{"id":"W3179960841","doi":"10.1080/00927872.2023.2173766","title":"Hilbert schemes with two Borel-fixed points in arbitrary characteristic","year":2023,"lang":"en","type":"article","venue":"Communications in Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Fixed point; Pure mathematics; Borel equivalence relation; Discrete mathematics; Mathematical analysis; Borel measure; Probability measure","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005333606,0.000204347,0.0003151429,0.0004745296,0.000190073,0.00004979428,0.001282558,0.00006853727,0.00009617213],"category_scores_gemma":[0.000402891,0.0001947334,0.00004977142,0.001960151,0.0002589494,0.0002167814,0.0005563485,0.0005418074,0.0002936795],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001058153,"about_ca_system_score_gemma":0.0001016596,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000643129,"about_ca_topic_score_gemma":0.000765021,"domain_scores_codex":[0.9984334,0.000241796,0.0005288261,0.0002797229,0.000181966,0.0003342495],"domain_scores_gemma":[0.9955218,0.001567552,0.0001518145,0.002608013,0.00008101376,0.00006978783],"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":[0.00002459481,0.0005170233,0.03201296,0.00004567217,0.00003882033,0.000009321211,0.002138784,0.000001981869,0.0004624299,0.9606442,0.001193338,0.002910854],"study_design_scores_gemma":[0.002038184,0.00006396637,0.2767203,0.0004200971,0.0000416636,0.00001537764,0.0008384385,0.004095429,0.0005623461,0.7012072,0.01339051,0.0006065577],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9794789,0.0002670381,0.0006507382,0.008208205,0.00002943753,0.0007449317,0.00002749082,0.0003107106,0.01028255],"genre_scores_gemma":[0.976127,0.0003230548,0.02208805,0.0002495762,0.0000174975,0.0006913807,0.0001581027,0.00005343243,0.0002918906],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2594371,"threshold_uncertainty_score":0.7940996,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0837754446970179,"score_gpt":0.3773153608663823,"score_spread":0.2935399161693644,"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."}}