{"id":"W4417293722","doi":"10.48550/arxiv.2512.10077","title":"Cleanliness and the Varchenko-Gelfand algebra","year":2025,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Complexification; Hyperplane; Complement (music); Class (philosophy); Algebra over a field; Statement (logic)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006712017,0.0002513113,0.0004394416,0.001664004,0.001550896,0.00150901,0.0004757266,0.0005016008,0.006372504],"category_scores_gemma":[0.001947089,0.0002922988,0.0004091208,0.001002404,0.003050927,0.003672696,0.001095618,0.0009578413,0.0006715328],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001203934,"about_ca_system_score_gemma":0.000431071,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001508753,"about_ca_topic_score_gemma":0.0008709145,"domain_scores_codex":[0.9995035,0.0001139411,0.00002287579,0.0001101904,0.0001664083,0.00008306309],"domain_scores_gemma":[0.9988392,0.0003562261,0.0003051546,0.0001400207,0.0001779718,0.0001813645],"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":[0.00002287521,0.000006308581,0.0003531167,0.0000197284,0.00000582084,0.00004869599,0.0001049043,0.00107005,0.0006945113,0.9940333,0.0006167715,0.003023981],"study_design_scores_gemma":[0.00001339934,0.00002345243,0.0008972499,0.00001182505,0.000006547158,0.0001720644,0.0001198845,0.003403354,0.0006822458,0.9879192,0.006734,0.00001686113],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7806322,0.003128291,0.1064807,0.002449789,0.0001950206,0.00003163347,0.0005488757,0.0002974037,0.106236],"genre_scores_gemma":[0.9816735,0.0007699699,0.0100583,0.0001169824,0.000152788,0.00001896198,0.0001834074,0.00003570506,0.006990311],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006372504,"threshold_uncertainty_score":0.0213182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08527806846224255,"score_gpt":0.2206499245874335,"score_spread":0.1353718561251909,"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."}}