{"id":"W1997354761","doi":"10.1112/s0010437x13007410","title":"The Chabauty–Coleman bound at a prime of bad reduction and Clifford bounds for geometric rank functions","year":2013,"lang":"en","type":"preprint","venue":"Compositio Mathematica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"National Defense Science and Engineering Graduate; National Security Agency","keywords":"Rank (graph theory); Mathematics; Prime (order theory); Good reduction; Combinatorics; Reduction (mathematics); Jacobian matrix and determinant; Genus; Field (mathematics); Algebraic number field; Divisor (algebraic geometry); Discrete mathematics; Pure mathematics; Geometry; Applied mathematics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001577294,0.0005313221,0.001002852,0.0004068764,0.001060542,0.0002638276,0.0005511456,0.0004330676,0.0002382955],"category_scores_gemma":[0.0006930999,0.0004111217,0.0004425163,0.0004129678,0.0006284897,0.0001282962,0.0008723161,0.0004953105,0.00006909448],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002007223,"about_ca_system_score_gemma":0.0001032374,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001056199,"about_ca_topic_score_gemma":0.000003375778,"domain_scores_codex":[0.9970044,0.0001842545,0.001203645,0.0006058363,0.0004776321,0.0005242414],"domain_scores_gemma":[0.9939367,0.003063753,0.001108862,0.001332996,0.0003873968,0.0001702726],"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":[0.001023181,0.002050397,0.00007529558,0.01544142,0.003170016,0.000004192322,0.005596617,0.00001857132,0.004246483,0.9025154,0.05723018,0.008628243],"study_design_scores_gemma":[0.0007994348,0.0002467,0.0001382652,0.0006107668,0.0007223939,0.0001599693,0.000409962,0.0009076193,0.003010649,0.9904118,0.002100768,0.0004817016],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9227949,0.001870627,0.0593205,0.001169846,0.001339975,0.004832176,0.0002016472,0.0002513998,0.008218895],"genre_scores_gemma":[0.9566244,0.0002486618,0.02494148,0.00003792339,0.000544795,0.001954459,0.0001790572,0.0001756271,0.0152936],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08789636,"threshold_uncertainty_score":0.9998341,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03279528919523367,"score_gpt":0.2927227194653673,"score_spread":0.2599274302701337,"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."}}