{"id":"W4415914303","doi":"10.28924/2291-8639-23-2025-272","title":"Generating Ruled Surfaces by Focal Curves and Their Characterizations in Minkowski 3-Space","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Northern Border University","keywords":"Frenet–Serret formulas; Minkowski space; Ruled surface; Surface (topology); Minkowski addition","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":[0.0004223239,0.0004980543,0.0003388368,0.002591164,0.001070073,0.002377469,0.0005925628,0.0007109704,0.002877741],"category_scores_gemma":[0.001653966,0.0002675101,0.0006456015,0.0009039453,0.001843556,0.001651738,0.001127295,0.0006564623,0.0003021075],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001138736,"about_ca_system_score_gemma":0.0003157483,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002176276,"about_ca_topic_score_gemma":0.000976275,"domain_scores_codex":[0.9995454,0.0000882714,0.00002242422,0.00008322707,0.0001759356,0.0000846802],"domain_scores_gemma":[0.9994459,0.0001675015,0.0001044413,0.00006263748,0.0001017601,0.0001177314],"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":[0.00006583878,0.0000242422,0.002261601,0.00007800116,0.00001632727,0.0004481736,0.0008750784,0.01708191,0.008003858,0.9498208,0.0005854859,0.02073876],"study_design_scores_gemma":[0.00002696132,0.0001201483,0.005806856,0.0000550646,0.00001895993,0.001333807,0.001164543,0.1279083,0.006866314,0.8461171,0.01050036,0.000081568],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.820406,0.0007155786,0.1592201,0.0002119497,0.00003498993,0.00005863523,0.0002238046,0.0001511083,0.01897777],"genre_scores_gemma":[0.9766595,0.0002395052,0.01943094,0.00002655619,0.00002388522,0.00002757441,0.0001918896,0.00005555515,0.003344636],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002877741,"threshold_uncertainty_score":0.009626985,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007714971053812138,"score_gpt":0.2810514279835421,"score_spread":0.27333645692973,"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."}}