{"id":"W3106260003","doi":"10.1112/s0010437x17007515","title":"Rational points on hyperelliptic curves having a marked non-Weierstrass point","year":2017,"lang":"en","type":"article","venue":"Compositio Mathematica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":26,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of Toronto","funders":"","keywords":"Mathematics; Hyperelliptic curve; Genus; Hyperelliptic curve cryptography; Pure mathematics; Fixed point; Infinity; Group (periodic table); Mathematical analysis; Algebra over a field","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","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001048141,0.0003352584,0.0005276783,0.0001086706,0.0008877698,0.0002288652,0.0007632971,0.0001169136,0.001474094],"category_scores_gemma":[0.001150954,0.0003003402,0.0002171058,0.00007080931,0.0002472099,0.0003188744,0.0001974623,0.0003041544,0.001027139],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007370419,"about_ca_system_score_gemma":0.00004817905,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002258207,"about_ca_topic_score_gemma":9.366463e-7,"domain_scores_codex":[0.9980188,0.0001170802,0.0005391896,0.0003919944,0.0005228498,0.0004101004],"domain_scores_gemma":[0.996617,0.001282684,0.0004399883,0.001371384,0.0001096922,0.000179227],"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":[0.000239778,0.001818943,0.0002688583,0.003379396,0.0004356938,0.0001724851,0.001417812,0.000003406114,0.004562122,0.9465857,0.0402868,0.0008289853],"study_design_scores_gemma":[0.0009916633,0.0001583436,0.002057411,0.00304872,0.0001763971,0.000216103,0.0001813157,0.001315958,0.005685861,0.9854649,0.0001631772,0.0005401244],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7160918,0.0001116345,0.03330435,0.007513945,0.0007066745,0.001402708,0.0000494978,0.000330351,0.240489],"genre_scores_gemma":[0.9752781,0.00001887111,0.02137696,0.0006666686,0.0001762228,0.00006851144,0.00001771795,0.00006107187,0.00233584],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2591863,"threshold_uncertainty_score":0.9999449,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04180980427589012,"score_gpt":0.311978235707418,"score_spread":0.2701684314315279,"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."}}