{"id":"W2952350480","doi":"10.48550/arxiv.math/0408153","title":"Root numbers and ranks in positive characteristic","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Conjecture; Elliptic curve; Rank (graph theory); Combinatorics; Parity (physics); Function field; Field (mathematics); Discrete mathematics; Pure mathematics; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000770033,0.0004776319,0.0004608332,0.002216371,0.00113086,0.002946772,0.0006176496,0.00044083,0.00388202],"category_scores_gemma":[0.004610852,0.0003603864,0.0003692306,0.001424786,0.004407062,0.004201551,0.002747495,0.001697907,0.0007331888],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001623353,"about_ca_system_score_gemma":0.0004560796,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009911668,"about_ca_topic_score_gemma":0.0008779148,"domain_scores_codex":[0.9993104,0.0001091837,0.00003534269,0.0001438032,0.0002078368,0.0001934365],"domain_scores_gemma":[0.9977838,0.001002693,0.0005223058,0.0002136182,0.0001669603,0.0003106112],"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":[0.0001365646,0.0000380889,0.005016488,0.00006662998,0.00001041467,0.0002943123,0.0007360595,0.004436261,0.001859402,0.9678515,0.001682687,0.01787154],"study_design_scores_gemma":[0.00003164083,0.00004021078,0.002624269,0.00002287657,0.00001648349,0.0004263279,0.0001769496,0.00496211,0.001237344,0.9860682,0.004367473,0.0000260426],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8997051,0.0009447894,0.02613218,0.001935448,0.00007973201,0.00002565607,0.0003180953,0.0002401468,0.07061895],"genre_scores_gemma":[0.9904312,0.00032979,0.003273259,0.00005397436,0.00008948464,0.00001784794,0.0001223978,0.00002252511,0.005659462],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00388202,"threshold_uncertainty_score":0.01298666,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03756999371242367,"score_gpt":0.293979514108774,"score_spread":0.2564095203963503,"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."}}