{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008487061,0.0005725806,0.001737293,0.0002144519,0.0001526975,0.00005590368,0.001230395,0.0001527192,0.00316089],"category_scores_gemma":[0.001072476,0.0005205856,0.0006119757,0.0004061671,0.0006707412,0.00003964898,0.00180157,0.0008841175,0.00006450386],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001151321,"about_ca_system_score_gemma":0.0001647319,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006612721,"about_ca_topic_score_gemma":0.000004703691,"domain_scores_codex":[0.9960558,0.0001968192,0.001511231,0.0007047111,0.001031556,0.0004998255],"domain_scores_gemma":[0.9939046,0.002008366,0.001589584,0.002121138,0.0001581174,0.0002182103],"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":[0.00003025285,0.002467574,0.00008252906,0.003857963,0.0004616661,0.000017806,0.003187428,0.0001793775,0.0002160785,0.9435439,0.04483662,0.001118875],"study_design_scores_gemma":[0.0001602053,0.0001307537,0.00005203105,0.0002535442,0.0002996146,0.000005397274,0.001246493,0.005464426,0.0001923954,0.9894896,0.002191548,0.000513972],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.196057,0.0003611011,0.05757705,0.001793928,0.0003617109,0.004003447,0.001196585,0.0008700242,0.7377791],"genre_scores_gemma":[0.5170058,0.0000420127,0.4774114,0.0001304757,0.0001978735,0.001382242,0.00008206518,0.0002464218,0.003501677],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.7342775,"threshold_uncertainty_score":0.9997246,"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."}}