{"id":"W3196006296","doi":"10.5539/jmr.v13n5p5","title":"Applying Differential Forms and the Generalized Sundman Transformations in Linearizing the Equation of Motion of a Free Particle in a Space of Constant Curvature","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Constant (computer programming); Transformation (genetics); Constant curvature; Motion (physics); Mathematical analysis; Linearization; Space (punctuation); Differential equation; Curvature; Nonlinear system; Classical mechanics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001725864,0.00004494075,0.0002327598,0.00007876621,0.00004388379,0.00002258205,0.0001218158,0.00002361998,0.00001963566],"category_scores_gemma":[0.0001303261,0.00002438248,0.00007724069,0.0002638427,0.0001321241,0.00008190963,0.00004620971,0.0002895696,7.83099e-8],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001155993,"about_ca_system_score_gemma":0.00009317829,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000799352,"about_ca_topic_score_gemma":0.00005524174,"domain_scores_codex":[0.9987499,0.0001903028,0.0005580892,0.00003751007,0.000351739,0.0001124386],"domain_scores_gemma":[0.9988341,0.0005180241,0.0002415661,0.0001347808,0.000250564,0.00002096854],"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":[0.0001834367,0.000979729,0.009230299,0.000498884,0.0001522919,0.000002411248,0.02765391,0.001411453,0.08056975,0.8757188,0.00001848516,0.003580517],"study_design_scores_gemma":[0.008619205,0.0001333745,0.003479616,0.0009338735,0.00007876036,0.00001141649,0.04040369,0.3966085,0.1308307,0.4187576,0.00003742895,0.0001057905],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9797874,0.0001406603,0.01873993,0.0007744905,0.00001225758,0.0002445119,0.00001434295,3.613602e-7,0.0002860598],"genre_scores_gemma":[0.9976297,0.00004941809,0.002264774,0.00000135558,0.00002895996,0.000007154152,0.0000018901,0.000004067108,0.00001267422],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4569612,"threshold_uncertainty_score":0.1258052,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07069229858655367,"score_gpt":0.3576836108959206,"score_spread":0.2869913123093669,"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."}}