{"id":"W3173971361","doi":"10.1007/s00029-021-00656-z","title":"The fundamental theorem of finite semidistributive lattices","year":2019,"lang":"","type":"article","venue":"ArXiv.org","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; National Science Foundation","keywords":"Distributive lattice; Mathematics; Partially ordered set; Representation theorem; Hyperplane; Distributivity; Lattice (music); Quotient; Distributive property; Structured program theorem; Pure mathematics; Finite set; Fundamental theorem; Discrete mathematics; Combinatorics","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005866689,0.0003334871,0.0003810407,0.00004385262,0.0004572549,0.000137406,0.001679371,0.0001258781,0.0002616177],"category_scores_gemma":[0.0001652832,0.0002264404,0.0002254101,0.0005806135,0.000593885,0.0006530225,0.0008449297,0.0004000432,0.001227199],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007490737,"about_ca_system_score_gemma":0.0001354479,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000117005,"about_ca_topic_score_gemma":0.000006523147,"domain_scores_codex":[0.9974049,0.0002271469,0.0005656292,0.0006634545,0.0004322585,0.0007066392],"domain_scores_gemma":[0.9965861,0.001419329,0.0005302127,0.001154722,0.0001735957,0.0001359782],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0001147354,0.0002274575,0.7642284,0.00007007844,0.0001758781,0.0000191895,0.002493521,0.0003680908,0.003419464,0.2070459,0.0001167524,0.02172052],"study_design_scores_gemma":[0.002529513,0.002136236,0.8160322,0.0004434911,0.0001379123,0.00003160858,0.004092305,0.02701217,0.05091193,0.0600425,0.03513714,0.00149293],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9781199,0.00243328,0.01153017,0.0009023858,0.001609417,0.0004284164,0.00004196434,0.00005200619,0.00488244],"genre_scores_gemma":[0.9967648,0.0003984966,0.0002442857,0.000310191,0.0001261039,0.000009092962,0.000006622051,0.00001630389,0.002124043],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1470034,"threshold_uncertainty_score":0.9995505,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02439413437402156,"score_gpt":0.2574933642259309,"score_spread":0.2330992298519093,"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."}}