{"id":"W1994957129","doi":"10.1090/s0002-9939-2011-11149-3","title":"On the lengths of irreducible pairs of complex matrices","year":2011,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Combinatorics; Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002585048,0.00166431,0.0009450264,0.004720559,0.002160434,0.004318826,0.001752505,0.00153403,0.01548285],"category_scores_gemma":[0.01641428,0.000998822,0.001124214,0.00219756,0.004088784,0.01102844,0.004006122,0.004425064,0.004099809],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002079454,"about_ca_system_score_gemma":0.0008327934,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001087593,"about_ca_topic_score_gemma":0.001128993,"domain_scores_codex":[0.9968801,0.0007204558,0.0002193858,0.0007558796,0.0008671762,0.0005570897],"domain_scores_gemma":[0.9911848,0.004214648,0.001419198,0.0009465642,0.001277744,0.0009570737],"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":[0.0001386608,0.00002234624,0.0006403519,0.0001180409,0.00001684355,0.00009509698,0.0004217575,0.002308402,0.000993599,0.9811654,0.002387183,0.01169228],"study_design_scores_gemma":[0.00001363862,0.00004659078,0.0005533308,0.00007991977,0.00001744088,0.0001103512,0.0001664367,0.008806809,0.00191094,0.982345,0.005902124,0.0000474408],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4236071,0.00583859,0.3256723,0.003699734,0.001400432,0.000143459,0.00170679,0.0009039406,0.2370277],"genre_scores_gemma":[0.9025013,0.002991408,0.05683288,0.0008165764,0.00129459,0.0003017733,0.00174044,0.0007788319,0.03274217],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01548285,"threshold_uncertainty_score":0.05179524,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02621858826301766,"score_gpt":0.2157802666580654,"score_spread":0.1895616783950477,"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."}}