{"id":"W4409511904","doi":"10.4153/s0008439525000463","title":"A counterexample regarding an equivalence relation on a product space","year":2025,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Counterexample; Mathematics; Equivalence relation; Equivalence (formal languages); Pure mathematics; Space (punctuation); Relation (database); Discrete mathematics; Data mining; Linguistics; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"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":[0.003010451,0.0006935625,0.001117914,0.00272072,0.004809239,0.006522348,0.00151409,0.004491115,0.01075564],"category_scores_gemma":[0.009777918,0.0007393556,0.001159916,0.002741504,0.008899793,0.01054912,0.006547268,0.005260411,0.0007398965],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001432837,"about_ca_system_score_gemma":0.0004926524,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001310382,"about_ca_topic_score_gemma":0.0006670207,"domain_scores_codex":[0.9953548,0.001132164,0.0003458293,0.001238802,0.001219853,0.0007085418],"domain_scores_gemma":[0.9934012,0.004167066,0.0003862227,0.0007898285,0.0007650671,0.0004906414],"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":[0.0001062226,0.00003872659,0.0004612759,0.00004444267,0.00001324781,0.0006767774,0.000649334,0.0003209719,0.0008159194,0.9929498,0.001875818,0.002047449],"study_design_scores_gemma":[0.00006046932,0.00005053249,0.0005277013,0.00005843258,0.00003927211,0.001265236,0.0008866069,0.00303757,0.002712018,0.9735603,0.01776615,0.00003585461],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6437156,0.002230248,0.1530501,0.02057062,0.002658461,0.0001234643,0.0009896128,0.001214358,0.1754476],"genre_scores_gemma":[0.9831548,0.0004168476,0.009283746,0.001107946,0.0004957466,0.00007198759,0.0003747034,0.0001114192,0.004982856],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01075564,"threshold_uncertainty_score":0.03598118,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03803164430414359,"score_gpt":0.3206398354417692,"score_spread":0.2826081911376256,"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."}}