{"id":"W4391045159","doi":"10.1017/jsl.2024.4","title":"POLISH SPACE PARTITION PRINCIPLES AND THE HALPERN–LÄUCHLI THEOREM","year":2024,"lang":"en","type":"article","venue":"Journal of Symbolic Logic","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; Akademie Věd České Republiky; National Science Foundation","keywords":"Mathematical proof; Partition (number theory); Mathematics; Forcing (mathematics); Combinatorial proof; Combinatorial principles; Combinatorics; Discrete mathematics; Consistency (knowledge bases); Combinatorial explosion; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002002652,0.0003298306,0.0007375845,0.001622319,0.001676382,0.003063438,0.0009585242,0.000948897,0.005312233],"category_scores_gemma":[0.004337783,0.0004137365,0.0008196657,0.001011274,0.007750845,0.005481453,0.003024009,0.002224432,0.0007225406],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002077262,"about_ca_system_score_gemma":0.0007682201,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001196303,"about_ca_topic_score_gemma":0.00118125,"domain_scores_codex":[0.9986338,0.0003013603,0.00007144008,0.0002996848,0.0004994156,0.000194326],"domain_scores_gemma":[0.9968727,0.001860302,0.0002328335,0.0004647976,0.0003642081,0.000205122],"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":[0.000009395006,0.000004581058,0.0001305969,0.00001303562,0.000003501495,0.00002708407,0.0001117568,0.000425404,0.000259477,0.9967974,0.0005529053,0.001664765],"study_design_scores_gemma":[0.00001181457,0.000007778463,0.0002015531,0.000007980448,0.000003931564,0.00004352676,0.00005987711,0.001677626,0.0004168271,0.9950312,0.002532595,0.000005143291],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3430293,0.002192808,0.4263853,0.006515077,0.0002138199,0.0001300147,0.0006877215,0.0006150406,0.2202308],"genre_scores_gemma":[0.9672068,0.000451818,0.02272031,0.0006260334,0.000162044,0.0001404976,0.0001591836,0.00007511909,0.008458349],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005312233,"threshold_uncertainty_score":0.01777118,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04644626764774502,"score_gpt":0.3254615466338696,"score_spread":0.2790152789861246,"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."}}