{"id":"W2142436396","doi":"10.48550/arxiv.1404.0063","title":"Discrete $d$-dimensional moduli of smoothness","year":2014,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba; University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Moduli; Smoothness; Combinatorics; Integer (computer science); Function (biology); Mathematics; Moduli space; Physics; Mathematical analysis; Geometry; Quantum mechanics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001713456,0.0002528519,0.0003911396,0.0001503736,0.00004632862,0.00002306049,0.001479154,0.0001824787,0.000008012707],"category_scores_gemma":[0.00006771336,0.0002746882,0.0001695661,0.000242499,0.00009112102,0.0002056037,0.002031789,0.0003815885,0.00002227572],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007685234,"about_ca_system_score_gemma":0.00005979051,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000114356,"about_ca_topic_score_gemma":9.956299e-7,"domain_scores_codex":[0.9986293,0.00004244061,0.000233403,0.0007166045,0.0001190004,0.000259228],"domain_scores_gemma":[0.9981244,0.0001698115,0.0002021816,0.001241874,0.0001375831,0.0001241675],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000003061407,0.00001906354,0.00001803638,0.0001122543,0.00001962292,0.00001497008,0.00002873916,0.7230893,0.0000634706,0.276531,0.000009962664,0.00009055035],"study_design_scores_gemma":[0.0001322421,0.00001492407,0.00004109877,0.00014572,0.0000180522,0.000001633297,0.000002617693,0.7845296,0.000261903,0.2146058,0.00002234992,0.0002240948],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09282833,0.00002270101,0.9057866,0.00002850808,0.0003738664,0.0001201158,0.000005047209,0.000196126,0.0006386776],"genre_scores_gemma":[0.9248728,0.000008142715,0.07481914,0.00002131414,0.00003461591,6.224367e-7,0.000003502267,0.00001837884,0.0002214898],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8320445,"threshold_uncertainty_score":0.9999706,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04895608198816212,"score_gpt":0.1896642254529584,"score_spread":0.1407081434647963,"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."}}