{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LCPTVYK4WTDBGAPPQYVGZIB6QZ","short_pith_number":"pith:LCPTVYK4","canonical_record":{"source":{"id":"1105.2632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-13T07:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"8a1b8203a2887623c52459574a3422d8bb9c8bb4cc06211a762e8d1404d9413f","abstract_canon_sha256":"c5cd7c2f978ed9595b8514b10c51175a263e4f24eabbde12bd5afd347ce1a1ff"},"schema_version":"1.0"},"canonical_sha256":"589f3ae15cb4c61301ef862a6ca03e8676d1fa235539766981eb45daa0f9fe4b","source":{"kind":"arxiv","id":"1105.2632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2632","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2632v1","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2632","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"LCPTVYK4WTDB","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LCPTVYK4WTDBGAPP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LCPTVYK4","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LCPTVYK4WTDBGAPPQYVGZIB6QZ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-13T07:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"8a1b8203a2887623c52459574a3422d8bb9c8bb4cc06211a762e8d1404d9413f","abstract_canon_sha256":"c5cd7c2f978ed9595b8514b10c51175a263e4f24eabbde12bd5afd347ce1a1ff"},"schema_version":"1.0"},"canonical_sha256":"589f3ae15cb4c61301ef862a6ca03e8676d1fa235539766981eb45daa0f9fe4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:09.955937Z","signature_b64":"vF+2JvMYbgboTccOyqgpet8Y41AgaaQZVcCMUCjrSlQtw99pVgEMbCmBbhqVRImFrIbaoiMihJYQmjzLXJWQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"589f3ae15cb4c61301ef862a6ca03e8676d1fa235539766981eb45daa0f9fe4b","last_reissued_at":"2026-05-18T04:22:09.955516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:09.955516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2632","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":"2026-05-18T04:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QG2O/fhh+ixBQ3t1WQpJ5vPi8xFQsJIWo7L1pMmylBzKgA218b7a/u08Gd/jBA2ggIaAZXD7Q/rRSDKEXe7/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:16:44.106479Z"},"content_sha256":"fa2f16b2116b6e7abcddec33f595038a7fbe224e452ed395ce554837faa97736","schema_version":"1.0","event_id":"sha256:fa2f16b2116b6e7abcddec33f595038a7fbe224e452ed395ce554837faa97736"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LCPTVYK4WTDBGAPPQYVGZIB6QZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Le Dung Muu, Tran Dinh Quoc","submitted_at":"2011-05-13T07:39:53Z","abstract_excerpt":"Unlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a local equilibrium point or even a stationary point of this problem is not an easy task. This paper deals with a numerical method for Nash-Cournot equilibrium models involving nonconvex cost functions. We develop a local method to compute a stationary point of this class of problems. The convergence of the algorithm is proved and its complexity is estimated under certain assumptions. Numerical examples are implemented to illustrate the convergence b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2632","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":"2026-05-18T04:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQcBSIEOTpH9dUve6dUsw2pst/2AwmptmqckhSi6hkrgzTckIOVXuV9Jjn6u/iR3s+RqtyLXyzO1co6s43R5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:16:44.107238Z"},"content_sha256":"ae0c349b4924e0ad3599ee9c9bd441b11702bd095a044de41f7b627371b61005","schema_version":"1.0","event_id":"sha256:ae0c349b4924e0ad3599ee9c9bd441b11702bd095a044de41f7b627371b61005"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/bundle.json","state_url":"https://pith.science/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/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":"2026-05-25T19:16:44Z","links":{"resolver":"https://pith.science/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ","bundle":"https://pith.science/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/bundle.json","state":"https://pith.science/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCPTVYK4WTDBGAPPQYVGZIB6QZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LCPTVYK4WTDBGAPPQYVGZIB6QZ","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":"c5cd7c2f978ed9595b8514b10c51175a263e4f24eabbde12bd5afd347ce1a1ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-13T07:39:53Z","title_canon_sha256":"8a1b8203a2887623c52459574a3422d8bb9c8bb4cc06211a762e8d1404d9413f"},"schema_version":"1.0","source":{"id":"1105.2632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2632","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2632v1","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2632","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"LCPTVYK4WTDB","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LCPTVYK4WTDBGAPP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LCPTVYK4","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:ae0c349b4924e0ad3599ee9c9bd441b11702bd095a044de41f7b627371b61005","target":"graph","created_at":"2026-05-18T04:22:09Z","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":"Unlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a local equilibrium point or even a stationary point of this problem is not an easy task. This paper deals with a numerical method for Nash-Cournot equilibrium models involving nonconvex cost functions. We develop a local method to compute a stationary point of this class of problems. The convergence of the algorithm is proved and its complexity is estimated under certain assumptions. Numerical examples are implemented to illustrate the convergence b","authors_text":"Le Dung Muu, Tran Dinh Quoc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-13T07:39:53Z","title":"A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2632","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:fa2f16b2116b6e7abcddec33f595038a7fbe224e452ed395ce554837faa97736","target":"record","created_at":"2026-05-18T04:22:09Z","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":"c5cd7c2f978ed9595b8514b10c51175a263e4f24eabbde12bd5afd347ce1a1ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-13T07:39:53Z","title_canon_sha256":"8a1b8203a2887623c52459574a3422d8bb9c8bb4cc06211a762e8d1404d9413f"},"schema_version":"1.0","source":{"id":"1105.2632","kind":"arxiv","version":1}},"canonical_sha256":"589f3ae15cb4c61301ef862a6ca03e8676d1fa235539766981eb45daa0f9fe4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"589f3ae15cb4c61301ef862a6ca03e8676d1fa235539766981eb45daa0f9fe4b","first_computed_at":"2026-05-18T04:22:09.955516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:09.955516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vF+2JvMYbgboTccOyqgpet8Y41AgaaQZVcCMUCjrSlQtw99pVgEMbCmBbhqVRImFrIbaoiMihJYQmjzLXJWQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:09.955937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa2f16b2116b6e7abcddec33f595038a7fbe224e452ed395ce554837faa97736","sha256:ae0c349b4924e0ad3599ee9c9bd441b11702bd095a044de41f7b627371b61005"],"state_sha256":"f6f4200a490c9a711b64172b7722917f9ad8cd9403943edd4a9e3bb54174f5e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xgBX1NM1nN0XQXCrnRPt19DHhys+NV+8k6jvXeJZhHNFsOfx+szVq2SXkZhbFlHwFWfadrUcdd/Y5A203EzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:16:44.111766Z","bundle_sha256":"8a8d89f9e8ccdf1e42c3ff3cef90aa6f01112ff66f4d3049cfed838d473d18cb"}}