{"id":"W4213342205","doi":"10.1090/tran/8664","title":"Sharing pizza in 𝑛 dimensions","year":2022,"lang":"en","type":"preprint","venue":"Transactions of the American Mathematical Society","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"Agence Nationale de la Recherche; Simons Foundation","keywords":"Coxeter group; Combinatorics; Hyperplane; Mathematics; Bounded function; Regular polygon; Ball (mathematics); Partition (number theory); Geometry; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000815413,0.0004720519,0.001357724,0.00008897402,0.0002784487,0.00002957828,0.00166175,0.0001590378,0.0005566785],"category_scores_gemma":[0.0004177373,0.0003806106,0.001331024,0.000926316,0.000679251,0.00006932588,0.0008567203,0.002081127,0.000007584368],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005109989,"about_ca_system_score_gemma":0.0001805713,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008554695,"about_ca_topic_score_gemma":0.00001159215,"domain_scores_codex":[0.9966523,0.000187119,0.001220797,0.000579379,0.0008740126,0.0004863709],"domain_scores_gemma":[0.9949515,0.001594168,0.001123686,0.002136436,0.00008805301,0.0001061186],"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":[0.0001535912,0.009189351,0.0006763299,0.01007172,0.001784054,0.00001333973,0.03075019,0.0322121,0.001830474,0.9090273,0.00193887,0.00235269],"study_design_scores_gemma":[0.0003364251,0.00005382888,0.00006966564,0.000411396,0.0002688405,0.000007683177,0.002299197,0.008120403,0.000350109,0.9876241,0.00008320806,0.0003751123],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7053559,0.00009729587,0.2860727,0.001150428,0.0009539871,0.002394662,0.0001561439,0.0003746211,0.003444336],"genre_scores_gemma":[0.7976933,0.0001004814,0.2005175,0.0001094413,0.0000511575,0.0005287682,0.000003402675,0.0001665572,0.0008293827],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09233743,"threshold_uncertainty_score":0.9998646,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04493452194484173,"score_gpt":0.3386680385524519,"score_spread":0.2937335166076102,"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."}}