{"id":"W2140090734","doi":"10.1017/s1446788714000044","title":"FROM SEPARABLE POLYNOMIALS TO NONEXISTENCE OF RATIONAL POINTS ON CERTAIN HYPERELLIPTIC CURVES","year":2014,"lang":"en","type":"article","venue":"Journal of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Hasse principle; Counterexample; Separable space; Pure mathematics; Mathematical analysis; Discrete mathematics; Algebraic number 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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002186354,0.0001924497,0.0005990409,0.00003057001,0.00009918492,0.00002656555,0.0006563315,0.0001206329,0.0009974249],"category_scores_gemma":[0.00230597,0.000119061,0.0006270849,0.0002312369,0.0001468882,0.00009457504,0.00008528119,0.000357328,0.0001075867],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006566687,"about_ca_system_score_gemma":0.00005320969,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004446063,"about_ca_topic_score_gemma":3.370986e-7,"domain_scores_codex":[0.9977068,0.0002709521,0.0009120869,0.0001487065,0.0007088875,0.000252615],"domain_scores_gemma":[0.9962753,0.002262788,0.0006844047,0.0004495172,0.0001446784,0.0001833131],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0004509556,0.002577029,0.0008674297,0.002643708,0.001465991,0.000007491249,0.009398157,0.0004911306,0.02528149,0.4682408,0.4879659,0.0006099871],"study_design_scores_gemma":[0.0005276131,0.0002076148,0.0007062094,0.001734804,0.0002054051,0.00003923594,0.0006750922,0.0001492936,0.0178408,0.9766678,0.001056063,0.0001900495],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9807872,0.00002504774,0.005004952,0.01166366,0.0002754389,0.0003566024,0.00002412372,0.00001392541,0.001849105],"genre_scores_gemma":[0.9501638,0.00001003302,0.04418686,0.001393014,0.000399306,0.000005761141,9.216464e-7,0.00002669191,0.003813596],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.508427,"threshold_uncertainty_score":0.9999158,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04943112108554451,"score_gpt":0.3179418422704769,"score_spread":0.2685107211849324,"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."}}