{"id":"W2044987315","doi":"10.1007/s00493-014-3132-1","title":"Sabidussi versus Hedetniemi for three variations of the chromatic number","year":2015,"lang":"en","type":"article","venue":"COMBINATORICA","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Cartesian product; Mathematics; Combinatorics; Conjecture; Chromatic scale; Homomorphism; Product (mathematics); Graph; Discrete mathematics; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002299797,0.0001563441,0.0002908887,0.00002196301,0.0001346527,0.00002276915,0.0004834298,0.0001174158,0.00004380571],"category_scores_gemma":[0.001164969,0.0001090333,0.0001681203,0.000292103,0.0000645752,0.00007034749,0.0001444596,0.0001132994,0.00001071893],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000137039,"about_ca_system_score_gemma":0.0001719948,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002463577,"about_ca_topic_score_gemma":0.000008276092,"domain_scores_codex":[0.9988527,0.0000476563,0.0003350953,0.0001775358,0.0003639752,0.0002229806],"domain_scores_gemma":[0.9981532,0.000618724,0.0002372569,0.0006476893,0.0002451233,0.00009799485],"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":[0.00004476652,0.0001051985,0.0004337258,0.00004376347,0.00005903416,1.626759e-7,0.0003130691,0.000004720079,0.000009776171,0.9905019,0.008291793,0.0001921277],"study_design_scores_gemma":[0.002517897,0.0001092564,0.0005188751,0.00002313831,0.0001032458,0.000001934731,0.00005742797,0.0005812656,0.0002708986,0.9936384,0.002043133,0.0001345102],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9185837,0.0002405723,0.01981984,0.001784828,0.0206229,0.002758529,0.00003289406,0.0002905097,0.03586626],"genre_scores_gemma":[0.9981567,9.124586e-7,0.001340832,0.00002062087,0.0001232676,0.00008566058,0.000001866788,0.0000304509,0.0002397262],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07957299,"threshold_uncertainty_score":0.4446249,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1227036518353448,"score_gpt":0.3417196628509759,"score_spread":0.2190160110156312,"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."}}