{"id":"W2919309530","doi":"","title":"Congruences modulo 16, 32 and 64 for bipartitions with distinct even parts.","year":2018,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Modulo; Mathematics; Congruence relation; Arithmetic; Combinatorics","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":[0.001547162,0.001080327,0.0008498313,0.002043436,0.004420279,0.004374897,0.0008490373,0.00130764,0.0298778],"category_scores_gemma":[0.004483764,0.0006457628,0.001489564,0.00133318,0.004810814,0.00581772,0.003864144,0.004192008,0.007587428],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001865674,"about_ca_system_score_gemma":0.001228296,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001227662,"about_ca_topic_score_gemma":0.001770247,"domain_scores_codex":[0.997277,0.0006338935,0.0002283033,0.0004217256,0.0007451304,0.0006940397],"domain_scores_gemma":[0.998516,0.0005129941,0.0002058962,0.0002660034,0.0002640179,0.0002350628],"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":[0.00004284694,0.00001699364,0.00006356624,0.00002506831,0.000003323047,0.0001217096,0.0003004271,0.00006231137,0.0005731398,0.9901775,0.00500879,0.003604362],"study_design_scores_gemma":[0.00003294594,0.00001416757,0.0001389305,0.00003711928,0.000007720295,0.0002194264,0.0001957964,0.0003314298,0.0007924612,0.9704727,0.02774153,0.00001575585],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.0708602,0.002466072,0.07633523,0.003304063,0.003408539,0.0001598159,0.0008061454,0.0006093081,0.8420506],"genre_scores_gemma":[0.8350956,0.001513772,0.04386653,0.001857945,0.001773237,0.0002536894,0.001086279,0.0007380174,0.1138149],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0298778,"threshold_uncertainty_score":0.09995121,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0374330647040655,"score_gpt":0.3154034122027414,"score_spread":0.2779703474986759,"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."}}