{"id":"W4412602582","doi":"10.3390/sym17081180","title":"Derivatives, Integrals, and Polynomials Arising from the Inhomogeneous Airy Equation","year":2025,"lang":"en","type":"article","venue":"Symmetry","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of New Brunswick","funders":"","keywords":"Airy function; Mathematics; Mathematical physics; Integro-differential equation; Mathematical analysis; Physics; Differential equation; Riccati equation","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":[0.00008264137,0.00007688854,0.0001052784,0.00001507408,0.0001744482,0.00004405471,0.00008829249,0.00002012569,0.00006625185],"category_scores_gemma":[0.00004097842,0.00005230221,0.00003112624,0.0001430477,0.00007105504,0.00004628008,0.00006901572,0.0000882403,0.00000988056],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009694986,"about_ca_system_score_gemma":0.00001709149,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001045084,"about_ca_topic_score_gemma":0.000001327237,"domain_scores_codex":[0.9995686,0.00002835765,0.0001360526,0.0001302452,0.00004190147,0.00009483886],"domain_scores_gemma":[0.9991996,0.000533798,0.00004984532,0.0001759845,0.00001903716,0.00002172882],"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":[0.000002522533,0.00001847465,0.001964707,0.000002520554,0.00003071972,4.210293e-8,0.0001015917,0.000004020714,0.0006798425,0.9216931,0.0003112839,0.07519111],"study_design_scores_gemma":[0.0001105062,0.00000384841,0.001399548,0.00003247506,0.00002144748,7.767295e-8,0.001217645,0.0002258772,0.006176321,0.9858825,0.004864834,0.00006490653],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2338454,0.0004436437,0.7418985,0.00158361,0.00007610669,0.000210561,0.00005325637,0.00002836123,0.02186051],"genre_scores_gemma":[0.9932575,0.000005883971,0.00598089,0.0002403635,0.000126401,0.00002597049,0.00002337599,0.000005746191,0.000333926],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.759412,"threshold_uncertainty_score":0.2132822,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01277937271259784,"score_gpt":0.2772349736754502,"score_spread":0.2644556009628524,"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."}}