{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003806539,0.0003305289,0.0006332401,0.0005262649,0.00005921524,0.00004750866,0.0005407099,0.0002997602,0.0002273615],"category_scores_gemma":[0.0003291866,0.0003384799,0.0003255359,0.0004782171,0.0002305488,0.00005477659,0.001501947,0.0005760943,0.00008744454],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001194287,"about_ca_system_score_gemma":0.0002840934,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002163602,"about_ca_topic_score_gemma":0.00009747679,"domain_scores_codex":[0.9985254,0.00006532777,0.000388785,0.0005993096,0.0001018324,0.0003192925],"domain_scores_gemma":[0.998247,0.0003516381,0.0003538139,0.0006573392,0.0002987008,0.00009154277],"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":[0.00004904747,0.0001148535,0.0006781781,0.005151338,0.0003994156,0.0002454533,0.0008341859,0.001110537,0.000009772909,0.9885126,0.002672348,0.0002222082],"study_design_scores_gemma":[0.000224015,0.00006216995,0.00002578326,0.0005765902,0.0004105936,0.000005045165,0.0009236056,0.006482404,0.0002125411,0.9893039,0.001387121,0.0003861624],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8880477,0.001488489,0.03185249,0.0001558222,0.001028099,0.0004820797,0.0005168702,0.0003954114,0.07603306],"genre_scores_gemma":[0.9678437,0.0004295075,0.001072968,0.00002172529,0.00007836019,9.526682e-7,0.00001455818,0.00003595247,0.03050228],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07979601,"threshold_uncertainty_score":0.9999067,"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."}}