{"id":"W7106782718","doi":"","title":"Extremality in semidistributive lattices","year":2025,"lang":"","type":"article","venue":"ArXiv.org","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Counterexample; Lattice (music); Chromatic scale; Complete lattice; Congruence (geometry); Galois connection; Torsion (gastropod); Distributive property","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005900913,0.0003786907,0.0004964627,0.0001821212,0.000273364,0.0001325113,0.001315043,0.0002223933,0.0001240789],"category_scores_gemma":[0.0003694853,0.0003748729,0.0001520316,0.001982107,0.0002760935,0.000893098,0.0009109785,0.0006003822,0.00030716],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002372348,"about_ca_system_score_gemma":0.0003029241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008745452,"about_ca_topic_score_gemma":0.000129684,"domain_scores_codex":[0.9968186,0.0002931845,0.0006779847,0.001118265,0.0002578936,0.0008340551],"domain_scores_gemma":[0.9980612,0.0004078129,0.0002171742,0.001025569,0.000145563,0.0001426166],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.00003003269,0.000305148,0.9151279,0.00008816391,0.00003911974,0.0001280012,0.0007290273,0.0001733137,0.000412261,0.06380999,0.0001942524,0.01896281],"study_design_scores_gemma":[0.0007190334,0.00007878179,0.9576566,0.0002843782,0.00002666224,0.000003772971,0.0002072165,0.006938292,0.003586718,0.02478372,0.005284857,0.0004299596],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8489918,0.003234028,0.1342809,0.002862473,0.001255932,0.0003259675,0.00001504258,0.0001108198,0.008923043],"genre_scores_gemma":[0.9953149,0.0002284889,0.0007876109,0.001144314,0.00009245116,0.00002355784,0.000005953574,0.000008556613,0.00239417],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1463231,"threshold_uncertainty_score":0.9998703,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04182551705983525,"score_gpt":0.3040611459194292,"score_spread":0.262235628859594,"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."}}