{"id":"W3217223167","doi":"10.1017/fms.2023.42","title":"Small elementary components of Hilbert schemes of points","year":2023,"lang":"en","type":"article","venue":"Forum of Mathematics Sigma","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"University of Waterloo","keywords":"Mathematics; Hilbert scheme; Dimension (graph theory); Hilbert space; Scheme (mathematics); Pure mathematics; Combinatorics; Algebra over a field; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005783185,0.0002666787,0.0005812567,0.001433779,0.001008104,0.002777673,0.0006155393,0.0004222411,0.003767278],"category_scores_gemma":[0.001669895,0.0002864589,0.000399642,0.0008447377,0.003964087,0.004020427,0.002547836,0.001194392,0.0003587674],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001028239,"about_ca_system_score_gemma":0.0004564777,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004670372,"about_ca_topic_score_gemma":0.0002443905,"domain_scores_codex":[0.9995574,0.00008387067,0.00002117891,0.0001035239,0.000148933,0.00008499555],"domain_scores_gemma":[0.9992521,0.0001731478,0.00008913683,0.0001356411,0.0001271168,0.0002228992],"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":[0.00002049924,0.000004541409,0.0004348448,0.00002078363,0.000003073856,0.00003463696,0.0002393773,0.0002046728,0.0006583548,0.9963652,0.0001953476,0.00181872],"study_design_scores_gemma":[0.00002445152,0.00004926256,0.00201343,0.00003488684,0.00001406543,0.0003915857,0.000486032,0.004059891,0.002689858,0.9754204,0.01479642,0.00001981255],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.895591,0.001978455,0.06359958,0.0007246355,0.0001094757,0.00006566996,0.0001935303,0.0001884431,0.03754924],"genre_scores_gemma":[0.9885512,0.0003731517,0.005912288,0.00004114775,0.00005694105,0.00002474941,0.00008662781,0.00002490236,0.004929092],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003767278,"threshold_uncertainty_score":0.01260281,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08303546145415458,"score_gpt":0.3172954586552662,"score_spread":0.2342599972011116,"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."}}