{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","scholarly_communication"],"consensus_categories":[],"category_scores_codex":[0.002306876,0.0003453405,0.0008834979,0.004377531,0.0005034895,0.001279295,0.002344531,0.0002369228,0.0006193829],"category_scores_gemma":[0.0005659574,0.0002582045,0.0007306135,0.009728026,0.0007856986,0.0004415785,0.0002680203,0.0007133255,0.0000599393],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001405839,"about_ca_system_score_gemma":0.0004921099,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002338756,"about_ca_topic_score_gemma":0.00002503775,"domain_scores_codex":[0.9950918,0.0002685708,0.001846863,0.0006812879,0.001807521,0.0003039784],"domain_scores_gemma":[0.9904307,0.003525438,0.001685214,0.0008493243,0.003200322,0.0003090386],"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":[0.0002565799,0.0006503049,0.01627311,0.0000225937,0.005610419,0.00001502243,0.0003801672,0.003327458,0.00009029469,0.9078411,0.0002738488,0.06525914],"study_design_scores_gemma":[0.001211836,0.0002299246,0.01804334,0.0002616237,0.006284126,0.00009554245,0.00278102,0.00246901,0.0002158712,0.8460318,0.1218819,0.0004939787],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01886429,0.005204052,0.9580755,0.01092502,0.0002612006,0.0004741432,0.0001101914,0.00001608828,0.0060695],"genre_scores_gemma":[0.9853268,0.003690029,0.007864667,0.0009338701,0.0005928873,0.0001177868,0.00001448816,0.00001538176,0.001444113],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9664625,"threshold_uncertainty_score":0.999987,"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."}}