{"id":"W3198633257","doi":"10.1007/s11139-023-00701-9","title":"Arithmetic statistics and diophantine stability for elliptic curves","year":2023,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Simons Foundation","keywords":"Mathematics; Diophantine equation; Elliptic curve; Number theory; Rational number; Prime (order theory); Rank (graph theory); Group (periodic table); Prime number; Stability (learning theory); Algebraic number field; Pure mathematics; Discrete mathematics; Arithmetic; Combinatorics","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.003491563,0.0001401926,0.0002476984,0.00006894712,0.0004071255,0.00007722295,0.0002307235,0.0000402304,0.0001971856],"category_scores_gemma":[0.00171884,0.00009010598,0.00007347002,0.0002341255,0.0001830901,0.00007908646,0.00007224624,0.0002904866,0.0000358066],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001679923,"about_ca_system_score_gemma":0.00003588787,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":7.718643e-7,"about_ca_topic_score_gemma":0.000001525738,"domain_scores_codex":[0.9987332,0.0002006046,0.0003544927,0.0001388571,0.0002389745,0.0003339218],"domain_scores_gemma":[0.9968826,0.002466224,0.0001697593,0.0002583276,0.0001089607,0.0001141184],"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":[0.0007750935,0.0006510897,0.005181566,0.006371946,0.001071895,0.0001813924,0.008804733,0.00002657471,0.001886088,0.7294566,0.1914061,0.05418691],"study_design_scores_gemma":[0.0005864459,0.0001259336,0.0023339,0.0001412257,0.0001565861,0.0002657312,0.0006471349,0.0007281204,0.0006514742,0.9927879,0.001424191,0.000151362],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9294866,0.0009669745,0.06571466,0.002525393,0.0004269935,0.0004541062,0.00007943657,0.00009556155,0.0002502431],"genre_scores_gemma":[0.9862494,0.0009909233,0.009828025,0.000267168,0.0005137304,0.00002499177,0.00001178176,0.00004989614,0.00206402],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2633313,"threshold_uncertainty_score":0.3674415,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06370577316792606,"score_gpt":0.3226428105491814,"score_spread":0.2589370373812554,"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."}}