{"id":"W2951670728","doi":"10.48550/arxiv.math/0607718","title":"Definable groups of partial automorphisms","year":2006,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Automorphism; Mathematics; Galois theory; Connection (principal bundle); Group (periodic table); Pure mathematics; Galois connection; Algebraic number; Differential Galois theory; Algebra over a field; Set (abstract data type); Galois group; Galois extension; Mathematical analysis; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00105008,0.0004997865,0.0005192757,0.001300975,0.001018153,0.002597599,0.0006084695,0.0005393218,0.002835626],"category_scores_gemma":[0.001778414,0.0002837722,0.0009452024,0.0006954269,0.004442912,0.003866604,0.002664626,0.001494718,0.0003420217],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001562336,"about_ca_system_score_gemma":0.0005896001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006002737,"about_ca_topic_score_gemma":0.0004161207,"domain_scores_codex":[0.9989021,0.0002927601,0.00007106321,0.0002929442,0.0002886311,0.0001524691],"domain_scores_gemma":[0.9988343,0.0004785377,0.0001541612,0.0002146827,0.0001346942,0.0001835755],"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":[0.00001042472,0.00000697061,0.0001482821,0.00001064195,0.000003666261,0.00003247993,0.0002486455,0.0004973316,0.0006490455,0.9962174,0.0001176292,0.002057426],"study_design_scores_gemma":[0.00001455826,0.00002341106,0.0001961908,0.000009204959,0.000007345766,0.00006845738,0.0001037745,0.002704899,0.0008593269,0.9901006,0.005905848,0.000006446261],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.6801409,0.001748108,0.216107,0.002165456,0.0002537713,0.0001036385,0.0003478153,0.0006151428,0.09851829],"genre_scores_gemma":[0.976832,0.0003296763,0.01401507,0.0001641931,0.0001588745,0.00007223191,0.0002058924,0.00003831023,0.008183925],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.002835626,"threshold_uncertainty_score":0.01133561,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08054992619532436,"score_gpt":0.2028611805098295,"score_spread":0.1223112543145052,"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."}}