{"id":"W2963406632","doi":"10.1017/fms.2017.24","title":"LOW-DEGREE BOOLEAN FUNCTIONS ON , WITH AN APPLICATION TO ISOPERIMETRY","year":2017,"lang":"en","type":"article","venue":"Forum of Mathematics Sigma","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Toronto; Hebrew University of Jerusalem","keywords":"Isoperimetric inequality; Mathematics; Conjecture; Combinatorics; Coset; Boolean function; Eigenvalues and eigenvectors; Degree (music); Tuple; Discrete mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.0003608612,0.0002309888,0.0003627105,0.0001316644,0.0006620727,0.0000732444,0.0007296142,0.000108269,0.00007733476],"category_scores_gemma":[0.000355474,0.0001651586,0.00009438858,0.00008352238,0.0001519427,0.000168921,0.0001705152,0.0001516718,0.00003586506],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002565376,"about_ca_system_score_gemma":0.00002182869,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000116382,"about_ca_topic_score_gemma":0.00005437533,"domain_scores_codex":[0.9986584,0.00002255594,0.0003742795,0.0002895476,0.0003773751,0.0002778664],"domain_scores_gemma":[0.9969994,0.0001852654,0.0004166682,0.002129225,0.0001254199,0.0001439697],"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":[0.0001274061,0.0007297598,0.0004239624,0.0003199437,0.00009623302,0.000002386459,0.001728424,0.00005451565,0.001415055,0.9840322,0.002042643,0.009027521],"study_design_scores_gemma":[0.0008547874,0.001686495,0.001355088,0.0003760606,0.0001278915,0.00002047956,0.002543648,0.001456869,0.02551203,0.9639881,0.001535312,0.0005432733],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8221347,0.00001004786,0.1340087,0.0004357866,0.0001968458,0.0009285698,0.00006858854,0.0001167016,0.04210001],"genre_scores_gemma":[0.9411696,0.000001295003,0.05767641,0.0001117901,0.00008103291,0.00005071276,0.000006211475,0.00005798863,0.0008449246],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1190349,"threshold_uncertainty_score":0.6734971,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03599891464791084,"score_gpt":0.3063161394844476,"score_spread":0.2703172248365368,"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."}}