{"id":"W4413601668","doi":"10.28924/2291-8639-23-2025-205","title":"Boundedness of the Higher Order Commutators of Marcinkiewicz Integral Operator on Grand Variable Herz-Morrey Spaces","year":2025,"lang":"en","type":"article","venue":"International Journal of Analysis and Applications","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Princess Nourah Bint Abdulrahman University","keywords":"Mathematics; Order (exchange); Commutator; Operator (biology); Variable (mathematics); Pure mathematics; Mathematical analysis; Algebra over a field","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004856951,0.0001029127,0.0004093335,0.0004805148,0.00009128061,0.00005166714,0.0006477945,0.00004598137,0.0002443557],"category_scores_gemma":[0.0001763853,0.00006515568,0.0002618297,0.001439591,0.0002074605,0.00008880234,0.0001226076,0.0002211859,9.31485e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006705847,"about_ca_system_score_gemma":0.0001505363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005505183,"about_ca_topic_score_gemma":0.00005608482,"domain_scores_codex":[0.9984885,0.00009393242,0.0006578987,0.0001226631,0.0005448453,0.00009214638],"domain_scores_gemma":[0.9972553,0.0004412465,0.0005787887,0.0002785086,0.001403752,0.00004243003],"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":[0.000173925,0.0009348543,0.04201529,0.00007114356,0.01006295,0.000001891633,0.0002900835,0.002591547,0.002807044,0.9333107,0.001936977,0.005803573],"study_design_scores_gemma":[0.004456969,0.0002434356,0.05249079,0.0008881887,0.009869073,0.00002527473,0.003260215,0.008792263,0.02632589,0.8052258,0.08780249,0.0006195306],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3675025,0.0008028909,0.6181733,0.006363933,0.0002121179,0.0003959949,0.0001134743,0.00001011293,0.006425657],"genre_scores_gemma":[0.9924782,0.000150048,0.005772223,0.00008496486,0.00004450076,0.0000133933,0.000004812433,0.000006820518,0.001445073],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6249757,"threshold_uncertainty_score":0.2675524,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02225765798574704,"score_gpt":0.3750881112334997,"score_spread":0.3528304532477526,"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."}}