{"id":"W4400597008","doi":"10.55016/ojs/cdm.v16i3.71250","title":"Bailey and Daum's q-Kummer Theorem and Extensions","year":2021,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Natural Science Foundation of China; National Science Foundation","keywords":"Mathematics; Integer (computer science); Linearization; Combinatorics; Algebra over a field; Pure mathematics; Nonlinear system; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001107935,0.0006156217,0.0005166971,0.001624922,0.001463774,0.001779773,0.001215934,0.0008584943,0.007066126],"category_scores_gemma":[0.002769029,0.0002493128,0.0007362941,0.001091462,0.00331193,0.003588281,0.001524603,0.001890785,0.002452223],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001024638,"about_ca_system_score_gemma":0.0005118189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000572342,"about_ca_topic_score_gemma":0.000442953,"domain_scores_codex":[0.9996343,0.000108783,0.00002339776,0.000059322,0.0001231291,0.00005110259],"domain_scores_gemma":[0.9994307,0.0002342053,0.0000613724,0.00007558695,0.0001356265,0.0000624903],"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":[0.000004048604,0.000006018915,0.00003332399,0.00001700391,0.000001204562,0.00003126069,0.0001253767,0.0002887312,0.0004427261,0.9951289,0.0005082487,0.003413169],"study_design_scores_gemma":[0.000004236358,0.00001146837,0.00005697314,0.00001189133,0.000002888716,0.0001119231,0.00006358129,0.003636535,0.0006870971,0.9890149,0.006387402,0.00001114159],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09716102,0.002667751,0.6324868,0.00266094,0.0006084256,0.00008659095,0.0001421199,0.000667089,0.2635193],"genre_scores_gemma":[0.8318304,0.002364593,0.09676069,0.001284695,0.0007758015,0.0001456939,0.00009969558,0.0003703448,0.06636811],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007066126,"threshold_uncertainty_score":0.02363855,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02723722376011221,"score_gpt":0.3481196197320979,"score_spread":0.3208823959719857,"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."}}