{"id":"W2069226673","doi":"10.1006/jath.2000.3550","title":"A Unified Calculus Using the Generalized Bernoulli Polynomials","year":2001,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical and Theoretical Analysis","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Mathematics; Bernoulli's principle; Remainder; Calculus (dental); Time-scale calculus; Differential calculus; Context (archaeology); Algebra over a field; Bessel function; Function (biology); Point (geometry); Pure mathematics; Mathematical analysis; Multivariable calculus; Arithmetic","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003455384,0.0001640191,0.0004695267,0.0001335746,0.0001646577,0.00007209915,0.0003503805,0.00008796276,0.001043371],"category_scores_gemma":[0.001367405,0.00008667589,0.0003590217,0.0003445545,0.000189927,0.0001568016,0.00005216305,0.0002370327,0.00001556127],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000588164,"about_ca_system_score_gemma":0.00004899303,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003360098,"about_ca_topic_score_gemma":9.264473e-7,"domain_scores_codex":[0.9976954,0.0005685454,0.0009323969,0.000107355,0.0004752651,0.0002209624],"domain_scores_gemma":[0.997381,0.001180476,0.0007581559,0.0002967534,0.0002639851,0.0001196085],"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":[0.0001648162,0.0001600203,0.000009596181,0.00003853383,0.000183448,0.00001338037,0.0006074761,0.00006803853,0.00190358,0.9951247,0.0003074505,0.001418981],"study_design_scores_gemma":[0.000520585,0.0000419831,0.000005667551,0.00005976967,0.0003511643,0.0002686756,0.0005235765,0.01462341,0.002524655,0.9804278,0.0005372573,0.0001154622],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4015598,0.0001672644,0.5897879,0.001311945,0.0001005283,0.0001772455,0.00000218934,0.00002316939,0.006869972],"genre_scores_gemma":[0.949743,0.00005358328,0.04775415,0.0004042951,0.0005292666,0.000005615951,0.000001281326,0.00003718083,0.001471679],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5481831,"threshold_uncertainty_score":0.9998698,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05931920575158067,"score_gpt":0.3273809673729354,"score_spread":0.2680617616213547,"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."}}