{"id":"W2077204451","doi":"10.1007/s10485-011-9262-3","title":"Essential Completeness in Categories of Completely Regular Frames","year":2011,"lang":"en","type":"article","venue":"Applied Categorical Structures","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Completeness (order theory); Mathematics; Theory of computation; Pure mathematics; Discrete mathematics; Algebra over a field; Algorithm; Mathematical analysis","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001666346,0.0003109944,0.0006844025,0.000141178,0.00009094604,0.00002608822,0.0004972752,0.000200173,0.0003324937],"category_scores_gemma":[0.00007015298,0.0002578748,0.0001133994,0.000316167,0.0003555017,0.000069705,0.0001444222,0.0002948591,0.00001059228],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004368799,"about_ca_system_score_gemma":0.00004056152,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004649804,"about_ca_topic_score_gemma":0.00009023396,"domain_scores_codex":[0.9980401,0.00005035944,0.0006516116,0.0004206366,0.0003890332,0.0004481955],"domain_scores_gemma":[0.9989005,0.0001903713,0.0002488203,0.0004844354,0.00006912509,0.0001067738],"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":[0.00008800733,0.0001086587,0.001191792,0.0001376419,0.0000463075,0.00001496137,0.00160492,0.000006724178,0.004932376,0.9898723,0.0003696664,0.001626584],"study_design_scores_gemma":[0.000526173,0.00003960678,0.02525205,0.000003058898,0.00003556112,0.00001170905,0.0005147509,0.00001993858,0.03832575,0.9347039,0.0002793248,0.000288145],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9753618,0.0001142413,0.01694622,0.00003756666,0.0002448396,0.0003724742,0.000006560459,0.0001132961,0.006802987],"genre_scores_gemma":[0.9947636,0.00001107249,0.004907131,0.00005425079,0.0001415477,0.00003271261,0.00001738149,0.00004402668,0.00002835356],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05516843,"threshold_uncertainty_score":0.9999874,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05060074585675606,"score_gpt":0.2675674770532661,"score_spread":0.2169667311965101,"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."}}