{"id":"W4392071666","doi":"10.1016/j.jcta.2024.105874","title":"Two conjectures of Andrews, Merca and Yee on truncated theta series","year":2024,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"Natural Science Foundation of Jiangsu Province; National Natural Science Foundation of China","keywords":"Mathematics; Series (stratigraphy); Euler's formula; Combinatorics; Truncation (statistics); Partition (number theory); Integer (computer science); Number theory; Pure mathematics; Mathematical analysis; Statistics","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":[0.001073802,0.000225831,0.0006591572,0.0001750355,0.00007566201,0.0001129754,0.0002232949,0.00009144927,0.0001702381],"category_scores_gemma":[0.001500217,0.0001582094,0.0001718866,0.0001738043,0.0004014572,0.0006097321,0.00008096157,0.0003462503,0.000003370676],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004076289,"about_ca_system_score_gemma":0.00008903795,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001362198,"about_ca_topic_score_gemma":0.000001697053,"domain_scores_codex":[0.9983178,0.0002116673,0.0007242037,0.0001368662,0.0004210581,0.0001884056],"domain_scores_gemma":[0.9974607,0.001615601,0.000374228,0.000223977,0.0002358662,0.00008958423],"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":[0.001028021,0.00009649733,0.000004585669,0.0004253467,0.0002358721,0.00005760096,0.001808036,0.000004484482,0.002284164,0.9929665,0.0008942595,0.0001945729],"study_design_scores_gemma":[0.0008096204,0.0009467895,0.000007542792,0.0005568869,0.0001635016,0.0002992975,0.001620935,0.000004887546,0.02625762,0.9666007,0.002583129,0.0001490606],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9576272,0.005596275,0.001024469,0.001036666,0.009047057,0.0005608469,0.00004975761,0.0001900751,0.02486762],"genre_scores_gemma":[0.9946303,0.0003356853,0.001680816,0.00001877754,0.0004606233,0.000004220866,7.623241e-7,0.00005272082,0.002816098],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03700306,"threshold_uncertainty_score":0.6451593,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01993207686066764,"score_gpt":0.3163920103492939,"score_spread":0.2964599334886262,"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."}}