{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GNJBIXFODCXWALSI6WOIASNBWZ","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":"ce7e74499c1f869c4ce94d823cae05b0fa0bb7f636dde85c7ec00b9659037d03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-09T15:57:40Z","title_canon_sha256":"6968d1e0ca20f97993d3c8657f3a4f4d04ddd0132c60831eaf603e2313ca40eb"},"schema_version":"1.0","source":{"id":"1710.03162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03162","created_at":"2026-05-18T00:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03162v1","created_at":"2026-05-18T00:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03162","created_at":"2026-05-18T00:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"GNJBIXFODCXW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNJBIXFODCXWALSI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNJBIXFO","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:a538d16ecf61d2eaa7e460e7aab07046276b63ca33c6745fd430eb6c6448412a","target":"graph","created_at":"2026-05-18T00:33:26Z","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":"A weighted complementarity problem (wCP) is to find a pair of vectors belonging to the intersection of a manifold and a cone such that the product of the vectors in a certain algebra equals a given weight vector. If the weight vector is zero, we get a complementarity problem. Examples of such problems include the Fisher market equilibrium problem and the linear programming and weighted centering problem. In this paper we consider the weighted horizontal linear complementarity problem (wHLCP) in the setting of Euclidean Jordan algebras and establish some existence and uniqueness results. For a ","authors_text":"Jiyuan Tao, M.Seetharama Gowda, Xiaoni Chi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-09T15:57:40Z","title":"The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03162","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":"sha256:467029fd8638afa4a16f78da6785325b93336ade9e410fee8528c7739348fd5c","target":"record","created_at":"2026-05-18T00:33:26Z","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":"ce7e74499c1f869c4ce94d823cae05b0fa0bb7f636dde85c7ec00b9659037d03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-09T15:57:40Z","title_canon_sha256":"6968d1e0ca20f97993d3c8657f3a4f4d04ddd0132c60831eaf603e2313ca40eb"},"schema_version":"1.0","source":{"id":"1710.03162","kind":"arxiv","version":1}},"canonical_sha256":"3352145cae18af602e48f59c8049a1b67c6e47d0167b9f572da257b4807ac8ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3352145cae18af602e48f59c8049a1b67c6e47d0167b9f572da257b4807ac8ed","first_computed_at":"2026-05-18T00:33:26.905652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:26.905652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZVagyHa8Fptid4iSYXF8B+9sf0nm3tW+9Qh4l0rsq5pSRbdgkp2PhekmpBbC98VMY8Zt7mjGXpVARi1Ph/rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:26.906216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:467029fd8638afa4a16f78da6785325b93336ade9e410fee8528c7739348fd5c","sha256:a538d16ecf61d2eaa7e460e7aab07046276b63ca33c6745fd430eb6c6448412a"],"state_sha256":"f16de8250b6085f493493ece03c6bd62df0c55374a07557784f3a6e6ce067e57"}