{"id":"W3215721344","doi":"10.2140/involve.2024.17.11","title":"Cones and ping-pong in three dimensions","year":2024,"lang":"en","type":"article","venue":"Involve a Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Combinatorics; Ping pong; Mathematics; Table (database); Sign (mathematics); Product (mathematics); Cone (formal languages); Physics; Geometry; Mathematical analysis; Computer science; Algorithm","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0002548326,0.0003145351,0.0002298742,0.0009285432,0.001279307,0.001435932,0.0004734439,0.0004865472,0.003252301],"category_scores_gemma":[0.000609298,0.0001675029,0.0002889109,0.0005125835,0.001500891,0.001036644,0.001018411,0.0008016702,0.0003759713],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008046477,"about_ca_system_score_gemma":0.0003568958,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0020484,"about_ca_topic_score_gemma":0.002016628,"domain_scores_codex":[0.9998067,0.00004272579,0.000007171273,0.00002660363,0.00005282063,0.00006408386],"domain_scores_gemma":[0.9997779,0.00004808422,0.00003475251,0.00002271513,0.00002788887,0.00008865585],"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":[0.00002325521,0.00001600374,0.0003251338,0.000009923715,0.000002979808,0.0001863447,0.0002088024,0.001740089,0.0009629428,0.9926354,0.0004535136,0.003435648],"study_design_scores_gemma":[0.00002046202,0.00003185348,0.0004519995,0.00001055036,0.000003371781,0.0002220463,0.0003475825,0.01504869,0.001201695,0.978095,0.004551276,0.00001556765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8953969,0.0002805539,0.0357809,0.0004794727,0.0001111139,0.00004694862,0.000105934,0.000168136,0.06763016],"genre_scores_gemma":[0.9894628,0.0001075354,0.005009895,0.00006205311,0.00002152721,0.00001989549,0.00005621284,0.00002305009,0.005236986],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003252301,"threshold_uncertainty_score":0.01087999,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0513411371432033,"score_gpt":0.3093397357643045,"score_spread":0.2579985986211012,"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."}}