{"id":"W4400064811","doi":"10.48550/arxiv.2406.17217","title":"High dimensional countable compactness and ultrafilters","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; York University","keywords":"Compact space; Countable set; Mathematics; Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009084304,0.0003411875,0.0003764153,0.001277104,0.000917327,0.001647527,0.0006957677,0.0005804542,0.002311482],"category_scores_gemma":[0.0028755,0.000238871,0.000490483,0.0007568586,0.003093494,0.004970507,0.002569671,0.001218229,0.0001768038],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008120841,"about_ca_system_score_gemma":0.0002235067,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000563954,"about_ca_topic_score_gemma":0.0004249522,"domain_scores_codex":[0.9993617,0.0001904141,0.00004316332,0.0001381121,0.0001742751,0.00009240326],"domain_scores_gemma":[0.9980252,0.0009271117,0.0003153009,0.0002308386,0.000222451,0.0002791843],"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":[0.00003161415,0.00001829038,0.001371213,0.00005564571,0.00001298903,0.000159022,0.0007231664,0.001737587,0.003581441,0.9876105,0.0002987902,0.004399858],"study_design_scores_gemma":[0.00001956589,0.0001140346,0.005636199,0.00006325132,0.00001769699,0.0008026739,0.0008658951,0.0244575,0.005564389,0.9514838,0.01093197,0.00004294624],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7153388,0.002435548,0.2465006,0.001116656,0.00006668045,0.00002889863,0.0002253221,0.0001783846,0.03410918],"genre_scores_gemma":[0.97697,0.00037404,0.01913148,0.00009330903,0.00005322432,0.00004252674,0.0001096927,0.00001356985,0.003212329],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002311482,"threshold_uncertainty_score":0.00773263,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08271234387726666,"score_gpt":0.2258304596348743,"score_spread":0.1431181157576076,"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."}}