{"id":"W54538453","doi":"","title":"The Basis Number of the Direct Product of a Theta Graph and a Path.","year":2005,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Direct product; Graph; Combinatorics; Path (computing); Basis (linear algebra); Product (mathematics); Discrete mathematics; Computer science; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.0006020209,0.0000909906,0.0001401588,0.00002468615,0.0001682097,0.00003355147,0.0006009202,0.00002624726,0.000002007572],"category_scores_gemma":[0.00009032682,0.0000477874,0.00007766747,0.0004689998,0.0001778403,0.0001027229,0.0002464799,0.00008671292,0.000003294836],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000004968256,"about_ca_system_score_gemma":0.00003577035,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005016632,"about_ca_topic_score_gemma":0.000004940091,"domain_scores_codex":[0.999033,0.0001166243,0.0002257063,0.0002131267,0.0002549137,0.0001566099],"domain_scores_gemma":[0.9987453,0.0001613256,0.0001479649,0.0007881192,0.0001220133,0.00003529269],"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":[0.00000366096,0.00008032388,0.009182726,0.000009470003,0.00002373502,2.284964e-7,0.0005129122,0.000006446423,0.0009466378,0.9820132,0.001262492,0.005958204],"study_design_scores_gemma":[0.0004108016,0.00003709176,0.007141762,0.00004666133,0.00001541552,0.000008853382,0.00001879414,0.0006794927,0.02385987,0.9661555,0.001527082,0.00009869124],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9920548,0.001187176,0.000008188379,0.002357008,0.0007297649,0.000169958,0.000001461336,0.00003736579,0.003454247],"genre_scores_gemma":[0.9989713,0.00008870589,0.0006921717,0.00006261097,0.000001159129,0.000007693153,9.72147e-8,0.000005261495,0.0001710045],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02291323,"threshold_uncertainty_score":0.1948714,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007262431607025712,"score_gpt":0.2159267809290735,"score_spread":0.2086643493220478,"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."}}