{"id":"W4416174446","doi":"10.28924/2291-8639-23-2025-294","title":"Novel Results in Cone Bipolar Metric Spaces With Application in Initial Value Fractional Caputo Differential Equations","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Fixed Point Theorems Analysis","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Prince Sattam bin Abdulaziz University","keywords":"Cone (formal languages); Initial value problem; Metric (unit); Metric space; Fixed-point theorem; Differential equation; Point (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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001576928,0.001251648,0.0009849272,0.001717677,0.001278862,0.001998682,0.0009408609,0.00136789,0.003560355],"category_scores_gemma":[0.002955416,0.000245693,0.001467268,0.001076419,0.002013647,0.00233387,0.001657887,0.002316334,0.0003571216],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001148363,"about_ca_system_score_gemma":0.0008286826,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001820859,"about_ca_topic_score_gemma":0.001091588,"domain_scores_codex":[0.9996133,0.0001263074,0.00002181444,0.00007264736,0.000115055,0.00005076481],"domain_scores_gemma":[0.9992531,0.0002674805,0.0001157167,0.00004514806,0.0002033693,0.0001152129],"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":[0.00001164724,0.00001355584,0.0001933625,0.0001134222,0.00001383788,0.0002053562,0.000153245,0.007215505,0.001633471,0.9843485,0.00106357,0.005034461],"study_design_scores_gemma":[0.0000177068,0.00008092433,0.0004514746,0.0001125443,0.0000313306,0.0004053366,0.0001779155,0.1502139,0.0008711863,0.8339019,0.01369884,0.00003694873],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03542868,0.009954128,0.881122,0.002168189,0.001084862,0.00009121816,0.0001864209,0.0001279515,0.0698365],"genre_scores_gemma":[0.81166,0.01242649,0.1488713,0.001165248,0.001722275,0.0002538585,0.0002403346,0.0001754963,0.02348496],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003560355,"threshold_uncertainty_score":0.01191062,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01487818793756741,"score_gpt":0.3223565113341936,"score_spread":0.3074783233966262,"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."}}