{"id":"W1976341314","doi":"10.1006/aama.1999.0661","title":"The Strong Independence Theorem for Automorphism Groups and Congruence Lattices of Arbitrary Lattices","year":2000,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":19,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Automorphism; Lattice (music); Algebraic number; Congruence (geometry); Independence (probability theory); Pure mathematics; Combinatorics; Automorphism group; Discrete mathematics; Algebra over a field; Mathematical analysis; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003303727,0.0008253035,0.001583892,0.00182148,0.003343252,0.005085127,0.001388271,0.001394708,0.004930919],"category_scores_gemma":[0.007247501,0.001480022,0.002813928,0.001702864,0.00829618,0.01329455,0.005796593,0.008092164,0.001147148],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001528048,"about_ca_system_score_gemma":0.00133211,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001087222,"about_ca_topic_score_gemma":0.001144849,"domain_scores_codex":[0.9964586,0.0007252276,0.000236663,0.0009007717,0.001103843,0.000574854],"domain_scores_gemma":[0.9905289,0.005527529,0.0005514629,0.001534519,0.0009672957,0.0008903377],"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":[0.00006637465,0.00002698025,0.0003147686,0.00003356491,0.00001880868,0.00004841429,0.0001995689,0.0005288285,0.000727697,0.9935656,0.0009803277,0.003489057],"study_design_scores_gemma":[0.00002022531,0.000008643803,0.0002215649,0.00000432199,0.000008856688,0.00005229771,0.00002572278,0.001359545,0.0005142321,0.9957146,0.00206159,0.000008339862],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1987582,0.001998066,0.6141813,0.006070773,0.00094569,0.0001487482,0.001100023,0.0005329589,0.1762643],"genre_scores_gemma":[0.9142945,0.001322311,0.05277736,0.001127581,0.002258617,0.0002733796,0.001445482,0.0002497589,0.02625109],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005085127,"threshold_uncertainty_score":0.01747197,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01191591219387377,"score_gpt":0.2628571735438551,"score_spread":0.2509412613499813,"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."}}