{"id":"W1583473912","doi":"10.37236/322","title":"Forbidden Configurations: Exact Bounds Determined by Critical Substructures","year":2010,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Universities Space Research Association; University of South Carolina","keywords":"Combinatorics; Mathematics; Simple (philosophy); Matrix (chemical analysis); Substructure; Permutation (music); Integer (computer science); Multiset; Discrete mathematics; Physics; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001289338,0.0002026471,0.0003309705,0.00008972069,0.0004632821,0.00009745218,0.0007932354,0.000157802,0.0001311924],"category_scores_gemma":[0.001655144,0.0001236231,0.0001966051,0.0001891878,0.0002883282,0.0001888974,0.00005338682,0.001573227,0.000001463919],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008116331,"about_ca_system_score_gemma":0.0002556356,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002320507,"about_ca_topic_score_gemma":0.000009050003,"domain_scores_codex":[0.9981241,0.0001554557,0.000559322,0.0001160288,0.0004816055,0.000563451],"domain_scores_gemma":[0.9972346,0.001532905,0.0003614785,0.0004167991,0.0003406397,0.0001135203],"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":[0.00004996233,0.00005634807,0.00006944234,0.00001329026,0.00007953188,0.000005476899,0.0003477295,2.502764e-7,0.005611912,0.9891168,0.00431353,0.00033572],"study_design_scores_gemma":[0.0005697165,0.0002956278,0.0001400141,0.00001009705,0.0001223615,0.0006102246,0.00009882297,0.00002643303,0.007150129,0.9832351,0.007591102,0.0001503253],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9893813,0.00138756,0.004051197,0.001062048,0.001959789,0.0001510781,0.000005018026,0.00003029853,0.00197173],"genre_scores_gemma":[0.9991432,0.0001147211,0.0001030863,0.0001232315,0.0002600902,0.000003089247,9.911597e-7,0.00003157337,0.0002200206],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009761915,"threshold_uncertainty_score":0.6834975,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01009595216472184,"score_gpt":0.2983239949131558,"score_spread":0.2882280427484339,"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."}}