{"id":"W4405360069","doi":"10.1016/j.aim.2024.110080","title":"Making the motivic group structure on the endomorphisms of the projective line explicit","year":2024,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Center for Advanced Study, University of Illinois at Urbana-Champaign; Norges Forskningsråd; Réseau de cancérologie Rossy; Trond Mohn stiftelse","keywords":"Mathematics; Endomorphism; Projective test; Projective line; Pure mathematics; Group (periodic table); Line (geometry); Projective representation; Algebra over a field; Projective space; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004269459,0.0003688185,0.0003218254,0.001409078,0.001304554,0.001827906,0.0005077053,0.0004326828,0.003565589],"category_scores_gemma":[0.0006213262,0.0002634319,0.0004165914,0.0005716212,0.003194265,0.002420136,0.002462698,0.001192768,0.0008018047],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006746858,"about_ca_system_score_gemma":0.0003771572,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007511768,"about_ca_topic_score_gemma":0.0006948704,"domain_scores_codex":[0.9995276,0.00008837393,0.00001755201,0.0001330149,0.0001277812,0.0001058613],"domain_scores_gemma":[0.9995766,0.0000625005,0.00009284436,0.00009665597,0.0000757997,0.00009560145],"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":[0.00002127841,0.00002132832,0.0006230948,0.0000250957,0.000004776643,0.0001667343,0.0008562899,0.0004209179,0.003138275,0.9874203,0.0003500601,0.006951974],"study_design_scores_gemma":[0.00004709344,0.0001865572,0.003859298,0.00006038504,0.00002640987,0.0008580182,0.0009227112,0.007096488,0.008325172,0.9163942,0.06216688,0.00005674846],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.551511,0.0004769075,0.2954159,0.001212348,0.0002530659,0.0001106986,0.0002754993,0.0004288705,0.1503157],"genre_scores_gemma":[0.9424986,0.000310839,0.03930096,0.0001785157,0.0001574722,0.00009665621,0.0002030749,0.00006808777,0.01718574],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003565589,"threshold_uncertainty_score":0.01192808,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0417528127529969,"score_gpt":0.3294000006431694,"score_spread":0.2876471878901725,"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."}}