{"id":"W1572428706","doi":"10.14321/realanalexch.37.1.0221","title":"On Riemann Sums","year":2012,"lang":"en","type":"article","venue":"Real Analysis Exchange","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Sequence (biology); Riemann hypothesis; Set (abstract data type); Variable (mathematics); Riemann sum; Pure mathematics; Discrete mathematics; Combinatorics; Mathematical analysis; Riemann Xi function; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00198964,0.000813505,0.000818543,0.002494119,0.001676725,0.002748124,0.0007634218,0.001189797,0.005756485],"category_scores_gemma":[0.007031338,0.0003194712,0.0009349764,0.001334583,0.003822745,0.00559973,0.002383566,0.0019521,0.001057544],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00150449,"about_ca_system_score_gemma":0.000413691,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007188281,"about_ca_topic_score_gemma":0.000491979,"domain_scores_codex":[0.999171,0.0003006742,0.00005610793,0.0001204696,0.0002516716,0.0001000796],"domain_scores_gemma":[0.9983243,0.000825841,0.0001598122,0.0002299157,0.0002747716,0.0001853008],"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":[0.000007541561,0.000003594257,0.00008378058,0.00001869856,0.000003272849,0.00003121532,0.00009658704,0.0005604476,0.0003866228,0.9952371,0.0004714896,0.003099706],"study_design_scores_gemma":[0.000002917352,0.000007202372,0.0001191596,0.00001465486,0.000002792409,0.00005913697,0.00003285541,0.004691617,0.0002390785,0.9921883,0.002637515,0.000004710723],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2973632,0.01346929,0.3440722,0.00831201,0.001759373,0.00005920523,0.0002885087,0.0002910895,0.3343852],"genre_scores_gemma":[0.884764,0.005384863,0.03444247,0.001310879,0.002130234,0.00008158191,0.0002795,0.0003192637,0.07128722],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005756485,"threshold_uncertainty_score":0.01925743,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08443320826215803,"score_gpt":0.345120287406682,"score_spread":0.2606870791445239,"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."}}