{"id":"W2057097927","doi":"10.4236/apm.2014.45024","title":"A Solution of a Problem of I. P. Natanson Concerning the Decomposition of an Interval into Disjoint Perfect Sets","year":2014,"lang":"en","type":"article","venue":"Advances in Pure Mathematics","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"York University","keywords":"Mathematics; Disjoint sets; Disjoint union (topology); Lebesgue measure; Bounded function; Interval (graph theory); Cardinality (data modeling); Real line; Discrete mathematics; Lebesgue integration; Measure (data warehouse); Combinatorics; Hilbert space; Pure mathematics; Mathematical 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001132917,0.0001640021,0.0005079242,0.0000893733,0.00005424415,0.000009681027,0.0003625057,0.00007073044,0.00001940829],"category_scores_gemma":[0.0002923509,0.0001172265,0.0001037715,0.0002368527,0.0001914407,0.0002305195,0.00009132402,0.0001431144,0.000001245735],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003431586,"about_ca_system_score_gemma":0.000021961,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009496954,"about_ca_topic_score_gemma":0.0001047898,"domain_scores_codex":[0.998274,0.0001089511,0.0009732969,0.000167738,0.0003143619,0.0001617125],"domain_scores_gemma":[0.9975111,0.0008128991,0.0009638369,0.0005258041,0.0001541759,0.00003214471],"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":[0.0000345623,0.001820646,0.0002874912,0.0111912,0.00006977798,4.826704e-7,0.02493178,0.0007559954,0.02862327,0.9111873,0.0001156206,0.02098189],"study_design_scores_gemma":[0.000393702,0.0002756398,0.00002637626,0.001381307,0.00007625139,0.000008376202,0.001347763,0.1127001,0.02400152,0.8593581,0.0002762718,0.0001546151],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7269365,0.0002955203,0.2690498,0.000149289,0.00003976336,0.0008175743,0.0000195346,0.00003217695,0.002659833],"genre_scores_gemma":[0.7233338,0.00003575567,0.2765173,0.000005544096,0.00001339435,0.00006101544,0.00000631413,0.00001857438,0.000008227308],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1119441,"threshold_uncertainty_score":0.4780359,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02293050171770427,"score_gpt":0.3479320855610586,"score_spread":0.3250015838433543,"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."}}