{"id":"W4320725624","doi":"10.14712/1213-7243.2023.003","title":"Counterexamples to Hedetniemi's conjecture and infinite Boolean lattices","year":2023,"lang":"en","type":"article","venue":"Commentationes Mathematicae Universitatis Carolinae","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Military College of Canada","funders":"","keywords":"Counterexample; Conjecture; Combinatorics; Mathematics; Exponential function; Lattice (music); Discrete mathematics; Base (topology); Physics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.002397306,0.0003401953,0.0008346543,0.001550274,0.002556986,0.002970918,0.001490062,0.001840679,0.007327712],"category_scores_gemma":[0.01597789,0.0004344211,0.0007231309,0.001518006,0.006616581,0.006858479,0.003784663,0.003115284,0.0003406285],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002177493,"about_ca_system_score_gemma":0.0006284117,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001540084,"about_ca_topic_score_gemma":0.001965493,"domain_scores_codex":[0.9979674,0.0005443699,0.00009415804,0.000495117,0.0005212419,0.0003777368],"domain_scores_gemma":[0.9869265,0.009245264,0.0007879328,0.001333184,0.0007892365,0.0009179469],"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":[0.0001074406,0.0000399086,0.001559948,0.00004439086,0.00001071649,0.0001958433,0.00048703,0.002163589,0.0006382092,0.9884375,0.002795265,0.003520176],"study_design_scores_gemma":[0.00005481131,0.00001969678,0.0009030444,0.0000272513,0.00001121687,0.0003055098,0.000565446,0.01488299,0.001157491,0.9748185,0.007230576,0.00002342978],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7719878,0.001204281,0.09096429,0.02457327,0.0003895116,0.00005329268,0.000629069,0.0003793471,0.109819],"genre_scores_gemma":[0.982035,0.0002449373,0.01106908,0.0008702135,0.000155385,0.00006978082,0.0002207165,0.0000340335,0.005300938],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007327712,"threshold_uncertainty_score":0.0245136,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02514872263584638,"score_gpt":0.2683470578078771,"score_spread":0.2431983351720307,"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."}}