{"id":"W4399197812","doi":"10.48550/arxiv.2405.18501","title":"Small volume bodies of constant width","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada; Norges Forskningsråd; National Science Foundation","keywords":"Unit sphere; Constant (computer programming); Volume (thermodynamics); Ball (mathematics); Combinatorics; Unit (ring theory); Mathematics; Physics; Mathematical physics; Geometry; Thermodynamics; 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":[0.0008233194,0.000645056,0.0006901319,0.001313268,0.001051253,0.002105505,0.001456473,0.001453449,0.008631744],"category_scores_gemma":[0.004608539,0.0005277948,0.001011319,0.0006937376,0.003013448,0.004620042,0.003911057,0.002166535,0.001346556],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007591539,"about_ca_system_score_gemma":0.0003149564,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004717177,"about_ca_topic_score_gemma":0.0005030442,"domain_scores_codex":[0.9994541,0.00009453402,0.00001995571,0.0001543132,0.0001469332,0.0001303152],"domain_scores_gemma":[0.9982616,0.0007930452,0.0002082564,0.0004142531,0.0001271614,0.0001956041],"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":[0.00008481747,0.00002800621,0.0004086054,0.00009725761,0.00001426212,0.00006799163,0.0001797781,0.009622639,0.005474152,0.9733344,0.002308298,0.008379785],"study_design_scores_gemma":[0.00003730244,0.0000567823,0.0006838771,0.00007018395,0.00002361843,0.0001902661,0.0001175489,0.06623701,0.00806368,0.9119211,0.01256996,0.00002870647],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2477906,0.001033507,0.6597803,0.001753037,0.0004146103,0.0000548645,0.0004218541,0.0006893449,0.08806185],"genre_scores_gemma":[0.817249,0.0008877461,0.128857,0.0009004671,0.0003062423,0.0003036239,0.0007261746,0.001159231,0.04961059],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008631744,"threshold_uncertainty_score":0.02887601,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1950767227604834,"score_gpt":0.2278306505289118,"score_spread":0.03275392776842845,"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."}}