{"id":"W2073148515","doi":"10.1016/j.laa.2008.12.032","title":"On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem","year":2009,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Rank (graph theory); Mathematics; Combinatorics; Guttman scale; Matrix (chemical analysis); Discrete mathematics; Statistics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003215892,0.00009263272,0.00007156206,0.00002643927,0.0006615673,0.0001485996,0.0003510911,0.00003228996,0.00001428174],"category_scores_gemma":[0.00002838995,0.00005012946,0.00003163352,0.0001621102,0.00006584737,0.0001227326,0.0000467363,0.00009429317,0.00001350076],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003796953,"about_ca_system_score_gemma":0.0000123244,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":5.656102e-7,"about_ca_topic_score_gemma":3.280598e-7,"domain_scores_codex":[0.9993817,0.00003650476,0.0001185047,0.0002331817,0.00009479876,0.0001353036],"domain_scores_gemma":[0.9988611,0.0006518582,0.00005374061,0.0003428888,0.00004358482,0.00004684372],"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":[0.000003698789,0.00004489949,3.146367e-7,0.000003212577,0.000005290492,1.032061e-7,0.0001957795,0.0000230646,0.0001641476,0.9742008,0.0004723116,0.02488641],"study_design_scores_gemma":[0.00030181,0.000183726,0.000786268,0.00001124455,0.0000232052,0.00001341704,0.0002102294,0.231437,0.002061175,0.7388952,0.02592028,0.0001564279],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02738488,0.001082331,0.9406835,0.02693431,0.00007004782,0.001440378,0.00002528275,0.0001190877,0.002260171],"genre_scores_gemma":[0.9956723,0.0001230288,0.001286842,0.002244744,0.0001359138,0.0002007576,0.000008180411,0.000004810233,0.0003233644],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9682875,"threshold_uncertainty_score":0.5088308,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01161436857517824,"score_gpt":0.2605060276295781,"score_spread":0.2488916590543998,"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."}}