{"id":"W4395443554","doi":"10.48550/arxiv.2404.14940","title":"Defective and Clustered Colouring of Graphs with Given Girth","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Australian Government","keywords":"Girth (graph theory); Combinatorics; Mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001928353,0.000241133,0.0003138046,0.0003963361,0.00008626853,0.00007707622,0.0005868301,0.0001639272,0.000002753273],"category_scores_gemma":[0.000009473612,0.0002266158,0.0001146772,0.0006392613,0.0001946585,0.0001158752,0.002072362,0.0004483823,0.000008459835],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003950988,"about_ca_system_score_gemma":0.0001241171,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001887484,"about_ca_topic_score_gemma":0.00006044891,"domain_scores_codex":[0.9985451,0.00008363776,0.0001522582,0.0009102153,0.00008654215,0.0002222222],"domain_scores_gemma":[0.9988047,0.00008433953,0.0001784768,0.0006493848,0.0001613915,0.000121705],"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":[0.00009916331,0.0001128625,0.009058977,0.0006614096,0.0004731998,0.0004957223,0.001455268,0.08751336,0.0001945908,0.8990995,0.0001761068,0.0006598371],"study_design_scores_gemma":[0.0008045904,0.00028865,0.001868574,0.0007231536,0.0001990927,0.00002149692,0.0001329978,0.1854481,0.0007335939,0.8092415,0.00003785483,0.0005003799],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9656763,0.0003713239,0.03165666,0.00008083345,0.0002439242,0.0002606156,0.00001188684,0.0002065452,0.001491893],"genre_scores_gemma":[0.9971735,0.0001017321,0.002350664,0.00002679915,0.000003247291,8.255759e-7,0.000002271589,0.00001431351,0.0003265912],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09793471,"threshold_uncertainty_score":0.9241126,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03617265969134468,"score_gpt":0.1642033243124293,"score_spread":0.1280306646210846,"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."}}