{"id":"W4226412996","doi":"10.48550/arxiv.2201.09819","title":"Stone Duality for Topological Convexity Spaces","year":2022,"lang":"en","type":"preprint","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":"Convexity; Mathematics; Topological space; Topological vector space; Topological tensor product; Locally convex topological vector space; Closure (psychology); Duality (order theory); Adjunction; Space (punctuation); Pure mathematics; Closed set; Topology (electrical circuits); Combinatorics; Computer science; Functional analysis","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":[0.001027423,0.0005570371,0.0005332144,0.001665942,0.001895398,0.003620149,0.0004731511,0.0006352188,0.004321751],"category_scores_gemma":[0.001840488,0.0002660821,0.0008555574,0.001196768,0.004572232,0.005773588,0.002875219,0.002027686,0.0004587082],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001576566,"about_ca_system_score_gemma":0.0008875364,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001196991,"about_ca_topic_score_gemma":0.0009575631,"domain_scores_codex":[0.9988663,0.0003386227,0.00005699471,0.0002190675,0.0003450727,0.000173908],"domain_scores_gemma":[0.9988764,0.0004369026,0.0001044416,0.0001165429,0.0002603167,0.0002054059],"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":[0.000006696244,0.000004866703,0.0001272695,0.0000116185,0.000003482783,0.00004390861,0.0001301346,0.0002850624,0.0003760012,0.9971502,0.0002781851,0.001582617],"study_design_scores_gemma":[0.000006500003,0.00002399873,0.0003104868,0.00001398067,0.000006965343,0.0001803318,0.0002576995,0.003877866,0.0009503995,0.9832678,0.01109322,0.00001068345],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.3433078,0.002799671,0.4986158,0.002776186,0.0004611098,0.00008998779,0.0005045664,0.0002890532,0.1511559],"genre_scores_gemma":[0.9456061,0.001034083,0.03489911,0.0003390019,0.0002581325,0.00009781949,0.0003380263,0.0001002045,0.01732739],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.004321751,"threshold_uncertainty_score":0.0144577,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1145104966157501,"score_gpt":0.343996946579694,"score_spread":0.2294864499639439,"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."}}