{"id":"W4232991583","doi":"10.5539/jmr.v9n2p100","title":"Arithmetic Triangle","year":2017,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Arithmetic progression; Pascal (unit); Arithmetic; Combinatorics; Product (mathematics); Discrete mathematics; Geometry","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":[0.0004381354,0.0004501338,0.0003623922,0.0008695754,0.001859038,0.002244188,0.0008084729,0.0006948864,0.03789689],"category_scores_gemma":[0.00181219,0.0002247464,0.000525169,0.0007838244,0.002581603,0.003754254,0.001903217,0.002399686,0.0097127],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001014221,"about_ca_system_score_gemma":0.0006726419,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001227065,"about_ca_topic_score_gemma":0.001296905,"domain_scores_codex":[0.9990807,0.0001254969,0.00004329025,0.0002949951,0.0003183749,0.0001372846],"domain_scores_gemma":[0.9992517,0.0001391033,0.00005637308,0.0001451636,0.0003205836,0.00008718877],"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":[0.00002034199,0.00000392004,0.00004344474,0.00003651174,0.000002052657,0.00005485198,0.0001488738,0.00009286056,0.0009370971,0.9792012,0.007503246,0.01195551],"study_design_scores_gemma":[0.00001439075,0.00003850264,0.0002403761,0.00003547452,0.000006104156,0.0005132784,0.0001624143,0.001007077,0.001697829,0.62925,0.3670169,0.00001760434],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.0208633,0.002330937,0.1164917,0.002600064,0.002534673,0.0000698529,0.000618481,0.0005330725,0.8539578],"genre_scores_gemma":[0.511224,0.003636927,0.1013593,0.00307963,0.002481852,0.0001929606,0.001326427,0.0007689915,0.3759299],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03789689,"threshold_uncertainty_score":0.1267778,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.578409407987905,"score_gpt":0.5805854917304106,"score_spread":0.002176083742505663,"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."}}