{"id":"W4409396902","doi":"10.1007/s10711-025-00996-6","title":"Broken toric varieties and cell-compatible sheaves","year":2025,"lang":"en","type":"article","venue":"Geometriae Dedicata","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Algebraic geometry; Mathematics; Differential geometry; Hyperbolic geometry; Toric variety; Pure mathematics; Projective geometry; Algebra over a field","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006086731,0.0009646933,0.0008748978,0.002587811,0.002617826,0.004642117,0.001296085,0.001109869,0.009131727],"category_scores_gemma":[0.001376037,0.0006089975,0.0007200235,0.001910846,0.004584425,0.005849805,0.003604408,0.003814007,0.0008661543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001673105,"about_ca_system_score_gemma":0.000394157,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001117323,"about_ca_topic_score_gemma":0.0007998777,"domain_scores_codex":[0.9994403,0.0001056469,0.00002742969,0.00012692,0.0001596195,0.0001401359],"domain_scores_gemma":[0.9992366,0.0001962086,0.0001324513,0.0001238953,0.0001058435,0.0002049352],"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":[0.00002753243,0.00001097537,0.0001794542,0.00001710855,0.000008065437,0.0001074441,0.0002980475,0.0002645598,0.0004730372,0.9966438,0.0004458352,0.001524209],"study_design_scores_gemma":[0.00002235855,0.0000155472,0.0004414623,0.00000913551,0.00001319781,0.0002041667,0.0003328761,0.0009468921,0.0004532998,0.9931881,0.004361007,0.00001201497],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7177176,0.003066536,0.06402313,0.002968889,0.0008847162,0.00007934399,0.0006632385,0.0002606162,0.2103359],"genre_scores_gemma":[0.9680359,0.0007652853,0.00392121,0.00014914,0.0002390311,0.00003412173,0.0002439418,0.00005093732,0.02656046],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009131727,"threshold_uncertainty_score":0.03054869,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01995541442414807,"score_gpt":0.2834004985242039,"score_spread":0.2634450841000558,"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."}}