{"id":"W244166733","doi":"10.13001/1081-3810.1438","title":"Multiplicative diagonals of matrix semigroups","year":2011,"lang":"en","type":"article","venue":"Electronic Journal of Linear Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of Prince Edward Island","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Diagonal; Multiplicative function; Diagonal matrix; Semigroup; Main diagonal; Special classes of semigroups; Matrix (chemical analysis); Product (mathematics); Pure mathematics; Combinatorics; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0009299234,0.0002073917,0.0005550373,0.0001769708,0.00005014849,0.000005080926,0.0005565823,0.0001170914,0.0003536562],"category_scores_gemma":[0.0008214007,0.000173703,0.0002746332,0.0002577137,0.0001171353,0.0002175674,0.00007884159,0.0007552069,0.00002164827],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001339496,"about_ca_system_score_gemma":0.0002818298,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004005787,"about_ca_topic_score_gemma":0.000007002499,"domain_scores_codex":[0.997792,0.0001074138,0.0009969157,0.0001669301,0.0004157888,0.0005209552],"domain_scores_gemma":[0.9973006,0.0005333496,0.001255394,0.000386649,0.0004133976,0.0001105621],"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":[0.0001744457,0.0004323991,0.0007815013,0.00006824767,0.0003864343,0.00001985906,0.002093749,0.00000373456,0.004796413,0.9891933,0.0003518357,0.001698124],"study_design_scores_gemma":[0.0008389701,0.0005778002,0.000313248,0.00007966891,0.0001037961,0.0001781898,0.0002315827,0.00003841036,0.09795976,0.8982793,0.001218771,0.0001805152],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9159594,0.002893211,0.07848036,0.0001434432,0.0001916633,0.0002665101,0.000007777048,0.00004044963,0.002017158],"genre_scores_gemma":[0.9244905,0.0003607525,0.07421795,0.00004032362,0.0002959414,0.000004439724,9.31236e-7,0.00005097196,0.0005382315],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09316335,"threshold_uncertainty_score":0.7083402,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0441982632141202,"score_gpt":0.3372767974101978,"score_spread":0.2930785341960777,"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."}}