{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004912892,0.0005473624,0.000410829,0.001652402,0.000845994,0.002708805,0.0007451117,0.000767144,0.005021112],"category_scores_gemma":[0.002988903,0.000337022,0.0004861442,0.0006608243,0.002330334,0.003075516,0.003184487,0.002257659,0.000443171],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008859272,"about_ca_system_score_gemma":0.0002752915,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006241204,"about_ca_topic_score_gemma":0.0003560375,"domain_scores_codex":[0.9995849,0.00005327626,0.00002286875,0.0001096448,0.0001341888,0.00009519147],"domain_scores_gemma":[0.999143,0.0002497265,0.0001740936,0.0001661798,0.00009211815,0.0001748214],"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":[0.00004373458,0.00001400134,0.000574599,0.00002760634,0.00000502168,0.00008323493,0.0001478227,0.002829833,0.00215779,0.9886364,0.000535811,0.00494411],"study_design_scores_gemma":[0.00002046393,0.00005028629,0.001832384,0.00002889726,0.00001750339,0.0003274022,0.0002457493,0.04403942,0.004745867,0.9408507,0.007796969,0.0000444275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7574371,0.0009038093,0.1413389,0.001659338,0.0002457103,0.00004174985,0.0005208385,0.0002413331,0.09761127],"genre_scores_gemma":[0.9768906,0.0003440146,0.0147494,0.0001262939,0.0001119955,0.00003409915,0.0002124209,0.00007551978,0.007455667],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005021112,"threshold_uncertainty_score":0.01679736,"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."}}