{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002017692,0.0002933579,0.0004130363,0.0001383217,0.0001383445,0.00002666147,0.000253983,0.0003313916,0.0001995292],"category_scores_gemma":[0.00004670967,0.0003039948,0.0001073465,0.0001294515,0.0003691968,0.00007602022,0.0007433796,0.0007945867,0.00008268798],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001139377,"about_ca_system_score_gemma":0.00008459169,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005632381,"about_ca_topic_score_gemma":0.00003149106,"domain_scores_codex":[0.9987646,0.00009755557,0.0001572443,0.0006538942,0.00005714892,0.0002695427],"domain_scores_gemma":[0.9988326,0.0004204116,0.0001142042,0.0004524137,0.0000611846,0.0001191583],"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":[0.0001027977,0.00006151246,0.0002012519,0.0003102254,0.0001967356,0.0004007188,0.0001656177,0.01696604,0.00004567789,0.9802068,0.001301773,0.00004079624],"study_design_scores_gemma":[0.000345808,0.00002272654,0.00008157942,0.0001655582,0.0002477625,0.00002166277,0.0001515076,0.008562196,0.0001552731,0.9897245,0.0001932631,0.0003281886],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9867384,0.0001829543,0.009206381,0.0001056177,0.0008494802,0.000208285,0.0001087759,0.0002177466,0.002382313],"genre_scores_gemma":[0.9927113,0.00008006355,0.0008135888,0.00008617334,0.00007426363,6.773241e-7,0.00003308225,0.00003376174,0.006167085],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009517618,"threshold_uncertainty_score":0.9999412,"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."}}