{"id":"W4206004776","doi":"10.4236/jamp.2021.912208","title":"A Proof of the Non-Singularity of the <i>D</i> Matrix Used in Deriving the Two—Step Butcher’s Hybrid Scheme for the Solution of Initial Value Problems","year":2021,"lang":"en","type":"article","venue":"Journal of Applied Mathematics and Physics","topic":"Material Science and Thermodynamics","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Butcher; Singularity; Mathematics; Scheme (mathematics); Matrix (chemical analysis); State (computer science); Order (exchange); Applied mathematics; Mathematical analysis; Pure mathematics; Algorithm; Law; Economics","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":[0.001182814,0.0001956448,0.0004569617,0.00002527371,0.0001457778,0.00006096804,0.0004888428,0.00006962129,0.000009011021],"category_scores_gemma":[0.00007603326,0.0001021507,0.0002150814,0.0003216098,0.0001939311,0.0000895093,0.0001616933,0.0002777895,3.833092e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004596301,"about_ca_system_score_gemma":0.0001213913,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001265209,"about_ca_topic_score_gemma":0.0001411927,"domain_scores_codex":[0.9983611,0.00003503076,0.0007766763,0.0001145265,0.0004710477,0.0002416334],"domain_scores_gemma":[0.9982582,0.0002970203,0.0007416912,0.0004726581,0.000193997,0.00003638652],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000041564,0.0002895707,0.00005185347,0.001343273,0.0001924216,2.675912e-7,0.006341853,0.03631199,0.9169802,0.03626877,0.00007035195,0.002107866],"study_design_scores_gemma":[0.002912498,0.00008511011,0.0006568684,0.002267415,0.0007131735,0.00009187799,0.0007605139,0.2843659,0.2601471,0.44522,0.002124973,0.0006546207],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7819345,0.0001405818,0.2164442,0.0001243992,0.0002313764,0.0005958124,0.00003482305,0.000005768795,0.0004885863],"genre_scores_gemma":[0.9776751,0.00004351591,0.02204967,0.00001527234,0.0001529858,0.00001749827,0.000002861888,0.00002949364,0.00001358701],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6568331,"threshold_uncertainty_score":0.4165584,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02366799821386029,"score_gpt":0.2696165408176228,"score_spread":0.2459485426037625,"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."}}