{"id":"W1993793648","doi":"10.1142/s1793042111004009","title":"ORTHOGONAL SYSTEMS OF MODULAR FORMS AND SUPERSINGULAR POLYNOMIALS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Modulo; Prime (order theory); Modular design; Pure mathematics; Algebra over a field; Order (exchange); Eisenstein series; Product (mathematics); Discrete mathematics; Combinatorics; Computer science; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001751375,0.0001423573,0.0003519686,0.0001802971,0.00003357824,0.00002231685,0.0004215237,0.00009277364,0.00178313],"category_scores_gemma":[0.0005573308,0.000112189,0.0001803706,0.00007220258,0.0001764524,0.0003143106,0.00008520091,0.00018327,0.00001348779],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000406737,"about_ca_system_score_gemma":0.00005745635,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007738623,"about_ca_topic_score_gemma":5.254897e-7,"domain_scores_codex":[0.9983391,0.0001813041,0.0007220157,0.0001114852,0.0004978178,0.0001483315],"domain_scores_gemma":[0.9980199,0.0006042243,0.0006330891,0.0001517566,0.0004901353,0.0001008775],"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":[0.0007364831,0.0002711421,0.005723382,0.00005662386,0.0008926015,0.0001188533,0.002307984,0.000002533222,0.001382051,0.9863098,0.0005159215,0.001682621],"study_design_scores_gemma":[0.0009756549,0.0001384639,0.002802688,0.0003055291,0.0001170075,0.002400859,0.0021121,0.00001257569,0.004685828,0.985253,0.001018467,0.0001778356],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9814569,0.0002792229,0.004539048,0.00002865347,0.0008621652,0.00007169202,0.00005457949,0.00001066904,0.01269712],"genre_scores_gemma":[0.9963043,0.00002662775,0.00289708,0.00004865017,0.0002732104,0.000001682027,0.000003023987,0.00002141369,0.0004239852],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01484747,"threshold_uncertainty_score":0.9991294,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03800595817072056,"score_gpt":0.2911574954047009,"score_spread":0.2531515372339803,"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."}}