{"id":"W4220987506","doi":"10.3390/axioms11030118","title":"Topological Transcendental Fields","year":2022,"lang":"en","type":"article","venue":"Axioms","topic":"Mathematical and Theoretical Analysis","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"Division of Mathematical Sciences; Fields Institute for Research in Mathematical Sciences","keywords":"Transcendental number; Mathematics; Metrization theorem; Topology (electrical circuits); Connected space; Subspace topology; Topological algebra; Field (mathematics); Separable space; Topological space; Topological vector space; Rational number; Isolated point; Pure mathematics; Combinatorics; Mathematical analysis","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002373702,0.00008184592,0.0001779774,0.00003115223,0.0001743231,0.00001075521,0.0002070008,0.00003373788,0.03290032],"category_scores_gemma":[0.00009280461,0.000060379,0.0001655558,0.0001595532,0.00008110629,0.00001837523,0.0001062076,0.0001957393,0.00008027474],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001891418,"about_ca_system_score_gemma":0.000005526655,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008234416,"about_ca_topic_score_gemma":0.000002621036,"domain_scores_codex":[0.9991191,0.00008118789,0.0001861825,0.0001514161,0.0002794738,0.0001826215],"domain_scores_gemma":[0.9994385,0.000275887,0.00002708271,0.00017995,0.000009020573,0.00006958855],"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":[0.0000115212,0.0002166092,0.00001107596,0.0000137183,0.0000264818,0.00002209604,0.0002800946,0.000001741123,0.00005885141,0.9981626,0.0004326261,0.0007625693],"study_design_scores_gemma":[0.0001571773,0.0001003065,0.00001675652,0.000001694781,0.0000407545,0.00002998022,0.0004169318,0.001057486,0.0002880279,0.9967585,0.001032709,0.00009973359],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7546193,0.00006343397,0.1120823,0.005016603,0.0002195413,0.0002220107,0.00002432488,0.0002473893,0.1275051],"genre_scores_gemma":[0.9960738,0.000001297469,0.0006302311,0.0003461334,0.00004224223,0.00003732235,0.000003187364,0.000007759298,0.002857997],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2414545,"threshold_uncertainty_score":0.9679837,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04378180168562312,"score_gpt":0.3060750670053357,"score_spread":0.2622932653197126,"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."}}