{"id":"W4407231844","doi":"10.48550/arxiv.2502.03464","title":"Improving the trivial bound for $\\ell$-torsion in class groups","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric and Algebraic Topology","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":"Torsion (gastropod); Mathematics; Class (philosophy); Pure mathematics; Combinatorics; Computer science; Medicine; Artificial intelligence; Anatomy","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":[0.005325159,0.003252365,0.002420448,0.003418349,0.00339775,0.005825632,0.006880004,0.002611058,0.04167453],"category_scores_gemma":[0.03518453,0.001212577,0.002186144,0.002769276,0.008881578,0.03320925,0.02121032,0.01031604,0.01519341],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002871273,"about_ca_system_score_gemma":0.002154529,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001376619,"about_ca_topic_score_gemma":0.002882048,"domain_scores_codex":[0.9924538,0.001733953,0.0003205109,0.001431436,0.002453804,0.001606507],"domain_scores_gemma":[0.9707217,0.01533377,0.000808268,0.009938268,0.001517239,0.001680743],"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":[0.001150076,0.0003362074,0.003788811,0.0007092245,0.00006832,0.0003845253,0.0007491161,0.008215043,0.00489962,0.8280443,0.04771469,0.1039401],"study_design_scores_gemma":[0.00008521171,0.0001113164,0.000704785,0.0001033647,0.00009796544,0.0003085986,0.000132373,0.02609452,0.005402604,0.9491525,0.01773608,0.00007071268],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1708728,0.00760467,0.4275148,0.0298712,0.003955298,0.0002163945,0.001976992,0.01117779,0.3468101],"genre_scores_gemma":[0.8500319,0.003473207,0.06987088,0.004375443,0.004252597,0.0003580133,0.002216153,0.004655982,0.06076577],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.04167453,"threshold_uncertainty_score":0.1394151,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07432103330375579,"score_gpt":0.3229581983227311,"score_spread":0.2486371650189753,"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."}}