{"id":"W4312078624","doi":"10.4171/rsmup/105","title":"On the extension of even families of non-congruent numbers","year":2022,"lang":"it","type":"article","venue":"Rendiconti del Seminario Matematico della Università di Padova","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"","keywords":"Extension (predicate logic); Mathematics; Combinatorics; Arithmetic; Computer science; Programming language","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":[],"category_scores_codex":[0.002850734,0.0007442553,0.001803402,0.0006078124,0.000960422,0.00003548147,0.0015801,0.000264273,0.004276488],"category_scores_gemma":[0.0005241011,0.0006471259,0.0007911284,0.0007881949,0.0007110985,0.0001817647,0.0008986586,0.0008221942,0.0001557997],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006335997,"about_ca_system_score_gemma":0.0002865817,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001932883,"about_ca_topic_score_gemma":0.00002319175,"domain_scores_codex":[0.994147,0.001017784,0.001822747,0.0006612094,0.001668454,0.0006827752],"domain_scores_gemma":[0.9913813,0.003447049,0.002597026,0.002035826,0.0003386031,0.0002001405],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"qualitative","study_design_scores_codex":[0.002041736,0.007116153,0.0002919997,0.01704608,0.003409857,0.0007170892,0.1156384,0.00798336,0.02098228,0.7198467,0.1033998,0.001526527],"study_design_scores_gemma":[0.01252294,0.007711271,0.0004715054,0.02358789,0.01119255,0.0008411141,0.4876946,0.1213138,0.03368791,0.2495819,0.04548733,0.005907228],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9173278,0.0007440645,0.004792617,0.0003595661,0.001006708,0.002129581,0.0004261575,0.00008844493,0.07312512],"genre_scores_gemma":[0.9703627,0.0002156378,0.001902482,0.0001036018,0.00003366703,0.00002208115,0.00003535469,0.000124352,0.02720007],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4702648,"threshold_uncertainty_score":0.999598,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01904070785603201,"score_gpt":0.235638659625624,"score_spread":0.216597951769592,"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."}}