{"id":"W4407580272","doi":"10.37236/12506","title":"On the Quantum Chromatic Numbers of Small Graphs","year":2025,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Chromatic scale; Quantum; Quantum graph; Mathematics; Computer science; Combinatorics; Physics; Quantum mechanics","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":[0.002014161,0.0001178784,0.0002254755,0.0001673218,0.0001707447,0.00004719172,0.001569081,0.00004219303,0.000002723335],"category_scores_gemma":[0.0001745222,0.00006049217,0.0001699243,0.001092579,0.00009263821,0.00007170958,0.00009337528,0.0005801126,0.000003733624],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007546111,"about_ca_system_score_gemma":0.0004431065,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001137675,"about_ca_topic_score_gemma":0.000002324807,"domain_scores_codex":[0.9985113,0.0002222605,0.0004523702,0.0001008455,0.0003693944,0.000343842],"domain_scores_gemma":[0.9979869,0.0007558445,0.0004410778,0.0005358331,0.0002447802,0.00003563695],"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":[0.0000111828,0.0001032301,0.00003532461,0.00001058905,0.00008339735,0.000001497131,0.0001814474,0.0001639721,0.0002899668,0.9976877,0.00121813,0.0002135936],"study_design_scores_gemma":[0.0004156015,0.0004347898,0.0000814891,0.0001008007,0.00003312855,0.00002660955,0.00004562999,0.002527203,0.00215423,0.9938865,0.0002352466,0.00005882236],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9279279,0.004548196,0.05405613,0.01007581,0.001236444,0.0001767402,2.067465e-7,0.00003241076,0.001946158],"genre_scores_gemma":[0.9991124,0.0002748858,0.00004486183,0.0004172024,0.000002716148,0.000001655017,5.55568e-8,0.000005196426,0.0001410858],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07118444,"threshold_uncertainty_score":0.291577,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007870199887265065,"score_gpt":0.2162875026383883,"score_spread":0.2084173027511232,"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."}}