{"id":"W4416174176","doi":"10.48550/arxiv.2508.19524","title":"Definable Galois theory for bimeromorphic geometry","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Derived algebraic geometry; Algebra over a field; Algebraic number; Group (periodic table); Galois group; Algebraic geometry; Meromorphic function; Differential algebraic geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.00119894,0.0006273477,0.0005101991,0.00187137,0.001580308,0.003659233,0.0007836698,0.0009331012,0.005275766],"category_scores_gemma":[0.0011531,0.0002675586,0.000668251,0.0008802166,0.006947795,0.005713552,0.002480713,0.002488244,0.0005457006],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002283369,"about_ca_system_score_gemma":0.0007005055,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007561489,"about_ca_topic_score_gemma":0.0004367245,"domain_scores_codex":[0.9992363,0.0002695885,0.00003699957,0.0001449063,0.000220071,0.00009201831],"domain_scores_gemma":[0.9993004,0.0002843697,0.00005532229,0.0001388088,0.00008893751,0.0001322007],"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":[0.00000123016,0.000002095718,0.00003132141,0.000007261422,8.596593e-7,0.00001137123,0.00007628917,0.0001157872,0.0000942984,0.9988511,0.0001170469,0.0006913548],"study_design_scores_gemma":[0.000002919091,0.000007280652,0.00009937811,0.00000677916,0.000001634164,0.00003835996,0.00006366152,0.001344184,0.0001682374,0.9939282,0.004335699,0.000003656908],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2331627,0.005925879,0.4847544,0.007197637,0.0006121621,0.0001344992,0.0007346975,0.0005411113,0.266937],"genre_scores_gemma":[0.9499932,0.001245146,0.03083113,0.0005070523,0.0004490221,0.0001046322,0.0002817349,0.00005984712,0.01652817],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005275766,"threshold_uncertainty_score":0.01764917,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08242154060291337,"score_gpt":0.337851769234743,"score_spread":0.2554302286318296,"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."}}