{"id":"W4321011964","doi":"10.48550/arxiv.2302.06735","title":"Homogeneous spaces not separated by arcs","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Homogeneity (statistics); Homogeneous; Mathematics; Dimension (graph theory); Arc (geometry); Pure mathematics; Mathematical analysis; Geometry; Combinatorics; Statistics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002502762,0.000390876,0.000513147,0.0001806663,0.0001971031,0.00002675515,0.0006889927,0.0006207144,0.0001995309],"category_scores_gemma":[0.00018682,0.0004475968,0.0002213383,0.0003027803,0.0003130272,0.00007753705,0.0007888119,0.0007852188,0.0005775189],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001361376,"about_ca_system_score_gemma":0.00009671741,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004899941,"about_ca_topic_score_gemma":0.00007343946,"domain_scores_codex":[0.9981873,0.0002124641,0.0002215223,0.0008702418,0.00007236556,0.0004361311],"domain_scores_gemma":[0.9979733,0.0006018097,0.0002750011,0.0009060334,0.000099819,0.0001440853],"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":[0.0004528695,0.0003143687,0.0007864985,0.0003893768,0.0007934737,0.002593144,0.0006596652,0.0554658,0.0004523165,0.9066123,0.03134532,0.0001348712],"study_design_scores_gemma":[0.0004579107,0.00004900386,0.00002928753,0.00007307615,0.000235891,0.00001105853,0.0002744396,0.008259143,0.001265997,0.9861707,0.002574886,0.0005985785],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9373169,0.0001063888,0.05539373,0.0001945631,0.0008396826,0.0004318855,0.0002985192,0.0009106796,0.004507671],"genre_scores_gemma":[0.9326252,0.0003319151,0.0005871829,0.00008869431,0.00007794293,0.000001816739,0.00009971158,0.00007046838,0.066117],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07955842,"threshold_uncertainty_score":0.9997976,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1654726779161316,"score_gpt":0.2501454586137062,"score_spread":0.08467278069757458,"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."}}