{"id":"W4392282123","doi":"10.1090/proc/16806","title":"Answer to a conjecture of Lau–Ülger","year":2024,"lang":"en","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Conjecture; Mathematics; Mathematical economics; Combinatorics","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":[0.003581308,0.001353713,0.002674005,0.001268332,0.003531694,0.004019028,0.002055892,0.004646636,0.03610131],"category_scores_gemma":[0.03295086,0.0007163846,0.001934977,0.001688091,0.006242599,0.01400091,0.005137069,0.006897787,0.008056826],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002447116,"about_ca_system_score_gemma":0.001647106,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002047744,"about_ca_topic_score_gemma":0.001260362,"domain_scores_codex":[0.9959986,0.001389459,0.0001515267,0.00108851,0.0008305625,0.0005413903],"domain_scores_gemma":[0.9842607,0.009520259,0.000947465,0.002049334,0.002273835,0.0009484657],"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":[0.0004378595,0.00009792092,0.001320777,0.0004916535,0.00006808006,0.0002315092,0.0004766546,0.001850875,0.0004489905,0.8196595,0.1568182,0.01809796],"study_design_scores_gemma":[0.00006755452,0.00003275073,0.0007224331,0.00007905286,0.00002429705,0.0001475905,0.000174757,0.004317327,0.0002483674,0.9667691,0.02738662,0.00003021804],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"commentary","genre_gemma":"empirical","genre_scores_codex":[0.08678152,0.01462727,0.1004551,0.4016148,0.01588963,0.0001092519,0.003231124,0.002511245,0.37478],"genre_scores_gemma":[0.7956609,0.006028997,0.02768185,0.0652264,0.0148464,0.0004015944,0.003830468,0.001127211,0.08519613],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03610131,"threshold_uncertainty_score":0.1207709,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02019636524710601,"score_gpt":0.316273642557707,"score_spread":0.296077277310601,"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."}}