{"id":"W2028125824","doi":"10.1063/1.3430567","title":"Two-dimensional symmetric and antisymmetric generalizations of sine functions","year":2010,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Antisymmetric relation; Sine; Trigonometric functions; Formalism (music); Lattice (music); Orthogonal functions; Euclidean geometry; Interpolation (computer graphics)","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":[],"consensus_categories":[],"category_scores_codex":[0.00133637,0.0001964666,0.0008170714,0.000348478,0.00009171345,0.00003309491,0.0001870351,0.00008998135,0.0003019076],"category_scores_gemma":[0.00196084,0.0001346521,0.0003502935,0.001203174,0.0001761762,0.000195598,0.00005096652,0.0004381454,0.000009354029],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000110138,"about_ca_system_score_gemma":0.00005943508,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001619351,"about_ca_topic_score_gemma":0.000001306678,"domain_scores_codex":[0.9977298,0.0000886795,0.001179804,0.0001373796,0.0006624206,0.000201889],"domain_scores_gemma":[0.9960997,0.002184764,0.0006530367,0.0002807991,0.0005775187,0.0002042041],"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":[0.00001274495,0.001145228,0.0001185831,0.0003843642,0.0002365092,0.000005164401,0.00009741697,0.00005928828,0.01033986,0.9822319,0.0004257963,0.004943104],"study_design_scores_gemma":[0.0007199635,0.0001284885,0.0001380666,0.0000950267,0.0006056512,0.0001645672,0.00003716339,0.00965099,0.004669216,0.9835644,0.00007358177,0.00015284],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.511539,0.0001064218,0.4821646,0.0003028552,0.0001828045,0.0001627968,0.00001483998,0.0000189408,0.005507805],"genre_scores_gemma":[0.6355491,0.00001197132,0.3639465,0.00002917207,0.0002372796,0.00000225025,0.000001487336,0.00002601503,0.0001962777],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1240101,"threshold_uncertainty_score":0.5490955,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04550623034398249,"score_gpt":0.3399037695472213,"score_spread":0.2943975392032389,"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."}}