{"id":"W7125639586","doi":"10.1093/qmath/haaf012","title":"Mazur’s Growth Number Conjecture in the Rank One Case","year":2025,"lang":"en","type":"article","venue":"The Quarterly Journal of Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada; University of Texas Rio Grande Valley","keywords":"Conjecture; Rank (graph theory); Elliptic curve; Prime (order theory); Quadratic equation; Field (mathematics); Quadratic field","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001378634,0.0004741629,0.0006298147,0.001679145,0.001659989,0.002857821,0.0008300194,0.0009336749,0.005892303],"category_scores_gemma":[0.005604155,0.0002302172,0.0005821147,0.000756701,0.004450481,0.005708859,0.002434117,0.001655878,0.000695309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001224452,"about_ca_system_score_gemma":0.0004902455,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001003338,"about_ca_topic_score_gemma":0.0007974188,"domain_scores_codex":[0.9993083,0.0001331911,0.00002991798,0.0001621643,0.0001631408,0.0002033534],"domain_scores_gemma":[0.9956448,0.002053017,0.0005110041,0.0005600104,0.0003870027,0.0008441763],"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":[0.0001898607,0.00004098917,0.003918923,0.00007222311,0.000009177952,0.0004314751,0.0004953077,0.002209091,0.002079494,0.9808292,0.002472838,0.007251366],"study_design_scores_gemma":[0.00004788458,0.00006255561,0.002278444,0.00003431821,0.00001222559,0.000481975,0.000449402,0.009781277,0.002341727,0.9801611,0.004321471,0.00002765494],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8969111,0.001181812,0.01624958,0.005528278,0.0001754409,0.00002803956,0.0002129783,0.0002613865,0.07945127],"genre_scores_gemma":[0.9948272,0.0002236731,0.001083636,0.0001044313,0.000127771,0.00001297305,0.00008218982,0.00001242254,0.003525626],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005892303,"threshold_uncertainty_score":0.01971173,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02444599603413371,"score_gpt":0.300442823037926,"score_spread":0.2759968270037923,"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."}}