{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ZKJEPDWKAKQRO5Y6UFPFHDYXOJ","short_pith_number":"pith:ZKJEPDWK","canonical_record":{"source":{"id":"2402.09807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:13:59Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"a918b49bd367e88904a415ec03794f5fe0fd5181259e6c1957d9669d36ecbb3c","abstract_canon_sha256":"63ccc1eca4f235903869fadda2a0a122ebc3eb37dfc09a1d0c7fa342ab5cbbb0"},"schema_version":"1.0"},"canonical_sha256":"ca92478eca02a117771ea15e538f17724f7c689b8a6693fe3bc8bcdf85b99a03","source":{"kind":"arxiv","id":"2402.09807","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.09807","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"2402.09807v1","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.09807","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZKJEPDWKAKQR","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZKJEPDWKAKQRO5Y6","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZKJEPDWK","created_at":"2026-07-05T07:45:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ZKJEPDWKAKQRO5Y6UFPFHDYXOJ","target":"record","payload":{"canonical_record":{"source":{"id":"2402.09807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:13:59Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"a918b49bd367e88904a415ec03794f5fe0fd5181259e6c1957d9669d36ecbb3c","abstract_canon_sha256":"63ccc1eca4f235903869fadda2a0a122ebc3eb37dfc09a1d0c7fa342ab5cbbb0"},"schema_version":"1.0"},"canonical_sha256":"ca92478eca02a117771ea15e538f17724f7c689b8a6693fe3bc8bcdf85b99a03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:45:37.272030Z","signature_b64":"CjvFxE1Exzj9zIrla3P2p2IQrSCf0SS25G1tfCfwTBMe209Foc1PQtdRigQJ+8eZ/qYvAE0AU6PhuRDn+a4mAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca92478eca02a117771ea15e538f17724f7c689b8a6693fe3bc8bcdf85b99a03","last_reissued_at":"2026-07-05T07:45:37.271624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:45:37.271624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.09807","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SmePrxbOWRpgz/hMX0KbWqL7vPFnifLLml9fC+w/I28l1IXUYugcb/S98ook/TqTvSPfIR0CNKB3FYIXmoUhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:55:31.645043Z"},"content_sha256":"4a8787aa0e512bd5477f909fb12feb0bd37605612fa9d8ed67a2f3bfa87487cb","schema_version":"1.0","event_id":"sha256:4a8787aa0e512bd5477f909fb12feb0bd37605612fa9d8ed67a2f3bfa87487cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ZKJEPDWKAKQRO5Y6UFPFHDYXOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two trust region type algorithms for solving nonconvex-strongly concave minimax problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Tongliang Yao, Zi Xu","submitted_at":"2024-02-15T09:13:59Z","abstract_excerpt":"In this paper, we propose a Minimax Trust Region (MINIMAX-TR) algorithm and a Minimax Trust Region Algorithm with Contractions and Expansions(MINIMAX-TRACE) algorithm for solving nonconvex-strongly concave minimax problems. Both algorithms can find an $(\\epsilon, \\sqrt{\\epsilon})$-second order stationary point(SSP) within $\\mathcal{O}(\\epsilon^{-1.5})$ iterations, which matches the best well known iteration complexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09807","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/2402.09807/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":"2026-07-05T07:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPd6/QRrflixEIW5ydsuffmVmNTd42CjGzOCi4oXmAvJ4jgF/pQnM26YazgjflV40H97IOQdvxjt/u+DInAwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:55:31.645722Z"},"content_sha256":"60c8e15b0cd0149586dba6e53f8ed98718be8fc0ab0d9b61d33d4a29c20ee31c","schema_version":"1.0","event_id":"sha256:60c8e15b0cd0149586dba6e53f8ed98718be8fc0ab0d9b61d33d4a29c20ee31c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/bundle.json","state_url":"https://pith.science/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/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":"2026-08-14T09:55:31Z","links":{"resolver":"https://pith.science/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ","bundle":"https://pith.science/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/bundle.json","state":"https://pith.science/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKJEPDWKAKQRO5Y6UFPFHDYXOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZKJEPDWKAKQRO5Y6UFPFHDYXOJ","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":"63ccc1eca4f235903869fadda2a0a122ebc3eb37dfc09a1d0c7fa342ab5cbbb0","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:13:59Z","title_canon_sha256":"a918b49bd367e88904a415ec03794f5fe0fd5181259e6c1957d9669d36ecbb3c"},"schema_version":"1.0","source":{"id":"2402.09807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.09807","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"2402.09807v1","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.09807","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZKJEPDWKAKQR","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZKJEPDWKAKQRO5Y6","created_at":"2026-07-05T07:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZKJEPDWK","created_at":"2026-07-05T07:45:37Z"}],"graph_snapshots":[{"event_id":"sha256:60c8e15b0cd0149586dba6e53f8ed98718be8fc0ab0d9b61d33d4a29c20ee31c","target":"graph","created_at":"2026-07-05T07:45:37Z","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/2402.09807/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a Minimax Trust Region (MINIMAX-TR) algorithm and a Minimax Trust Region Algorithm with Contractions and Expansions(MINIMAX-TRACE) algorithm for solving nonconvex-strongly concave minimax problems. Both algorithms can find an $(\\epsilon, \\sqrt{\\epsilon})$-second order stationary point(SSP) within $\\mathcal{O}(\\epsilon^{-1.5})$ iterations, which matches the best well known iteration complexity.","authors_text":"Tongliang Yao, Zi Xu","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:13:59Z","title":"Two trust region type algorithms for solving nonconvex-strongly concave minimax problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09807","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":"sha256:4a8787aa0e512bd5477f909fb12feb0bd37605612fa9d8ed67a2f3bfa87487cb","target":"record","created_at":"2026-07-05T07:45:37Z","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":"63ccc1eca4f235903869fadda2a0a122ebc3eb37dfc09a1d0c7fa342ab5cbbb0","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-15T09:13:59Z","title_canon_sha256":"a918b49bd367e88904a415ec03794f5fe0fd5181259e6c1957d9669d36ecbb3c"},"schema_version":"1.0","source":{"id":"2402.09807","kind":"arxiv","version":1}},"canonical_sha256":"ca92478eca02a117771ea15e538f17724f7c689b8a6693fe3bc8bcdf85b99a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca92478eca02a117771ea15e538f17724f7c689b8a6693fe3bc8bcdf85b99a03","first_computed_at":"2026-07-05T07:45:37.271624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:45:37.271624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CjvFxE1Exzj9zIrla3P2p2IQrSCf0SS25G1tfCfwTBMe209Foc1PQtdRigQJ+8eZ/qYvAE0AU6PhuRDn+a4mAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:45:37.272030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.09807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8787aa0e512bd5477f909fb12feb0bd37605612fa9d8ed67a2f3bfa87487cb","sha256:60c8e15b0cd0149586dba6e53f8ed98718be8fc0ab0d9b61d33d4a29c20ee31c"],"state_sha256":"7cf72d77703735012315956a7d6286ef9d791c4486bb5bfa2525b98fa29dc4f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTjFLbfSELwagJtFdYFT3GI45EmpBhBSc6xh9axP0PctcSK/28VuSQ2aHMeoYlY3c4kE7bpZ2FxzfuAr4fLGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T09:55:31.650271Z","bundle_sha256":"bb9f5cc463a9a2e6b14fea3338836cabb8254f8fef4071fe859e1ee7b6d4aa58"}}