{"id":"W4388684986","doi":"10.48550/arxiv.2311.06872","title":"Ramsey theorem for trees with successor operation","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Grantová Agentura České Republiky; European Commission; Univerzita Karlova v Praze; National Science Foundation","keywords":"Successor cardinal; Mathematics; Ramsey's theorem; Ramsey theory; Combinatorics; Generalization; Discrete mathematics; Forcing (mathematics); Tree (set theory); Mathematical analysis; Graph","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":[0.0003234024,0.0002793107,0.0003763309,0.0001442025,0.0002205345,0.00002752045,0.0004572472,0.0003575962,0.00007054276],"category_scores_gemma":[0.0001548546,0.0002561699,0.0001464678,0.0001481161,0.0002347837,0.0001394933,0.0002763644,0.0003753208,0.0000469722],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000912182,"about_ca_system_score_gemma":0.00009760348,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001653158,"about_ca_topic_score_gemma":0.0003738638,"domain_scores_codex":[0.9987338,0.00012288,0.0001646079,0.000649715,0.00004732765,0.0002817368],"domain_scores_gemma":[0.9983485,0.0006288795,0.0002027712,0.0006224096,0.0001256673,0.00007172192],"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":[0.0004320942,0.00006442792,0.0004328579,0.0001392262,0.0001705305,0.00007079414,0.0002616552,0.04181745,0.00001596856,0.9561723,0.0003544037,0.00006830603],"study_design_scores_gemma":[0.0008505225,0.0001023099,0.0001086203,0.0000933448,0.0002254998,0.000002796785,0.0005089807,0.02210605,0.0002729234,0.9751576,0.0002270287,0.0003442977],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3584975,0.00001615244,0.6379534,0.0001387508,0.0003233039,0.0007991921,0.0000893555,0.000386314,0.001796018],"genre_scores_gemma":[0.981111,0.00005633054,0.003528645,0.0000455186,0.0001144026,0.000009231005,0.00009361476,0.00006205762,0.01497913],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6344247,"threshold_uncertainty_score":0.999989,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1590190650424416,"score_gpt":0.2534032070647728,"score_spread":0.09438414202233111,"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."}}