{"id":"W2336634865","doi":"10.48550/arxiv.1112.0298","title":"Ranks of 0-1 arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Tensor decomposition and applications","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Product (mathematics); Mathematics; Field (mathematics); Combinatorics; Set (abstract data type); Boolean algebra; Discrete mathematics; Pure mathematics; Computer science; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001197934,0.0001748671,0.0004172551,0.0001036806,0.00003869407,0.000005455023,0.0003275018,0.0002131486,0.0002765414],"category_scores_gemma":[0.00006132343,0.0001963251,0.0001623828,0.0001540695,0.0002139396,0.00004379787,0.0003298511,0.0002385929,0.000007978141],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002216513,"about_ca_system_score_gemma":0.00004270915,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005854835,"about_ca_topic_score_gemma":0.00001150457,"domain_scores_codex":[0.99914,0.00005564169,0.0002686103,0.0003646907,0.00005001667,0.0001210531],"domain_scores_gemma":[0.9983694,0.0002968417,0.0004431368,0.0006493096,0.0001613807,0.00007992933],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006957096,0.000326778,0.0009527974,0.0005902826,0.000176136,0.00001128459,0.0006260626,0.0004657531,0.001831831,0.9942678,0.0005945254,0.00008724167],"study_design_scores_gemma":[0.0007103576,0.00004445764,0.001857086,0.0001603898,0.000339705,0.000003908406,0.0002210716,0.001501692,0.004952346,0.9897058,0.0002161823,0.0002869921],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9492655,0.00003477139,0.03172117,0.00002649556,0.00007052717,0.0003227312,0.0001001606,0.00006673962,0.01839191],"genre_scores_gemma":[0.993229,0.0001515062,0.00545924,0.00001222253,0.00001816039,0.000001024371,0.000007350536,0.00001800428,0.001103521],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04396347,"threshold_uncertainty_score":0.8005906,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1288657503439549,"score_gpt":0.2241643475553765,"score_spread":0.09529859721142162,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}