{"id":"W4417261048","doi":"10.1093/imrn/rnaf356","title":"Block Complexity and Idempotent Schur Multipliers","year":2025,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Idempotence; Conjecture; Identity matrix; Dimension (graph theory); Matrix (chemical analysis); Schur's theorem; Idempotent matrix; Block matrix; Multiplier (economics); Schur algebra","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":[0.001121466,0.0005790071,0.0006627773,0.001340276,0.0009292637,0.00247759,0.001027077,0.0007894509,0.009384328],"category_scores_gemma":[0.008920088,0.0004234849,0.0004542598,0.0009025421,0.002603033,0.004737428,0.001558264,0.002128025,0.001378872],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001949431,"about_ca_system_score_gemma":0.000991223,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001126985,"about_ca_topic_score_gemma":0.001551478,"domain_scores_codex":[0.9984596,0.0003042039,0.00005039652,0.0002537268,0.0006314184,0.0003007545],"domain_scores_gemma":[0.9922693,0.005081251,0.0006974434,0.0008012213,0.000642213,0.0005085616],"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":[0.0001398123,0.00004862247,0.0005687534,0.00007155982,0.00001059735,0.00008519783,0.0001040456,0.0111272,0.004857115,0.9726115,0.002348365,0.008027297],"study_design_scores_gemma":[0.00002932725,0.00006443955,0.0004224028,0.00002258618,0.000008193982,0.00008531856,0.00003472833,0.07953105,0.005305252,0.9111455,0.003321988,0.00002924299],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6405162,0.001365068,0.2633753,0.002975454,0.0001808652,0.0001113597,0.0009261239,0.0004385935,0.0901109],"genre_scores_gemma":[0.9669119,0.0003990011,0.02396422,0.0002632751,0.0001719411,0.0001238991,0.0003219522,0.00008914142,0.007754708],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009384328,"threshold_uncertainty_score":0.03139371,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2928848482527465,"score_gpt":0.5131089594961111,"score_spread":0.2202241112433647,"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."}}