{"id":"W153015188","doi":"10.4086/toc.2006.v002a004","title":"","year":2006,"lang":"en","type":"article","venue":"Theory of Computing","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":67,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematical proof; Rank (graph theory); Combinatorics; Mathematics; Pigeonhole principle; Discrete mathematics; Upper and lower bounds","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":[0.002234987,0.0002212435,0.0003763126,0.0002458715,0.0003749601,0.0001124768,0.002147899,0.00005282154,0.000003005213],"category_scores_gemma":[0.00005583499,0.0002218756,0.0001981546,0.0008799383,0.000300404,0.0004862027,0.0008898583,0.0001923725,0.000002186516],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001905085,"about_ca_system_score_gemma":0.00003922258,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000924897,"about_ca_topic_score_gemma":0.000005493649,"domain_scores_codex":[0.9975355,0.0003764076,0.0006661053,0.0004726818,0.0004261897,0.0005231453],"domain_scores_gemma":[0.9973971,0.001160265,0.0003474664,0.0008771244,0.000150513,0.00006755713],"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":[0.00000990234,0.0001183371,0.001230758,0.0000190441,0.00001241193,0.000009049694,0.0008789822,0.005524941,0.002028469,0.9128605,0.00001213982,0.07729544],"study_design_scores_gemma":[0.0004686467,0.00008695853,0.03968773,0.00005901033,0.000005042979,0.00003943812,0.0000946626,0.1439071,0.01418129,0.8011931,0.00003994316,0.0002370598],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4417699,0.000111532,0.5563591,0.0001317033,0.0001873853,0.00007305925,5.444197e-7,0.0002548266,0.001112016],"genre_scores_gemma":[0.7879429,7.411631e-7,0.2117769,0.0001121251,0.0001411697,9.220727e-7,0.000001072282,0.000007392309,0.00001675516],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.346173,"threshold_uncertainty_score":0.9047822,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01345998444829758,"score_gpt":0.2270239102562561,"score_spread":0.2135639258079585,"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."}}