{"id":"W4405277727","doi":"10.1007/s10485-024-09796-7","title":"A Tangent Category Perspective on Connections in Algebraic Geometry","year":2024,"lang":"en","type":"article","venue":"Applied Categorical Structures","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University; Mount Allison University","funders":"Australian Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Connection (principal bundle); Mathematics; Tangent; Tangent cone; Sheaf; Affine connection; Pure mathematics; Tangent space; Tangent vector; Affine transformation; Perspective (graphical); Algebra over a field; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003025921,0.0003475148,0.0003863667,0.0005120912,0.0001459912,0.00009498472,0.0002786602,0.000249913,0.001253138],"category_scores_gemma":[0.000221112,0.0002807866,0.0001494181,0.001366779,0.0001351863,0.00006899158,0.00008533365,0.0007888583,0.000277475],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005595688,"about_ca_system_score_gemma":0.00007485175,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001004553,"about_ca_topic_score_gemma":0.00002323725,"domain_scores_codex":[0.9980069,0.00006703968,0.0003656637,0.0006761802,0.0003851731,0.0004990805],"domain_scores_gemma":[0.998289,0.001075117,0.00005438267,0.0003868685,0.00003888147,0.0001557243],"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":[0.00006203543,0.00009442437,0.00001967402,0.00006974817,0.0001029832,0.00007573739,0.001629522,0.00003072075,0.0004207828,0.9922505,0.003055754,0.002188121],"study_design_scores_gemma":[0.0003117618,0.00007358823,0.0008615761,0.000005514892,0.00004921343,0.00004902648,0.002697162,0.00003462878,0.001869925,0.9902655,0.003447357,0.0003347133],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8123476,0.002241919,0.01509386,0.003205376,0.002017211,0.001365166,0.00002251253,0.001264682,0.1624417],"genre_scores_gemma":[0.998382,0.00001996944,0.0001588774,0.0003891623,0.0003719165,0.000119541,0.00001166423,0.00005963571,0.0004872776],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1860344,"threshold_uncertainty_score":0.9999644,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02361378263965393,"score_gpt":0.302991590070943,"score_spread":0.279377807431289,"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."}}