{"id":"W4409019450","doi":"10.5539/jmr.v17n1p40","title":"Pillai&amp;#39;s Problem Involving Narayana&amp;#39;s Cows Sequence and Padovan Sequence","year":2025,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Language, Linguistics, Cultural Analysis","field":"Arts and Humanities","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Sequence (biology); Combinatorics; Genetics; Biology","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":[0.003396213,0.0002390016,0.0005929189,0.0006213059,0.0007144355,0.0008439405,0.0006835416,0.00009229001,0.0007520447],"category_scores_gemma":[0.003026848,0.0001622846,0.0001794111,0.0003119507,0.0007227617,0.0002931393,0.0003002035,0.0009513944,0.00009116073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000265314,"about_ca_system_score_gemma":0.0002777904,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004765731,"about_ca_topic_score_gemma":0.00205432,"domain_scores_codex":[0.9966826,0.0002513869,0.001015232,0.0002611234,0.001243646,0.0005460061],"domain_scores_gemma":[0.9955345,0.0008559555,0.0004404896,0.000406535,0.002559304,0.0002032271],"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":[0.00006814925,0.000587595,0.0007292157,0.003060522,0.0009800041,0.0002839436,0.1372044,0.00009878333,0.0300339,0.7994811,0.02375152,0.003720881],"study_design_scores_gemma":[0.00111732,0.0003439409,0.00006589288,0.00374363,0.0003941459,0.0003163832,0.05191762,0.002706501,0.0007550797,0.5697137,0.3681382,0.0007875779],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8725269,0.008280694,0.005203734,0.01017164,0.001076384,0.001281566,0.0001257792,0.0001500583,0.1011833],"genre_scores_gemma":[0.8877649,0.001535511,0.0479157,0.0003078968,0.00131136,0.00001884916,0.0000140474,0.00005812329,0.06107356],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3443867,"threshold_uncertainty_score":0.8234363,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2481880050366781,"score_gpt":0.4077419882571776,"score_spread":0.1595539832204995,"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."}}