{"id":"W4399212399","doi":"10.28924/2291-8639-22-2024-93","title":"On the Affine and Affine Polarized k-Symplectic Manifolds","year":2024,"lang":"en","type":"article","venue":"International Journal of Analysis and Applications","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Affine transformation; Mathematics; Symplectic geometry; Pure mathematics; Affine hull; Affine space","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":[],"consensus_categories":[],"category_scores_codex":[0.000401631,0.00008787153,0.0001707545,0.0004262217,0.00008912892,0.0002253742,0.0002254295,0.00002884444,0.0004792027],"category_scores_gemma":[0.00008582677,0.00005482814,0.0001577707,0.0005468687,0.00003587403,0.00007557582,0.00004971109,0.0001474098,0.000007493904],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000237428,"about_ca_system_score_gemma":0.00001847858,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001112323,"about_ca_topic_score_gemma":0.00002598394,"domain_scores_codex":[0.9991726,0.00003227137,0.0003146168,0.0001217038,0.0002868178,0.00007202572],"domain_scores_gemma":[0.9987842,0.0007299599,0.0001363045,0.0001242996,0.000178075,0.00004713515],"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":[0.00001811661,0.00009777346,0.0003046298,0.00001054154,0.002161816,0.0000100367,0.0001200775,0.00001510319,0.001445346,0.9885949,0.0009624442,0.006259179],"study_design_scores_gemma":[0.0005041949,0.000154691,0.009353908,0.00008752743,0.002685959,0.0003397898,0.0003497911,0.007861809,0.0003736486,0.9354929,0.04256466,0.0002310907],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5522004,0.001486232,0.4076873,0.03109807,0.0002284949,0.0003034627,0.00006090995,0.00005987577,0.006875302],"genre_scores_gemma":[0.9976946,0.0001523449,0.0009275418,0.0001713025,0.000273055,0.00001147873,0.000003945021,0.000007053921,0.0007586576],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4454943,"threshold_uncertainty_score":0.5246934,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02446714570475497,"score_gpt":0.3164959361384945,"score_spread":0.2920287904337396,"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."}}