{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FM2IQRGDESIWMGJRDEMXYYAJUO","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":"6ee496888d996c91fccf1179065aff5a5d8c52c32745ea90caab1e22b830f677","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-02T17:59:46Z","title_canon_sha256":"33c4cca219715b4ca0b085fc7269780dbefdb1bbcbb0d6ae18a5b187e5f50f1e"},"schema_version":"1.0","source":{"id":"2505.01423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.01423","created_at":"2026-06-30T01:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"2505.01423v2","created_at":"2026-06-30T01:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01423","created_at":"2026-06-30T01:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"FM2IQRGDESIW","created_at":"2026-06-30T01:17:23Z"},{"alias_kind":"pith_short_16","alias_value":"FM2IQRGDESIWMGJR","created_at":"2026-06-30T01:17:23Z"},{"alias_kind":"pith_short_8","alias_value":"FM2IQRGD","created_at":"2026-06-30T01:17:23Z"}],"graph_snapshots":[{"event_id":"sha256:93b2459a1d55cd5f008f3f3c32b07099750f620c692bf534a4a6ff7738488913","target":"graph","created_at":"2026-06-30T01:17:23Z","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/2505.01423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Efficient computation of min-max problems is a central question in optimization, learning, games, and control. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued that GDA fails to converge even on simple problems. This failure spurred an extensive literature on modifying GDA with additional building blocks such as extragradients, optimism, momentum, anchoring, etc. In contrast, we show that GDA converges in its original form by simply using a judicious choice of stepsizes.\n  The key innovation is the proposal of unconv","authors_text":"Henry Shugart, Jason M. Altschuler","cross_cats":["cs.DS","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-02T17:59:46Z","title":"Negative Stepsizes Make Gradient-Descent-Ascent Converge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01423","kind":"arxiv","version":2},"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":"sha256:8b0f564f5377f7d71747c64475666839745bd4d787361d19b4be9866f85fdff7","target":"record","created_at":"2026-06-30T01:17:23Z","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":"6ee496888d996c91fccf1179065aff5a5d8c52c32745ea90caab1e22b830f677","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-02T17:59:46Z","title_canon_sha256":"33c4cca219715b4ca0b085fc7269780dbefdb1bbcbb0d6ae18a5b187e5f50f1e"},"schema_version":"1.0","source":{"id":"2505.01423","kind":"arxiv","version":2}},"canonical_sha256":"2b348844c3249166193119197c6009a3912dfe0e145a4f184c93c6fda115dbe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b348844c3249166193119197c6009a3912dfe0e145a4f184c93c6fda115dbe5","first_computed_at":"2026-06-30T01:17:23.221009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:23.221009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kvC9XN0ytMApAFt31IdxBa2AzNb4IZOQnad9XUAWzg/eOPUFCf3w2SBlFXU35OOYb7kRUm6ji6uzqfmLc1uPCg==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:23.221804Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.01423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b0f564f5377f7d71747c64475666839745bd4d787361d19b4be9866f85fdff7","sha256:93b2459a1d55cd5f008f3f3c32b07099750f620c692bf534a4a6ff7738488913"],"state_sha256":"4f522e944a9abc05b7fb617a253af8bad29ad03f7f7e4b5732693843b1c95d6e"}