{"id":"W3020108609","doi":"10.1134/s0001434620030128","title":"Some Congruences for Overpartitions with Restriction","year":2020,"lang":"en","type":"article","venue":"Mathematical Notes","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Congruence relation; Modulo; Ramanujan's sum; Mathematics; Combinatorics","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":[],"consensus_categories":[],"category_scores_codex":[0.0001522145,0.0002203608,0.0004251621,0.00004261312,0.0001653549,0.000093419,0.0001936547,0.00007871776,0.0001997607],"category_scores_gemma":[0.005233556,0.0001618433,0.0001115236,0.0001892384,0.0002097335,0.0004092706,0.00005208193,0.0001325947,0.0001548895],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002838254,"about_ca_system_score_gemma":0.00003442649,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000142822,"about_ca_topic_score_gemma":0.000002970974,"domain_scores_codex":[0.9985503,0.00002812912,0.0004388426,0.0002997506,0.0003445234,0.0003384364],"domain_scores_gemma":[0.9957295,0.00355432,0.0001414564,0.0002507219,0.000118744,0.0002052326],"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":[0.00003749314,0.0001351675,0.00001984528,0.000713244,0.00003874607,0.000004380773,0.0003791971,0.00001749493,0.0005271221,0.9964798,0.001592496,0.00005498995],"study_design_scores_gemma":[0.000434368,0.0002674961,0.00001204481,0.0001346396,0.0001069909,0.0000083798,0.0002862521,0.002152773,0.005061893,0.9909483,0.0003573366,0.0002295616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05402495,0.00008403776,0.9306415,0.009236174,0.00007845878,0.001450923,0.00007298959,0.0007349075,0.003676065],"genre_scores_gemma":[0.5175186,0.0000269104,0.4798091,0.0007115513,0.0006143154,0.0005646497,0.00001407462,0.0001117141,0.0006290217],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.4634937,"threshold_uncertainty_score":0.6599779,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1178041842532907,"score_gpt":0.3459879651105259,"score_spread":0.2281837808572352,"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."}}