{"id":"W2759885580","doi":"","title":"Four-way combinatorial interpretations of some Rogers-Ramanujan type identities.","year":2017,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Ramanujan's sum; Type (biology); Combinatorics; Pure mathematics; Biology; Paleontology","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000431244,0.0002771623,0.0006164843,0.0001337596,0.0004985648,0.0002286423,0.001022844,0.0001591553,0.0001851913],"category_scores_gemma":[0.003931748,0.0002837082,0.0001962997,0.0001036716,0.0004815948,0.00109601,0.0004361026,0.0002747044,0.0001342732],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001019517,"about_ca_system_score_gemma":0.00007535597,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003113889,"about_ca_topic_score_gemma":0.000009123904,"domain_scores_codex":[0.9979991,0.00007461292,0.0006740831,0.0003107687,0.0005548176,0.0003866237],"domain_scores_gemma":[0.9966528,0.0006732306,0.0007113984,0.001429195,0.0003968331,0.0001365407],"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":[0.00002561718,0.0002305947,0.0004391917,0.0002193722,0.0001052106,0.00001684408,0.0006145498,9.039388e-7,0.000377306,0.9942457,0.003655939,0.00006877368],"study_design_scores_gemma":[0.00116975,0.0001317017,0.0003927897,0.0001827104,0.0001086092,0.000008141551,0.0002259294,0.00008871104,0.004552583,0.9926985,0.0001639341,0.0002766707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9579993,0.0001305278,0.000266389,0.0002057361,0.01020609,0.0005418627,0.00002263496,0.0002111292,0.03041626],"genre_scores_gemma":[0.9944885,0.00003328773,0.001963101,0.00001921616,0.00004666257,0.00003079212,0.000005342573,0.00006651317,0.00334659],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03648913,"threshold_uncertainty_score":0.9999615,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05239297243019262,"score_gpt":0.3361411058628289,"score_spread":0.2837481334326363,"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."}}