{"id":"W1978359906","doi":"10.1215/00127094-2009-039","title":"Maximal averages over linear and monomial polyhedra","year":2009,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Monomial; Polyhedron; Mathematics; Monomial ideal; Combinatorics; Monomial basis; Pure mathematics; Discrete mathematics; Mathematical analysis; Polynomial; Polynomial ring","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":[0.001287423,0.0006180503,0.0008403286,0.001647264,0.001559049,0.002581814,0.001680334,0.0004230849,0.005617825],"category_scores_gemma":[0.005324727,0.0003709918,0.001023829,0.001172025,0.002609795,0.004951208,0.002310875,0.001982854,0.000471101],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001389664,"about_ca_system_score_gemma":0.0004646626,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00109126,"about_ca_topic_score_gemma":0.001358605,"domain_scores_codex":[0.9985244,0.0002910007,0.00008028388,0.0002683193,0.0004794763,0.000356597],"domain_scores_gemma":[0.9965271,0.001789874,0.0004275319,0.0003369969,0.0004742684,0.0004441624],"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":[0.00002709778,0.000009495267,0.0003603181,0.00003194943,0.00001026947,0.00004524434,0.00009601721,0.003069208,0.001476067,0.9907138,0.0003082424,0.003852293],"study_design_scores_gemma":[0.000005624981,0.00003160369,0.0007651495,0.00002181138,0.00001593993,0.0001212481,0.0001233151,0.03848496,0.003507371,0.9544463,0.002456582,0.00002014243],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4813127,0.0009706491,0.4628761,0.0005730733,0.0001365514,0.00003840775,0.0005553069,0.0002253017,0.0533118],"genre_scores_gemma":[0.9619476,0.0004390196,0.02953179,0.0001000093,0.0001979756,0.00008423076,0.0003130364,0.00009250269,0.007293842],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005617825,"threshold_uncertainty_score":0.01879352,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02254449586756808,"score_gpt":0.3023759259001284,"score_spread":0.2798314300325603,"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."}}