{"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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002201523,0.000122389,0.0001826316,0.00005902135,0.00007773366,0.00003944853,0.00009175674,0.00006589056,0.002120533],"category_scores_gemma":[0.0000201415,0.00008835985,0.00006431092,0.00005132289,0.00004824138,0.0001617213,0.00003556244,0.00009035991,0.00009899899],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000101769,"about_ca_system_score_gemma":0.000005842264,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002483735,"about_ca_topic_score_gemma":0.00003395232,"domain_scores_codex":[0.9992322,0.00003033726,0.0003045098,0.000144097,0.0001184438,0.0001704274],"domain_scores_gemma":[0.9994506,0.00009657701,0.00005059698,0.0002587904,0.00004146333,0.000101978],"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":[0.00001024071,0.0003824517,0.0001839766,0.0002706879,0.00005280283,0.000004427295,0.008633047,6.919784e-8,0.0002747483,0.9851604,0.002883274,0.002143854],"study_design_scores_gemma":[0.0005337109,0.0001145086,0.002166392,0.00008598573,0.00007344349,0.00006803379,0.0006152689,0.008373488,0.001138291,0.9840074,0.002453553,0.0003699407],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1772033,0.00004570263,0.5277592,0.0013162,0.00009054546,0.0008243074,0.00006553886,0.000219948,0.2924753],"genre_scores_gemma":[0.9386587,0.00003661705,0.05951644,0.0002344693,0.00002316723,0.00005348774,0.00000675733,0.0000168069,0.001453539],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7614554,"threshold_uncertainty_score":0.9987916,"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."}}