{"id":"W4388221631","doi":"10.1007/s00454-023-00579-w","title":"On the Structure of Pointsets with Many Collinear Triples","year":2023,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Hungarian Scientific Research Fund","keywords":"Mathematics; Combinatorics; Conic section; Conjecture; General position; Set (abstract data type); Finite set; Plane (geometry); Point (geometry); Regular polygon; Position (finance); Discrete geometry; Discrete mathematics; Geometry; Mathematical analysis; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008633902,0.0006501668,0.001203902,0.003424506,0.003699772,0.004492313,0.00183607,0.001931275,0.009548453],"category_scores_gemma":[0.005177932,0.0007532789,0.0006887442,0.003050196,0.005220732,0.008055146,0.004006031,0.002957398,0.001290521],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001145967,"about_ca_system_score_gemma":0.0006157227,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001292217,"about_ca_topic_score_gemma":0.001062373,"domain_scores_codex":[0.9991748,0.0002104012,0.00004034444,0.0001769849,0.0002354881,0.0001619598],"domain_scores_gemma":[0.9958753,0.001879722,0.0007388836,0.0004312657,0.0004891127,0.0005856773],"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":[0.00004208894,0.00001455439,0.00028764,0.00002151697,0.000005315948,0.0001076826,0.0003024782,0.001482476,0.000367128,0.9942765,0.0008445281,0.002248045],"study_design_scores_gemma":[0.000008000439,0.000009975945,0.0001221095,0.00001251734,0.000003735208,0.00007720816,0.0001839829,0.003048386,0.0001374814,0.9953999,0.0009887848,0.000007893646],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8000202,0.00107886,0.1049643,0.002768434,0.0002621434,0.00007962401,0.0008115285,0.0003747152,0.08964012],"genre_scores_gemma":[0.9741849,0.0004907203,0.01350384,0.0003060455,0.0001978043,0.00006981619,0.0004935627,0.0001398754,0.0106134],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009548453,"threshold_uncertainty_score":0.03194278,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02227051781392568,"score_gpt":0.2856425737357282,"score_spread":0.2633720559218025,"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."}}