{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3DSEGPZEN65BSGZFML45CCTCA2","short_pith_number":"pith:3DSEGPZE","canonical_record":{"source":{"id":"1808.02211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T04:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"d56f6454c2238c9c4b6e622d224ef8ea69400b76cdb3cbc44bb370ccd1e5f7d0","abstract_canon_sha256":"4a225ba34194721f1e33f5ebbc9e8a400f8bf7554f0eeb85296f7b5b6715a422"},"schema_version":"1.0"},"canonical_sha256":"d8e4433f246fba191b2562f9d10a6206bd15cf490c593db7772f85d59c406798","source":{"kind":"arxiv","id":"1808.02211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02211","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02211v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02211","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"3DSEGPZEN65B","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3DSEGPZEN65BSGZF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3DSEGPZE","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3DSEGPZEN65BSGZFML45CCTCA2","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T04:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"d56f6454c2238c9c4b6e622d224ef8ea69400b76cdb3cbc44bb370ccd1e5f7d0","abstract_canon_sha256":"4a225ba34194721f1e33f5ebbc9e8a400f8bf7554f0eeb85296f7b5b6715a422"},"schema_version":"1.0"},"canonical_sha256":"d8e4433f246fba191b2562f9d10a6206bd15cf490c593db7772f85d59c406798","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:47.222635Z","signature_b64":"jf8PLcrDLgN/CHTrwiEKXnJSb/FATcw3ydmlwZ1LCGLnRv46S/49fN6QmcdTamOpfIm1/MbYFV5YPG3BV6v9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8e4433f246fba191b2562f9d10a6206bd15cf490c593db7772f85d59c406798","last_reissued_at":"2026-05-18T00:08:47.222043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:47.222043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02211","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":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6OSKOgyxOcXBoj++OMOHW061HPY0Yq6gW4+WwI16UhlvCugj4V2LWpuTfz9bBUFn1nEbjHNClcJH0LvKwQ/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:40:35.121928Z"},"content_sha256":"3cab4c24784fb5198c03fb08242205446bded2a5cdd514d59b3044bc3d19e926","schema_version":"1.0","event_id":"sha256:3cab4c24784fb5198c03fb08242205446bded2a5cdd514d59b3044bc3d19e926"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3DSEGPZEN65BSGZFML45CCTCA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Completely Positive Binary Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anwa Zhou, Jiawang Nie, Jinyan Fan","submitted_at":"2018-08-07T04:58:23Z","abstract_excerpt":"A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative vectors. This paper characterizes completely positive binary tensors. We show that a binary tensor is completely positive if and only if it satisfies two linear matrix inequalities. This result can be used to determine whether a binary tensor is completely positive or not. When it is, we give an algorithm for computing its cp-rank and the decomposition. When the order is odd, we show that the cp-rank decomposition is unique. When the order is even, we completely characterize when the cp-rank decomposi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02211","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":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsgKMJtVGXGrpW4EjhOfY0+L6626/9/bTaPFzvR4+y7kO+ooiSe2q8C2/cp4QljuUkGnqoaKWq1voCBEAIO8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:40:35.122295Z"},"content_sha256":"bacacfb7ab399e1a4f226a8b0ca5a8da622a67eb24004b8a71de81797588046e","schema_version":"1.0","event_id":"sha256:bacacfb7ab399e1a4f226a8b0ca5a8da622a67eb24004b8a71de81797588046e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DSEGPZEN65BSGZFML45CCTCA2/bundle.json","state_url":"https://pith.science/pith/3DSEGPZEN65BSGZFML45CCTCA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DSEGPZEN65BSGZFML45CCTCA2/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":"2026-06-01T18:40:35Z","links":{"resolver":"https://pith.science/pith/3DSEGPZEN65BSGZFML45CCTCA2","bundle":"https://pith.science/pith/3DSEGPZEN65BSGZFML45CCTCA2/bundle.json","state":"https://pith.science/pith/3DSEGPZEN65BSGZFML45CCTCA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DSEGPZEN65BSGZFML45CCTCA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3DSEGPZEN65BSGZFML45CCTCA2","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":"4a225ba34194721f1e33f5ebbc9e8a400f8bf7554f0eeb85296f7b5b6715a422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T04:58:23Z","title_canon_sha256":"d56f6454c2238c9c4b6e622d224ef8ea69400b76cdb3cbc44bb370ccd1e5f7d0"},"schema_version":"1.0","source":{"id":"1808.02211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02211","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02211v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02211","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"3DSEGPZEN65B","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3DSEGPZEN65BSGZF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3DSEGPZE","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:bacacfb7ab399e1a4f226a8b0ca5a8da622a67eb24004b8a71de81797588046e","target":"graph","created_at":"2026-05-18T00:08:47Z","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":"A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative vectors. This paper characterizes completely positive binary tensors. We show that a binary tensor is completely positive if and only if it satisfies two linear matrix inequalities. This result can be used to determine whether a binary tensor is completely positive or not. When it is, we give an algorithm for computing its cp-rank and the decomposition. When the order is odd, we show that the cp-rank decomposition is unique. When the order is even, we completely characterize when the cp-rank decomposi","authors_text":"Anwa Zhou, Jiawang Nie, Jinyan Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T04:58:23Z","title":"Completely Positive Binary Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02211","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":"sha256:3cab4c24784fb5198c03fb08242205446bded2a5cdd514d59b3044bc3d19e926","target":"record","created_at":"2026-05-18T00:08:47Z","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":"4a225ba34194721f1e33f5ebbc9e8a400f8bf7554f0eeb85296f7b5b6715a422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-07T04:58:23Z","title_canon_sha256":"d56f6454c2238c9c4b6e622d224ef8ea69400b76cdb3cbc44bb370ccd1e5f7d0"},"schema_version":"1.0","source":{"id":"1808.02211","kind":"arxiv","version":1}},"canonical_sha256":"d8e4433f246fba191b2562f9d10a6206bd15cf490c593db7772f85d59c406798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8e4433f246fba191b2562f9d10a6206bd15cf490c593db7772f85d59c406798","first_computed_at":"2026-05-18T00:08:47.222043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:47.222043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jf8PLcrDLgN/CHTrwiEKXnJSb/FATcw3ydmlwZ1LCGLnRv46S/49fN6QmcdTamOpfIm1/MbYFV5YPG3BV6v9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:47.222635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cab4c24784fb5198c03fb08242205446bded2a5cdd514d59b3044bc3d19e926","sha256:bacacfb7ab399e1a4f226a8b0ca5a8da622a67eb24004b8a71de81797588046e"],"state_sha256":"39b44e0d808a4b935143763262ba0d9ee429c1f8e00b86dab02c9cdfcfa091a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owX6tcnQATn81Ymwi+Sbmh87VL5FNcUTK4U0s/NV+LBzXqrYEbypg6qZeuNFCsiRBLVIVfaweamIvQM6xx/dDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:40:35.124165Z","bundle_sha256":"2fdefde24e431f5e666e877238f662c59c04071583cb862239dcb105b26d3ed7"}}