{"id":"W4293768525","doi":"10.1090/proc/16106","title":"Ramsey theory over partitions III: Strongly Luzin sets and partition relations","year":2022,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"H2020 European Research Council; Natural Sciences and Engineering Research Council of Canada; Israel Science Foundation","keywords":"Partition (number theory); Mathematics; Ramsey theory; Combinatorics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009324558,0.0001558928,0.0003560686,0.00002290488,0.0007072798,0.0000164817,0.0002619167,0.0000406951,0.0005083289],"category_scores_gemma":[0.000431142,0.0001197856,0.0002410637,0.000335802,0.001169398,0.0001411321,0.0003759004,0.0004137544,0.00000465819],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007738829,"about_ca_system_score_gemma":0.00002420719,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002421679,"about_ca_topic_score_gemma":3.469307e-7,"domain_scores_codex":[0.9987647,0.0000636192,0.0003659413,0.0002286919,0.0003088902,0.0002681506],"domain_scores_gemma":[0.998375,0.0008454748,0.0004744387,0.0001657797,0.00006813997,0.00007114312],"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":[0.00004109911,0.0002171484,0.0009673621,0.00008087399,0.00009780282,1.342893e-7,0.003208971,0.00001536696,0.0007818379,0.9901769,0.004216579,0.000195897],"study_design_scores_gemma":[0.0002815014,0.00008445703,0.001062605,0.00002769937,0.0001343251,0.0000191544,0.009220505,0.0006540989,0.0003032281,0.9877418,0.0003334084,0.0001372693],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9875737,0.00003707021,0.003650885,0.001156073,0.00003810501,0.0003765764,0.00004235307,0.00009988694,0.007025289],"genre_scores_gemma":[0.9819875,0.00001147136,0.01643944,0.0003150486,0.00002724607,0.0001576475,0.000002727025,0.00002657391,0.001032342],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01278855,"threshold_uncertainty_score":0.5565845,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01838454958307207,"score_gpt":0.2954668410609177,"score_spread":0.2770822914778456,"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."}}