c+5vb6KWNxuRjejqAgYrYUA+b27DgbrmvdJAtAA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:26.953925Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c135723c0c211dcbc043005a2b1dab5e5db8b2773bad2ee091d0efd71594178","sha256:eaa4ccdc52c1fec4420a3117615b911b9b48c68bf904628d9385fde168713845"],"state_sha256":"fb46b500d1a06d6e52673c8a913bbeea72aeb22f8f2ba84a4c1a8b15a0fd561a"}