{"id":"W3174325142","doi":"10.1142/s179352532350005x","title":"Systolic inequalities for the number of vertices","year":2023,"lang":"en","type":"article","venue":"Journal of Topology and Analysis","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"FP7 Ideas: European Research Council; European Commission; Russian Foundation for Basic Research; Agence Nationale de la Recherche; National Science Foundation","keywords":"Mathematics; Mathematical proof; Upper and lower bounds; Corollary; Path (computing); Combinatorics; Ideal (ethics); Inequality; Isoperimetric inequality; Pure mathematics; Mathematical analysis; Geometry; Law","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001844771,0.001162296,0.00106731,0.003224171,0.001357991,0.002987635,0.002174726,0.0009681783,0.0120569],"category_scores_gemma":[0.01050971,0.0004863699,0.001184101,0.001727073,0.003841969,0.008500699,0.004042846,0.003107754,0.001383946],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001906292,"about_ca_system_score_gemma":0.000754028,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007254817,"about_ca_topic_score_gemma":0.000956626,"domain_scores_codex":[0.9983347,0.0002951059,0.00008950814,0.00042637,0.0005232972,0.0003310353],"domain_scores_gemma":[0.992507,0.004404838,0.0004645486,0.001024273,0.0007647999,0.0008345818],"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":[0.00005197318,0.00001808272,0.0007144783,0.00008465027,0.00001544171,0.00006572557,0.000131855,0.003341389,0.00308725,0.9794447,0.001820267,0.01122419],"study_design_scores_gemma":[0.00001144153,0.00004262096,0.001306066,0.0000395164,0.00002455984,0.0001329963,0.00006378436,0.03576574,0.002816666,0.9531764,0.006592907,0.00002735308],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.203651,0.003121429,0.6513886,0.003641536,0.000582788,0.00007010173,0.001017389,0.0004846295,0.1360423],"genre_scores_gemma":[0.8905682,0.001755808,0.08446403,0.0008917664,0.001526005,0.0002851808,0.0009373404,0.0003668669,0.01920481],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0120569,"threshold_uncertainty_score":0.04033428,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03374346195479653,"score_gpt":0.3249142138594727,"score_spread":0.2911707519046761,"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."}}