{"id":"W4288704391","doi":"10.1007/s13226-022-00278-x","title":"Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56","year":2022,"lang":"en","type":"article","venue":"Indian Journal of Pure and Applied Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Diagonal; Discriminant; Quadratic form (statistics); Mathematics; Pure mathematics; Quadratic equation; Cusp (singularity); Integer (computer science); Cusp form; Definite quadratic form; Combinatorics; Eisenstein series; Quadratic field; Quadratic function; Modular form; 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":[],"consensus_categories":[],"category_scores_codex":[0.0006940412,0.0003075744,0.001008472,0.0002980587,0.0001932752,0.00003422425,0.0003775719,0.00007075888,0.0002318354],"category_scores_gemma":[0.0001384137,0.0001954737,0.000203322,0.000288406,0.0002651872,0.0002213812,0.0001890672,0.0004378109,0.000003058758],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005205471,"about_ca_system_score_gemma":0.0001823706,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001825985,"about_ca_topic_score_gemma":0.00001238989,"domain_scores_codex":[0.9973459,0.00003932009,0.001341757,0.0001708872,0.0007965843,0.000305611],"domain_scores_gemma":[0.9966066,0.0009813613,0.001747792,0.0003398838,0.0001781422,0.0001462498],"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":[0.001876273,0.006431203,0.000520256,0.01482237,0.003214097,0.0009183467,0.1129292,0.0008718812,0.02496817,0.8282753,0.003012789,0.002160094],"study_design_scores_gemma":[0.001758285,0.001670375,0.0001248785,0.0008960328,0.0007517812,0.001688009,0.03737919,0.0001758038,0.007685279,0.9474467,0.00003967338,0.0003840209],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9431078,0.0001486552,0.05094232,0.0002130068,0.0001021067,0.0007390309,0.0002850645,0.00002142002,0.004440535],"genre_scores_gemma":[0.9443307,0.00002197325,0.05433669,0.00002128148,0.0000650345,0.0000388023,0.000005497526,0.00006740866,0.001112595],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1191713,"threshold_uncertainty_score":0.7971187,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03817933553408972,"score_gpt":0.2820438354458315,"score_spread":0.2438644999117418,"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."}}