{"id":"W2888140268","doi":"10.4153/cmb-2018-038-5","title":"Nonexistence of Idempotent Means on Free Binary Systems","year":2018,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Idempotence; Extension (predicate logic); Binary number; Conjecture; Pure mathematics; Idempotent matrix; Binary operation; Algebra over a field; Combinatorics; Arithmetic; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0008203503,0.0002041247,0.0003862438,0.0002069138,0.0001492992,0.00003102761,0.0004640149,0.0001430977,0.005473861],"category_scores_gemma":[0.006791639,0.0001795287,0.0001132977,0.0002417694,0.0003837701,0.00002266383,0.00005684497,0.000172672,0.007280672],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002971471,"about_ca_system_score_gemma":0.0002649287,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001768618,"about_ca_topic_score_gemma":0.001685825,"domain_scores_codex":[0.9979634,0.0001182451,0.0006659788,0.0003240116,0.000519924,0.0004084094],"domain_scores_gemma":[0.9966059,0.001411869,0.0001528347,0.001055624,0.0003253772,0.0004484193],"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":[0.00004023251,0.0001913545,0.00002313596,0.0004035719,0.00004211614,0.00001568945,0.0004073022,0.00003020234,0.0001294064,0.9210762,0.07756323,0.00007760141],"study_design_scores_gemma":[0.001169165,0.001169094,0.0003646981,0.001167544,0.0001165228,0.00007726463,0.0008868624,0.008581615,0.0006671316,0.9145828,0.07050661,0.0007106568],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3745174,0.0001277447,0.01308699,0.02386001,0.001101055,0.002681526,0.0007739235,0.0003026715,0.5835487],"genre_scores_gemma":[0.9854944,0.000001318101,0.01000108,0.0002937455,0.0001987252,0.00006392464,0.000008368429,0.00004355215,0.003894938],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6109769,"threshold_uncertainty_score":0.9954353,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05869933408659772,"score_gpt":0.280564845129177,"score_spread":0.2218655110425792,"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."}}