{"id":"W7096154645","doi":"","title":"Outer Billiards, Quarter Turn Compositions, and Polytope Exchange Transformations , preprint","year":2011,"lang":"en","type":"article","venue":"","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Polytope; Euclidean geometry; Lattice (music); Affine transformation; Quarter (Canadian coin); Preprint; Euclidean distance","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001203834,0.0002401819,0.000224111,0.0004092053,0.0005592435,0.001058394,0.0002357075,0.0003225506,0.002653862],"category_scores_gemma":[0.0005007161,0.0001650415,0.0002295135,0.0002496397,0.00116285,0.001319849,0.0005715254,0.0006573125,0.0002941643],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002846783,"about_ca_system_score_gemma":0.0001177519,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003341957,"about_ca_topic_score_gemma":0.0002394833,"domain_scores_codex":[0.9998991,0.00001673965,0.000004429412,0.00001982975,0.00004066354,0.0000192709],"domain_scores_gemma":[0.9998533,0.00002684852,0.00004443384,0.00002857105,0.00001573736,0.00003106376],"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":[0.00005474535,0.00001729381,0.0007981164,0.00002325082,0.00000636597,0.0002328967,0.0002029326,0.006179839,0.006737182,0.9766455,0.00055907,0.008542822],"study_design_scores_gemma":[0.00002214642,0.00009588002,0.003446239,0.00001522445,0.00001150248,0.001347087,0.000575557,0.05739198,0.01050649,0.9082208,0.01834333,0.00002371405],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8578219,0.000798503,0.09230793,0.0003966694,0.0001324405,0.00002268908,0.0000927653,0.0001239223,0.04830322],"genre_scores_gemma":[0.9758863,0.000297079,0.01188614,0.00004897064,0.00005742281,0.00001501582,0.00008803778,0.00005041544,0.01167045],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002653862,"threshold_uncertainty_score":0.008878052,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06246902690236802,"score_gpt":0.2823042944679425,"score_spread":0.2198352675655745,"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."}}