{"id":"W4395670166","doi":"10.1142/s1793042124501094","title":"A function related to the Mordell–Weil rank of elliptic curves","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Elliptic curve; Rank (graph theory); Pure mathematics; Function (biology); Modular elliptic curve; Algebra over a field; Combinatorics; Quarter period","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002688511,0.000139403,0.0002377119,0.0001945124,0.00003764639,0.00004470851,0.0006020283,0.00006794918,0.007145429],"category_scores_gemma":[0.001190602,0.00009055324,0.0002841894,0.0003268198,0.00008715122,0.0002277172,0.00008233339,0.0003781921,0.0003619553],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006207715,"about_ca_system_score_gemma":0.00008809681,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002032672,"about_ca_topic_score_gemma":7.716114e-7,"domain_scores_codex":[0.9980142,0.0002933912,0.000731859,0.0001271228,0.0006976826,0.0001357069],"domain_scores_gemma":[0.9967252,0.002214898,0.0003061931,0.0001985464,0.0004858554,0.00006933333],"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":[0.0009514794,0.0002107186,0.000129539,0.0001900476,0.001815383,0.0001191741,0.001998224,0.00008988492,0.0004799084,0.8792807,0.1012199,0.01351498],"study_design_scores_gemma":[0.0003255199,0.00009184859,0.0002349439,0.001440845,0.000201307,0.0008360376,0.0005167731,0.00007464393,0.000635772,0.9517691,0.04375582,0.0001173488],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8211107,0.008961952,0.07307237,0.01552104,0.01749902,0.0006025263,0.0001969358,0.000173332,0.06286212],"genre_scores_gemma":[0.9918025,0.0002197274,0.0005195223,0.0005975473,0.0004991863,0.000005552778,0.000005925398,0.00003062633,0.006319472],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1706917,"threshold_uncertainty_score":0.9937622,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01783951758261028,"score_gpt":0.3174259228380064,"score_spread":0.2995864052553961,"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."}}