{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001862381,0.0001639723,0.0002696496,0.00004155767,0.0002591285,0.00007096283,0.0001403279,0.00005369124,0.00007821064],"category_scores_gemma":[0.0006409294,0.0001304198,0.00003874042,0.0001129966,0.0004616979,0.0002410648,0.00006296889,0.00007151361,0.00002269819],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003863369,"about_ca_system_score_gemma":0.00003133036,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001422624,"about_ca_topic_score_gemma":0.0001586571,"domain_scores_codex":[0.9990171,0.00002669691,0.0002420797,0.000243733,0.0001878315,0.0002825364],"domain_scores_gemma":[0.9985647,0.0007058072,0.0001177195,0.0002994047,0.0002072778,0.0001050636],"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":[0.00002034644,0.0001058342,0.0005785712,0.0001295764,0.00003854594,0.000001688903,0.0003286873,2.156212e-7,0.00002969931,0.9937636,0.004931419,0.00007178359],"study_design_scores_gemma":[0.0006928,0.0003133826,0.000267914,0.0001035607,0.00007108985,0.000009370105,0.0002683142,0.0001516369,0.001317675,0.9947679,0.001844769,0.0001916046],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9808728,0.00007750808,0.007691561,0.0004209629,0.0006098519,0.0008045653,0.00004362041,0.0002115349,0.009267623],"genre_scores_gemma":[0.9886756,0.000005488198,0.00875059,0.00002959804,0.00003001338,0.0001921811,0.000006117066,0.00003353014,0.002276859],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00780285,"threshold_uncertainty_score":0.5318363,"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."}}