{"id":"W3183622905","doi":"10.1080/00029890.2022.2115779","title":"Extremal Values of Pi","year":2022,"lang":"en","type":"preprint","venue":"American Mathematical Monthly","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Pi; Euclidean geometry; Quarter (Canadian coin); Norm (philosophy); Mathematics; Euclidean distance; Value (mathematics); Combinatorics; Symmetry (geometry); Geometry; Law; Statistics; Political science; Geography","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"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":[0.0006297811,0.0008653991,0.0004553559,0.002284442,0.001221831,0.002812075,0.00084594,0.0005584139,0.01150623],"category_scores_gemma":[0.002149307,0.0002648737,0.0003503872,0.001274839,0.002418253,0.003409295,0.002240158,0.002549442,0.002212378],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008670676,"about_ca_system_score_gemma":0.0003097804,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000496065,"about_ca_topic_score_gemma":0.0003004559,"domain_scores_codex":[0.9994479,0.00008753877,0.00002738662,0.0001081512,0.0001786828,0.0001503344],"domain_scores_gemma":[0.9995203,0.0001344278,0.00008812695,0.00005904569,0.000104334,0.00009374054],"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":[0.00002444431,0.00001146045,0.0004484256,0.00004397065,0.000004855347,0.00007206116,0.0001304802,0.00110773,0.001201837,0.9833639,0.002514041,0.01107673],"study_design_scores_gemma":[0.000004584676,0.00003761219,0.001026275,0.0000611692,0.000007242865,0.0003504884,0.0002553549,0.005104229,0.00297061,0.9665319,0.02362316,0.000027408],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2659886,0.006191846,0.199611,0.003227174,0.0006715225,0.00008453047,0.001008847,0.0004113336,0.522805],"genre_scores_gemma":[0.9392045,0.003780769,0.02806178,0.0003380898,0.0005681116,0.0001223497,0.000751949,0.000257723,0.0269147],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01150623,"threshold_uncertainty_score":0.03849214,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05678324148336746,"score_gpt":0.3497349630849785,"score_spread":0.2929517216016111,"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."}}