{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KLOGCMRKPGA3NSJ4V3XYI5MLP5","short_pith_number":"pith:KLOGCMRK","schema_version":"1.0","canonical_sha256":"52dc61322a7981b6c93caeef84758b7f7d9b615fd2dcdfa832fb9bafa69fe39b","source":{"kind":"arxiv","id":"1701.07677","version":1},"attestation_state":"computed","paper":{"title":"Introduction to Tensor Variational Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liqun Qi, Yong Wang, Zheng-Hai Huang","submitted_at":"2017-01-26T12:46:16Z","abstract_excerpt":"In this paper, we introduce a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; and we call it the tensor variational inequality (TVI). The TVI is a natural extension of the affine variational inequality and the tensor complementarity problem. We show that a class of multi-person noncooperative games can be formulated as a TVI. In particular, we investigate the global uniqueness and solvability of the TVI. To this end, we first introduce two classes of structured tensors and discuss some rela"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-26T12:46:16Z","cross_cats_sorted":[],"title_canon_sha256":"c0fd2294ff1c4fd2b169bf463f135aa19713c40ebc5c522d2b7df4b1e67110c9","abstract_canon_sha256":"0bf98023a0f8ec5cedbdd167e0ff38abcf899fd35e0e6b2a355677cf566b7de1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.872863Z","signature_b64":"UckuoKjQS9INANJVQnVpZgzNXfMK1GH7Y0wHd9olk8yopMlw4Dka4Sz370Zfi2jgKLh1MtzTLNT6uJ3bfK2IDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52dc61322a7981b6c93caeef84758b7f7d9b615fd2dcdfa832fb9bafa69fe39b","last_reissued_at":"2026-05-18T00:52:02.872232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.872232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Introduction to Tensor Variational Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liqun Qi, Yong Wang, Zheng-Hai Huang","submitted_at":"2017-01-26T12:46:16Z","abstract_excerpt":"In this paper, we introduce a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; and we call it the tensor variational inequality (TVI). The TVI is a natural extension of the affine variational inequality and the tensor complementarity problem. We show that a class of multi-person noncooperative games can be formulated as a TVI. In particular, we investigate the global uniqueness and solvability of the TVI. To this end, we first introduce two classes of structured tensors and discuss some rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07677","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.07677","created_at":"2026-05-18T00:52:02.872331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.07677v1","created_at":"2026-05-18T00:52:02.872331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07677","created_at":"2026-05-18T00:52:02.872331+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLOGCMRKPGA3","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLOGCMRKPGA3NSJ4","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLOGCMRK","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5","json":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5.json","graph_json":"https://pith.science/api/pith-number/KLOGCMRKPGA3NSJ4V3XYI5MLP5/graph.json","events_json":"https://pith.science/api/pith-number/KLOGCMRKPGA3NSJ4V3XYI5MLP5/events.json","paper":"https://pith.science/paper/KLOGCMRK"},"agent_actions":{"view_html":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5","download_json":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5.json","view_paper":"https://pith.science/paper/KLOGCMRK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.07677&json=true","fetch_graph":"https://pith.science/api/pith-number/KLOGCMRKPGA3NSJ4V3XYI5MLP5/graph.json","fetch_events":"https://pith.science/api/pith-number/KLOGCMRKPGA3NSJ4V3XYI5MLP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5/action/storage_attestation","attest_author":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5/action/author_attestation","sign_citation":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5/action/citation_signature","submit_replication":"https://pith.science/pith/KLOGCMRKPGA3NSJ4V3XYI5MLP5/action/replication_record"}},"created_at":"2026-05-18T00:52:02.872331+00:00","updated_at":"2026-05-18T00:52:02.872331+00:00"}