{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:25FJDZVCWLJJJHV6Q6CVQMBPRE","short_pith_number":"pith:25FJDZVC","canonical_record":{"source":{"id":"1508.06012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-08-25T02:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"89a066273b138ccb778dc274c71435cf9bb3d52191814316f30e8976ba52d9ee","abstract_canon_sha256":"91cbb9671f6a809eddd40530e4474cb792fc244d135795bf2194c4d70f1dbe46"},"schema_version":"1.0"},"canonical_sha256":"d74a91e6a2b2d2949ebe878558302f891dfa82d3fbe5e6b721a95fae47289a15","source":{"kind":"arxiv","id":"1508.06012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06012","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06012v1","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06012","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"25FJDZVCWLJJ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"25FJDZVCWLJJJHV6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"25FJDZVC","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:25FJDZVCWLJJJHV6Q6CVQMBPRE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-08-25T02:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"89a066273b138ccb778dc274c71435cf9bb3d52191814316f30e8976ba52d9ee","abstract_canon_sha256":"91cbb9671f6a809eddd40530e4474cb792fc244d135795bf2194c4d70f1dbe46"},"schema_version":"1.0"},"canonical_sha256":"d74a91e6a2b2d2949ebe878558302f891dfa82d3fbe5e6b721a95fae47289a15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:47.127340Z","signature_b64":"T3Zoa55e5x+pC9Z6Z5l7FYUSboUhHDx4n7+gr9a5zNBkYFzfNB7WEYBnb8Hpy1fqgTEEFCED+NuRd8la4jQIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d74a91e6a2b2d2949ebe878558302f891dfa82d3fbe5e6b721a95fae47289a15","last_reissued_at":"2026-05-18T01:34:47.126866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:47.126866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06012","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":"2026-05-18T01:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzH4yHbKCNf4dOUng/7tr88AJqcWkTg7U8K17MkbDtV/HaqLYvJMXgn4bTFUnpgn9skPHXNBsIa0aP8erSgiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:42:40.751479Z"},"content_sha256":"c28abbfd4604881acd13a914ff31ddfa40d39b57501d8f3c789ef69273273c05","schema_version":"1.0","event_id":"sha256:c28abbfd4604881acd13a914ff31ddfa40d39b57501d8f3c789ef69273273c05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:25FJDZVCWLJJJHV6Q6CVQMBPRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Uniqueness and Solvability for Tensor Complementarity Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xue-Li Bai, Yong Wang, Zheng-Hai Huang","submitted_at":"2015-08-25T02:22:03Z","abstract_excerpt":"Recently, the tensor complementarity problem (TCP for short) has been investigated in the literature. An important question involving the property of global uniqueness and solvability (GUS-property) for a class of TCPs was proposed by Song and Qi in their paper \"Properties of Some Classes of Structured Tensors\". In the present paper, we give an answer to this question by constructing two counter-examples. We also show that the solution set of this class of TCPs is nonempty and compact. In particular, we introduce a class of related structured tensors, and show that the corresponding TCP has th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06012","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":"2026-05-18T01:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SRw6+2/XFwI0z+YBolkXPGWrnbTWKJIuECEKC3vubUl22iPlIt+hwRcxCvpzGXABDntIzjD1nvbZdFfz8IBcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:42:40.752185Z"},"content_sha256":"3f639920f90009d117bbcc147501fc01816bf4ad02293a6c0661312ee88ca607","schema_version":"1.0","event_id":"sha256:3f639920f90009d117bbcc147501fc01816bf4ad02293a6c0661312ee88ca607"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/bundle.json","state_url":"https://pith.science/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/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":"2026-06-06T07:42:40Z","links":{"resolver":"https://pith.science/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE","bundle":"https://pith.science/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/bundle.json","state":"https://pith.science/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25FJDZVCWLJJJHV6Q6CVQMBPRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:25FJDZVCWLJJJHV6Q6CVQMBPRE","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":"91cbb9671f6a809eddd40530e4474cb792fc244d135795bf2194c4d70f1dbe46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-08-25T02:22:03Z","title_canon_sha256":"89a066273b138ccb778dc274c71435cf9bb3d52191814316f30e8976ba52d9ee"},"schema_version":"1.0","source":{"id":"1508.06012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06012","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06012v1","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06012","created_at":"2026-05-18T01:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"25FJDZVCWLJJ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"25FJDZVCWLJJJHV6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"25FJDZVC","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:3f639920f90009d117bbcc147501fc01816bf4ad02293a6c0661312ee88ca607","target":"graph","created_at":"2026-05-18T01:34:47Z","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":"Recently, the tensor complementarity problem (TCP for short) has been investigated in the literature. An important question involving the property of global uniqueness and solvability (GUS-property) for a class of TCPs was proposed by Song and Qi in their paper \"Properties of Some Classes of Structured Tensors\". In the present paper, we give an answer to this question by constructing two counter-examples. We also show that the solution set of this class of TCPs is nonempty and compact. In particular, we introduce a class of related structured tensors, and show that the corresponding TCP has th","authors_text":"Xue-Li Bai, Yong Wang, Zheng-Hai Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-08-25T02:22:03Z","title":"Global Uniqueness and Solvability for Tensor Complementarity Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06012","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:c28abbfd4604881acd13a914ff31ddfa40d39b57501d8f3c789ef69273273c05","target":"record","created_at":"2026-05-18T01:34:47Z","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":"91cbb9671f6a809eddd40530e4474cb792fc244d135795bf2194c4d70f1dbe46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-08-25T02:22:03Z","title_canon_sha256":"89a066273b138ccb778dc274c71435cf9bb3d52191814316f30e8976ba52d9ee"},"schema_version":"1.0","source":{"id":"1508.06012","kind":"arxiv","version":1}},"canonical_sha256":"d74a91e6a2b2d2949ebe878558302f891dfa82d3fbe5e6b721a95fae47289a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d74a91e6a2b2d2949ebe878558302f891dfa82d3fbe5e6b721a95fae47289a15","first_computed_at":"2026-05-18T01:34:47.126866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:47.126866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T3Zoa55e5x+pC9Z6Z5l7FYUSboUhHDx4n7+gr9a5zNBkYFzfNB7WEYBnb8Hpy1fqgTEEFCED+NuRd8la4jQIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:47.127340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c28abbfd4604881acd13a914ff31ddfa40d39b57501d8f3c789ef69273273c05","sha256:3f639920f90009d117bbcc147501fc01816bf4ad02293a6c0661312ee88ca607"],"state_sha256":"cd3cd0fbac46f82e78398b141699e17e0e5562963c4313f4b7f3ee9c4d559961"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bm5YtQ3lLbX4wjN4+DSURquYmbTd+q5ZZjR3LsnSyXnqC9FO5rtCDy74mkl92EHHcfl9mS1BNQrIXtoWAXhmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T07:42:40.756192Z","bundle_sha256":"0bf35d970d85301237463fee1ffd9030815d73ab57d55b44b5d0b4787423a0f9"}}