{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WIIZQA34N2OEDLRQZD67LW276P","short_pith_number":"pith:WIIZQA34","canonical_record":{"source":{"id":"1106.0144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-06-01T11:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"bd46f88363c0ba9b4c7fa696da8a125ab50e5f63193e23d4b7cd78aef59edab6","abstract_canon_sha256":"6d70adc75384b7111bfdd6787b8c5d38ba5ca41bd90bb8c204a25b0c4c2486e0"},"schema_version":"1.0"},"canonical_sha256":"b21198037c6e9c41ae30c8fdf5db5ff3fd8c9c08d7a70dcd3aba39cdd2cf4ae6","source":{"kind":"arxiv","id":"1106.0144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0144","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0144v1","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0144","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"WIIZQA34N2OE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WIIZQA34N2OEDLRQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WIIZQA34","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WIIZQA34N2OEDLRQZD67LW276P","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-06-01T11:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"bd46f88363c0ba9b4c7fa696da8a125ab50e5f63193e23d4b7cd78aef59edab6","abstract_canon_sha256":"6d70adc75384b7111bfdd6787b8c5d38ba5ca41bd90bb8c204a25b0c4c2486e0"},"schema_version":"1.0"},"canonical_sha256":"b21198037c6e9c41ae30c8fdf5db5ff3fd8c9c08d7a70dcd3aba39cdd2cf4ae6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:52.037659Z","signature_b64":"+uoHCPahb9gc5JNq6OY1Kj+D4Q1YUsAWIUkrBJqTKBr9xdOWS8R1AJ/fqv3A9HnTLArKOXq27lhuItIMaNcqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b21198037c6e9c41ae30c8fdf5db5ff3fd8c9c08d7a70dcd3aba39cdd2cf4ae6","last_reissued_at":"2026-05-18T04:20:52.037224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:52.037224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0144","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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nISLhMluxyeFOjfdgfWB9zrkCd18caWUBM+CHi92UsykV/m5dA2BP9NNlqFONp2fABXe2AZfKOJETU7CeSIeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:56:27.519773Z"},"content_sha256":"4c674352136474e9ee1df88538dff28d4e1ab2b142fbbef87dadd4a57eac705f","schema_version":"1.0","event_id":"sha256:4c674352136474e9ee1df88538dff28d4e1ab2b142fbbef87dadd4a57eac705f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WIIZQA34N2OEDLRQZD67LW276P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone Operator Methods for Nash Equilibria in Non-Potential Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Luis M. Briceno-Arias, Patrick L. Combettes","submitted_at":"2011-06-01T11:02:47Z","abstract_excerpt":"We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximity problems are demonstrated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0144","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":""},"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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6kI/ZPkeIvdlwPRX8UH7ZW7+e2N9WFmhxWq06uU0fGXihQAjt19sguecXCaBeWsHmpQQ7A4xE4qeoBJ2F9CkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:56:27.520110Z"},"content_sha256":"70c212128e62897550c6af6de3bc87a49d255a6234b583c9ab5736ff202a2199","schema_version":"1.0","event_id":"sha256:70c212128e62897550c6af6de3bc87a49d255a6234b583c9ab5736ff202a2199"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIIZQA34N2OEDLRQZD67LW276P/bundle.json","state_url":"https://pith.science/pith/WIIZQA34N2OEDLRQZD67LW276P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIIZQA34N2OEDLRQZD67LW276P/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":"2026-06-27T14:56:27Z","links":{"resolver":"https://pith.science/pith/WIIZQA34N2OEDLRQZD67LW276P","bundle":"https://pith.science/pith/WIIZQA34N2OEDLRQZD67LW276P/bundle.json","state":"https://pith.science/pith/WIIZQA34N2OEDLRQZD67LW276P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIIZQA34N2OEDLRQZD67LW276P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WIIZQA34N2OEDLRQZD67LW276P","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":"6d70adc75384b7111bfdd6787b8c5d38ba5ca41bd90bb8c204a25b0c4c2486e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-06-01T11:02:47Z","title_canon_sha256":"bd46f88363c0ba9b4c7fa696da8a125ab50e5f63193e23d4b7cd78aef59edab6"},"schema_version":"1.0","source":{"id":"1106.0144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0144","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0144v1","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0144","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"WIIZQA34N2OE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WIIZQA34N2OEDLRQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WIIZQA34","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:70c212128e62897550c6af6de3bc87a49d255a6234b583c9ab5736ff202a2199","target":"graph","created_at":"2026-05-18T04:20:52Z","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"},"paper":{"abstract_excerpt":"We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximity problems are demonstrated.","authors_text":"Luis M. Briceno-Arias, Patrick L. Combettes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-06-01T11:02:47Z","title":"Monotone Operator Methods for Nash Equilibria in Non-Potential Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0144","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":"sha256:4c674352136474e9ee1df88538dff28d4e1ab2b142fbbef87dadd4a57eac705f","target":"record","created_at":"2026-05-18T04:20:52Z","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":"6d70adc75384b7111bfdd6787b8c5d38ba5ca41bd90bb8c204a25b0c4c2486e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-06-01T11:02:47Z","title_canon_sha256":"bd46f88363c0ba9b4c7fa696da8a125ab50e5f63193e23d4b7cd78aef59edab6"},"schema_version":"1.0","source":{"id":"1106.0144","kind":"arxiv","version":1}},"canonical_sha256":"b21198037c6e9c41ae30c8fdf5db5ff3fd8c9c08d7a70dcd3aba39cdd2cf4ae6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b21198037c6e9c41ae30c8fdf5db5ff3fd8c9c08d7a70dcd3aba39cdd2cf4ae6","first_computed_at":"2026-05-18T04:20:52.037224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:52.037224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+uoHCPahb9gc5JNq6OY1Kj+D4Q1YUsAWIUkrBJqTKBr9xdOWS8R1AJ/fqv3A9HnTLArKOXq27lhuItIMaNcqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:52.037659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c674352136474e9ee1df88538dff28d4e1ab2b142fbbef87dadd4a57eac705f","sha256:70c212128e62897550c6af6de3bc87a49d255a6234b583c9ab5736ff202a2199"],"state_sha256":"0aa6e7b22fe6e48b0742b54d1779143c2e577f23cd30aa4590464a121f46de3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NapPJuLWFgCMza63JcQTm/PlmRS5tl6/noEFC0BSTIjgBU+sIQhKDRgYiEcXsor0CQnBVvqg0wpEIn9pGKS9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:56:27.522223Z","bundle_sha256":"ee610c45bc96f6e02ae563f827a56f158a11c78f46b88304c8464c4adc3c1c2f"}}