{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OEYIIYGCLP5QKPUIVNACTQK5RN","short_pith_number":"pith:OEYIIYGC","canonical_record":{"source":{"id":"2409.09961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-16T03:26:15Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"24505c936ac4cd4f4d41e011d527643383a528e241e5ee900f0017e0ffd714b5","abstract_canon_sha256":"22ae88b4e684946a61837f59f98abebf934921122a59f406e00b8ad7b5b47be2"},"schema_version":"1.0"},"canonical_sha256":"71308460c25bfb053e88ab4029c15d8b74507f4a0587418ad1f1f16e4c83bf22","source":{"kind":"arxiv","id":"2409.09961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09961","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09961v1","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09961","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"OEYIIYGCLP5Q","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"OEYIIYGCLP5QKPUI","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"OEYIIYGC","created_at":"2026-07-05T09:07:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OEYIIYGCLP5QKPUIVNACTQK5RN","target":"record","payload":{"canonical_record":{"source":{"id":"2409.09961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-16T03:26:15Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"24505c936ac4cd4f4d41e011d527643383a528e241e5ee900f0017e0ffd714b5","abstract_canon_sha256":"22ae88b4e684946a61837f59f98abebf934921122a59f406e00b8ad7b5b47be2"},"schema_version":"1.0"},"canonical_sha256":"71308460c25bfb053e88ab4029c15d8b74507f4a0587418ad1f1f16e4c83bf22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:07:32.666686Z","signature_b64":"i/1FLiPe3mOFdJf9Y5s/+bcGhMituxhST4+xR+f8sheOiLTC9tUWoREcsUH22u3Ur5KRxYRKgRuocUTNPDUZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71308460c25bfb053e88ab4029c15d8b74507f4a0587418ad1f1f16e4c83bf22","last_reissued_at":"2026-07-05T09:07:32.666247Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:07:32.666247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.09961","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":"2026-07-05T09:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onvoVvpfmrzhdhelDtLQ/mjOkqs1cihUgtIDgyui7Y3+Qh0oWauU6fAblKFd7/rem/M4OAUclnM85i5Um8BMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:03:42.384546Z"},"content_sha256":"796021baaaca2ae7c2baf3a49b9e6f7cdb70ae5930342958e58e4394cc868f42","schema_version":"1.0","event_id":"sha256:796021baaaca2ae7c2baf3a49b9e6f7cdb70ae5930342958e58e4394cc868f42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OEYIIYGCLP5QKPUIVNACTQK5RN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Monotone Variational Inequalities with Best Response Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Can Kizilkale, Murat Arcak, Yu-Wen Chen","submitted_at":"2024-09-16T03:26:15Z","abstract_excerpt":"We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents select the best response to the current distribution of strategies. We apply the method to generalize population games with additional convex constraints. Furthermore, we explore the robustness of the method by introducing various types of time-varying disturbances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09961","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/2409.09961/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":"2026-07-05T09:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lU4yMUvAGQGXfTnWlksUMi/+PZUvBcMx2odon8cFuojOI7DaeUUO7Z2fy/c5K8VGXNFFPIpdvuwUbH4wgGxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:03:42.385143Z"},"content_sha256":"31459d64e08af2fa19740d79a5f0966ba37c3d3407a93595ce4601f8bb9d8f98","schema_version":"1.0","event_id":"sha256:31459d64e08af2fa19740d79a5f0966ba37c3d3407a93595ce4601f8bb9d8f98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/bundle.json","state_url":"https://pith.science/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/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":"2026-08-11T00:03:42Z","links":{"resolver":"https://pith.science/pith/OEYIIYGCLP5QKPUIVNACTQK5RN","bundle":"https://pith.science/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/bundle.json","state":"https://pith.science/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OEYIIYGCLP5QKPUIVNACTQK5RN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OEYIIYGCLP5QKPUIVNACTQK5RN","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":"22ae88b4e684946a61837f59f98abebf934921122a59f406e00b8ad7b5b47be2","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-16T03:26:15Z","title_canon_sha256":"24505c936ac4cd4f4d41e011d527643383a528e241e5ee900f0017e0ffd714b5"},"schema_version":"1.0","source":{"id":"2409.09961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09961","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09961v1","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09961","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"OEYIIYGCLP5Q","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"OEYIIYGCLP5QKPUI","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"OEYIIYGC","created_at":"2026-07-05T09:07:32Z"}],"graph_snapshots":[{"event_id":"sha256:31459d64e08af2fa19740d79a5f0966ba37c3d3407a93595ce4601f8bb9d8f98","target":"graph","created_at":"2026-07-05T09:07:32Z","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/2409.09961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents select the best response to the current distribution of strategies. We apply the method to generalize population games with additional convex constraints. Furthermore, we explore the robustness of the method by introducing various types of time-varying disturbances.","authors_text":"Can Kizilkale, Murat Arcak, Yu-Wen Chen","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-16T03:26:15Z","title":"Solving Monotone Variational Inequalities with Best Response Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09961","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":"sha256:796021baaaca2ae7c2baf3a49b9e6f7cdb70ae5930342958e58e4394cc868f42","target":"record","created_at":"2026-07-05T09:07:32Z","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":"22ae88b4e684946a61837f59f98abebf934921122a59f406e00b8ad7b5b47be2","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-16T03:26:15Z","title_canon_sha256":"24505c936ac4cd4f4d41e011d527643383a528e241e5ee900f0017e0ffd714b5"},"schema_version":"1.0","source":{"id":"2409.09961","kind":"arxiv","version":1}},"canonical_sha256":"71308460c25bfb053e88ab4029c15d8b74507f4a0587418ad1f1f16e4c83bf22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71308460c25bfb053e88ab4029c15d8b74507f4a0587418ad1f1f16e4c83bf22","first_computed_at":"2026-07-05T09:07:32.666247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:07:32.666247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/1FLiPe3mOFdJf9Y5s/+bcGhMituxhST4+xR+f8sheOiLTC9tUWoREcsUH22u3Ur5KRxYRKgRuocUTNPDUZAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:07:32.666686Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.09961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:796021baaaca2ae7c2baf3a49b9e6f7cdb70ae5930342958e58e4394cc868f42","sha256:31459d64e08af2fa19740d79a5f0966ba37c3d3407a93595ce4601f8bb9d8f98"],"state_sha256":"03f70b7df35b738289f5a8c41441fff01f6365a39562a9a275ba5a61c84782b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RmbwVgaYm+mOayOnbe/BqOIP2D70XNzhk4rlXqmoVN7x25A7i1KWBki3toQ93CoImFqNIgvn7Ys8SAZ0RjORDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:03:42.390619Z","bundle_sha256":"ca36859732045b653e946df3922c823f2ca1cd6fe7451a371becc1a229b427db"}}