{"id":"W2919484032","doi":"10.5565/publmat6722309","title":"Some extensions of the modular method and Fermat equations of signature $(13,13,n)$","year":2023,"lang":"ca","type":"article","venue":"Publicacions Matemàtiques","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche; Fundación BBVA","keywords":"Mathematics; Fermat's Last Theorem; Signature (topology); Modular design; Algebra over a field; Calculus (dental); Applied mathematics; Pure mathematics; Geometry; Computer science; Programming language","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001501757,0.0008307596,0.0007280324,0.00229192,0.001605054,0.001934953,0.001242714,0.001357966,0.01522046],"category_scores_gemma":[0.003348493,0.0004108644,0.001846031,0.001395306,0.002476506,0.004361746,0.002401422,0.002664384,0.001583849],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001466789,"about_ca_system_score_gemma":0.0009128328,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007984213,"about_ca_topic_score_gemma":0.0009722062,"domain_scores_codex":[0.9992091,0.0002808006,0.00004626995,0.0001370714,0.0001879426,0.0001388279],"domain_scores_gemma":[0.9987648,0.0004387253,0.0002566037,0.0001587641,0.0001802035,0.0002009012],"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":[0.00002440249,0.00001945284,0.0002759965,0.00003386067,0.000007322129,0.0001182876,0.0001284176,0.000521833,0.0002908811,0.9892619,0.002064144,0.007253607],"study_design_scores_gemma":[0.00002116439,0.00002480116,0.0004211108,0.00001811808,0.00000648133,0.0002497332,0.0000420101,0.003882323,0.0002323768,0.9900091,0.0050735,0.00001944762],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4344699,0.007745387,0.1713955,0.01141129,0.003095786,0.0001277454,0.0006562985,0.0003284246,0.3707697],"genre_scores_gemma":[0.8807824,0.002724441,0.0392528,0.0009388475,0.003141916,0.0001181776,0.000424855,0.0001816312,0.07243493],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01522046,"threshold_uncertainty_score":0.05091751,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03447049998953174,"score_gpt":0.3191142583855754,"score_spread":0.2846437583960437,"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."}}