{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PT76NEWKIPGOVEIXC5CZMRJWIX","short_pith_number":"pith:PT76NEWK","canonical_record":{"source":{"id":"1502.02209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-08T05:29:55Z","cross_cats_sorted":[],"title_canon_sha256":"002636b7509c77f99be67114a228df6efb1f31853ab5251add4d2534934d36f5","abstract_canon_sha256":"43c18467309761ac25c26cab20707754be2834d693072b438e892243906b94a6"},"schema_version":"1.0"},"canonical_sha256":"7cffe692ca43ccea9117174596453645cabd2c2685db85dbb507f38e812a519b","source":{"kind":"arxiv","id":"1502.02209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02209","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02209v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02209","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"PT76NEWKIPGO","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PT76NEWKIPGOVEIX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PT76NEWK","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PT76NEWKIPGOVEIXC5CZMRJWIX","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-08T05:29:55Z","cross_cats_sorted":[],"title_canon_sha256":"002636b7509c77f99be67114a228df6efb1f31853ab5251add4d2534934d36f5","abstract_canon_sha256":"43c18467309761ac25c26cab20707754be2834d693072b438e892243906b94a6"},"schema_version":"1.0"},"canonical_sha256":"7cffe692ca43ccea9117174596453645cabd2c2685db85dbb507f38e812a519b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:43.328645Z","signature_b64":"TPEYLb3VLZq8RA6+nvy59CGXJI6Yqs0E4fMSHts604ztTgrjfJH8CiFuMOLgnLvaKC1e2SkeUeRdsdjdcamfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cffe692ca43ccea9117174596453645cabd2c2685db85dbb507f38e812a519b","last_reissued_at":"2026-05-18T02:27:43.328131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:43.328131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02209","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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CFDpJ6vw9jt9/EZlnphWKGEGORt4H1QIbpr1VpJevxK1Txz1JC8OIstArUYHrWUjyx/4mvcR5qlxRUd8d8BcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:53:07.705639Z"},"content_sha256":"6758e28bfdddc1da32a459976b67602a8fb587ab7f7c1cbb936cdff8f05dad25","schema_version":"1.0","event_id":"sha256:6758e28bfdddc1da32a459976b67602a8fb587ab7f7c1cbb936cdff8f05dad25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PT76NEWKIPGOVEIXC5CZMRJWIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor Complementarity Problem and Semi-positive Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liqun Qi, Yisheng Song","submitted_at":"2015-02-08T05:29:55Z","abstract_excerpt":"The tensor complementarity problem $(\\q, \\mathcal{A})$ is to\n  $$\\mbox{ find } \\x \\in \\mathbb{R}^n\\mbox{ such that }\\x \\geq \\0, \\q + \\mathcal{A}\\x^{m-1} \\geq \\0, \\mbox{ and }\\x^\\top (\\q + \\mathcal{A}\\x^{m-1}) = 0.$$ We prove that a real tensor $\\mathcal{A}$ is a (strictly) semi-positive tensor if and only if the tensor complementarity problem $(\\q, \\mathcal{A})$ has a unique solution for $\\q>\\0$ ($\\q\\geq\\0$), and a symmetric real tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive. That is, for a strictly copositive symmetric tensor $\\mathcal{A}$, the tensor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02209","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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfRjNfHACF3QEzSJggpw5UhDWX86Macv2u5eh400+790/7Jxm0kB874fzepDGQGm1ulTsYFQL56mekrJuO8rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:53:07.705977Z"},"content_sha256":"775b86b3eb9c46463ebc6e13558cc862e1b8d397c29336ebcca0ea77f1a03db0","schema_version":"1.0","event_id":"sha256:775b86b3eb9c46463ebc6e13558cc862e1b8d397c29336ebcca0ea77f1a03db0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/bundle.json","state_url":"https://pith.science/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/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":"2026-06-08T09:53:07Z","links":{"resolver":"https://pith.science/pith/PT76NEWKIPGOVEIXC5CZMRJWIX","bundle":"https://pith.science/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/bundle.json","state":"https://pith.science/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PT76NEWKIPGOVEIXC5CZMRJWIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PT76NEWKIPGOVEIXC5CZMRJWIX","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":"43c18467309761ac25c26cab20707754be2834d693072b438e892243906b94a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-08T05:29:55Z","title_canon_sha256":"002636b7509c77f99be67114a228df6efb1f31853ab5251add4d2534934d36f5"},"schema_version":"1.0","source":{"id":"1502.02209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02209","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02209v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02209","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"PT76NEWKIPGO","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PT76NEWKIPGOVEIX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PT76NEWK","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:775b86b3eb9c46463ebc6e13558cc862e1b8d397c29336ebcca0ea77f1a03db0","target":"graph","created_at":"2026-05-18T02:27:43Z","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":"The tensor complementarity problem $(\\q, \\mathcal{A})$ is to\n  $$\\mbox{ find } \\x \\in \\mathbb{R}^n\\mbox{ such that }\\x \\geq \\0, \\q + \\mathcal{A}\\x^{m-1} \\geq \\0, \\mbox{ and }\\x^\\top (\\q + \\mathcal{A}\\x^{m-1}) = 0.$$ We prove that a real tensor $\\mathcal{A}$ is a (strictly) semi-positive tensor if and only if the tensor complementarity problem $(\\q, \\mathcal{A})$ has a unique solution for $\\q>\\0$ ($\\q\\geq\\0$), and a symmetric real tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive. That is, for a strictly copositive symmetric tensor $\\mathcal{A}$, the tensor ","authors_text":"Liqun Qi, Yisheng Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-08T05:29:55Z","title":"Tensor Complementarity Problem and Semi-positive Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02209","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":"sha256:6758e28bfdddc1da32a459976b67602a8fb587ab7f7c1cbb936cdff8f05dad25","target":"record","created_at":"2026-05-18T02:27:43Z","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":"43c18467309761ac25c26cab20707754be2834d693072b438e892243906b94a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-08T05:29:55Z","title_canon_sha256":"002636b7509c77f99be67114a228df6efb1f31853ab5251add4d2534934d36f5"},"schema_version":"1.0","source":{"id":"1502.02209","kind":"arxiv","version":1}},"canonical_sha256":"7cffe692ca43ccea9117174596453645cabd2c2685db85dbb507f38e812a519b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cffe692ca43ccea9117174596453645cabd2c2685db85dbb507f38e812a519b","first_computed_at":"2026-05-18T02:27:43.328131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:43.328131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPEYLb3VLZq8RA6+nvy59CGXJI6Yqs0E4fMSHts604ztTgrjfJH8CiFuMOLgnLvaKC1e2SkeUeRdsdjdcamfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:43.328645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6758e28bfdddc1da32a459976b67602a8fb587ab7f7c1cbb936cdff8f05dad25","sha256:775b86b3eb9c46463ebc6e13558cc862e1b8d397c29336ebcca0ea77f1a03db0"],"state_sha256":"6da61a5f47e1a1843245aeb2af7d27598996e179aa189afc5884dff4fe829aa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfeNW4PK1lE/vBcYLIwoFUSbGdndCkgQ5DAUZYxjfMGCyEKm/cf//83+0wBbEepwCrPbQzqwQmb2rpVjobxEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:53:07.707846Z","bundle_sha256":"bbc126f1c4126230dab60152d7ac4ea85a28f658e0447382cab89408965d48a1"}}