{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FM2IQRGDESIWMGJRDEMXYYAJUO","short_pith_number":"pith:FM2IQRGD","canonical_record":{"source":{"id":"2505.01423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-02T17:59:46Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"33c4cca219715b4ca0b085fc7269780dbefdb1bbcbb0d6ae18a5b187e5f50f1e","abstract_canon_sha256":"6ee496888d996c91fccf1179065aff5a5d8c52c32745ea90caab1e22b830f677"},"schema_version":"1.0"},"canonical_sha256":"2b348844c3249166193119197c6009a3912dfe0e145a4f184c93c6fda115dbe5","source":{"kind":"arxiv","id":"2505.01423","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FM2IQRGDESIWMGJRDEMXYYAJUO","target":"record","payload":{"canonical_record":{"source":{"id":"2505.01423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-02T17:59:46Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"33c4cca219715b4ca0b085fc7269780dbefdb1bbcbb0d6ae18a5b187e5f50f1e","abstract_canon_sha256":"6ee496888d996c91fccf1179065aff5a5d8c52c32745ea90caab1e22b830f677"},"schema_version":"1.0"},"canonical_sha256":"2b348844c3249166193119197c6009a3912dfe0e145a4f184c93c6fda115dbe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:23.221804Z","signature_b64":"kvC9XN0ytMApAFt31IdxBa2AzNb4IZOQnad9XUAWzg/eOPUFCf3w2SBlFXU35OOYb7kRUm6ji6uzqfmLc1uPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b348844c3249166193119197c6009a3912dfe0e145a4f184c93c6fda115dbe5","last_reissued_at":"2026-06-30T01:17:23.221009Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:23.221009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.01423","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAn4Yg+g9jafuAS953GnlmAJ6OBCNNOUihng5fnvGTV5RIOPYa0i85qpWC3UIPGA6FVZdnN1wjNpi+CcDbL2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T15:47:14.495082Z"},"content_sha256":"8b0f564f5377f7d71747c64475666839745bd4d787361d19b4be9866f85fdff7","schema_version":"1.0","event_id":"sha256:8b0f564f5377f7d71747c64475666839745bd4d787361d19b4be9866f85fdff7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FM2IQRGDESIWMGJRDEMXYYAJUO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Negative Stepsizes Make Gradient-Descent-Ascent Converge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"math.OC","authors_text":"Henry Shugart, Jason M. Altschuler","submitted_at":"2025-05-02T17:59:46Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01423","kind":"arxiv","version":2},"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/2505.01423/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bvuak5SgU/fp5/Odeo1GrRW3BX1udx5lCZWXk8Nv+rwxpL+lCu6LoCug8LgSzPZKcgUTSB70WD+/eOHUyZvWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T15:47:14.495483Z"},"content_sha256":"93b2459a1d55cd5f008f3f3c32b07099750f620c692bf534a4a6ff7738488913","schema_version":"1.0","event_id":"sha256:93b2459a1d55cd5f008f3f3c32b07099750f620c692bf534a4a6ff7738488913"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/bundle.json","state_url":"https://pith.science/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T15:47:14Z","links":{"resolver":"https://pith.science/pith/FM2IQRGDESIWMGJRDEMXYYAJUO","bundle":"https://pith.science/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/bundle.json","state":"https://pith.science/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FM2IQRGDESIWMGJRDEMXYYAJUO/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTJ90WJNMfr8aMwreA6STji9PqJyhTm0HNIDrAjyqes8RrnvHwKScNpT14lPrZ23Ijav/s2o3ZCaHrp436/CAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T15:47:14.497559Z","bundle_sha256":"6d5d4acf31ddb6768718822d6a4b7a38d3185db37a2c951baad581189e216bab"}}