{"id":"W4416785427","doi":"10.28924/2291-8639-23-2025-311","title":"Optimal Difference Formulas for the Approximate Solution of the Second-Order Cauchy Problem","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Differential Equations and Boundary Problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Cauchy problem; Sobolev space; Simple (philosophy); Cauchy distribution; Initial value problem; Type (biology); Differential (mechanical device)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002721349,0.0006486505,0.0007616476,0.001275869,0.0003206099,0.0009991127,0.001019996,0.001196593,0.002401974],"category_scores_gemma":[0.007063588,0.0002439566,0.0006822109,0.0005337928,0.00136841,0.002044388,0.001417351,0.00215246,0.0004788607],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00104283,"about_ca_system_score_gemma":0.001063236,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001013751,"about_ca_topic_score_gemma":0.001290197,"domain_scores_codex":[0.9992781,0.0002232219,0.00005161394,0.00007202253,0.0003242747,0.00005078536],"domain_scores_gemma":[0.9984714,0.0008128545,0.0001091274,0.00008309983,0.0004379574,0.00008549634],"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":[0.00005581915,0.00005825895,0.0004539186,0.0002729182,0.00002209587,0.0001187089,0.0002322201,0.07092936,0.009212255,0.8774161,0.001538525,0.03968982],"study_design_scores_gemma":[0.00001426402,0.00006650276,0.0001755903,0.00004464358,0.00001253952,0.0001005443,0.00003647952,0.8435763,0.002401316,0.1469968,0.006555264,0.0000197596],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.00863187,0.001073161,0.9842754,0.0003381179,0.0002172423,0.00003454584,0.00003818632,0.00003813533,0.005353477],"genre_scores_gemma":[0.386242,0.003493096,0.5896791,0.0005160812,0.0004384787,0.0003721271,0.0002516238,0.0002720827,0.01873539],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002721349,"threshold_uncertainty_score":0.01439208,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01953625756948231,"score_gpt":0.3069297542999161,"score_spread":0.2873934967304339,"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."}}