{"id":"W4417272097","doi":"10.28924/2291-8639-23-2025-333","title":"Neutrosophic MR-Metric Spaces: A Topos-Theoretic Framework with Applications","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Fuzzy and Soft Set Theory","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Soundness; Functor; Topos theory; Fuzzy logic; Construct (python library); Falsity; Category theory; Topological space; Completeness (order theory); Graph","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":[0.002113046,0.0008230606,0.0008272538,0.003672968,0.001779858,0.00340177,0.001275784,0.001291618,0.003030462],"category_scores_gemma":[0.002886312,0.0003686796,0.001313808,0.002601944,0.006913709,0.006023799,0.003312652,0.002521349,0.000437544],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001798884,"about_ca_system_score_gemma":0.001010224,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001756358,"about_ca_topic_score_gemma":0.0009659155,"domain_scores_codex":[0.9984533,0.0005701063,0.0001030305,0.0002893308,0.0004648863,0.0001192819],"domain_scores_gemma":[0.9983909,0.0005862465,0.000174447,0.0002151904,0.0004151457,0.0002181006],"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":[0.000002856876,0.000004470217,0.0000719431,0.00002346316,0.000004974405,0.0000401042,0.0001022019,0.0008135093,0.0002244192,0.995746,0.0002271625,0.002738975],"study_design_scores_gemma":[0.000002652566,0.00001422856,0.0001042235,0.00001763206,0.000004489948,0.00009910241,0.0000999542,0.007691336,0.0001487251,0.9838449,0.00796392,0.000008906892],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02779961,0.005153865,0.9226632,0.00396423,0.0003865666,0.00006719484,0.0002635505,0.0001595058,0.03954232],"genre_scores_gemma":[0.6678077,0.004151155,0.3179336,0.0009385216,0.001191934,0.0002055872,0.000229299,0.00008009245,0.007462112],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003672968,"threshold_uncertainty_score":0.01305187,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01391618331698292,"score_gpt":0.3482628595159331,"score_spread":0.3343466761989501,"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."}}