{"id":"W2931154226","doi":"10.5539/jmr.v11n2p39","title":"Zero Product of Three Two Level Toeplitz Operators","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Toeplitz matrix; Mathematics; Zero (linguistics); Hardy space; Bounded function; Product (mathematics); Combinatorics; Pure mathematics; Discrete mathematics; Algebra over a field; Mathematical analysis; Geometry; Linguistics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008142588,0.0005826275,0.0004422138,0.0009313936,0.0007754287,0.002337276,0.0008032221,0.0007246513,0.00808877],"category_scores_gemma":[0.001967422,0.0002791066,0.0005477982,0.0004970841,0.001630077,0.002248432,0.001549972,0.001013207,0.001038091],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004991017,"about_ca_system_score_gemma":0.000574026,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004728567,"about_ca_topic_score_gemma":0.000325082,"domain_scores_codex":[0.9991586,0.0001145483,0.00005207845,0.0002243763,0.0002571187,0.0001932515],"domain_scores_gemma":[0.9985971,0.00031974,0.0002330786,0.0001380039,0.000292967,0.0004191243],"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":[0.0002933675,0.0001106686,0.001815561,0.00009574235,0.00003073622,0.0009368946,0.0006830607,0.004010998,0.04543678,0.934547,0.0005835835,0.01145553],"study_design_scores_gemma":[0.0001208287,0.0007325117,0.003447884,0.00004703697,0.00005528807,0.0026076,0.001264348,0.1386333,0.05660906,0.7902464,0.006049306,0.0001862772],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7265317,0.000197762,0.2446572,0.0001630528,0.000107016,0.00005004109,0.00007411678,0.0002124467,0.02800664],"genre_scores_gemma":[0.9739962,0.00006688057,0.01642145,0.0000610418,0.00003181707,0.00003458545,0.00006408036,0.00006167099,0.009262249],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00808877,"threshold_uncertainty_score":0.02705961,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2826489821444513,"score_gpt":0.4429351628738507,"score_spread":0.1602861807293994,"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."}}