{"id":"W3106216040","doi":"","title":"Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups","year":2008,"lang":"en","type":"article","venue":"","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":121,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Braid group; Artin group; Braid; Combinatorics; Graph; Braid theory; Embedding; Artin L-function; Euler characteristic; Group (periodic table); Coxeter graph; Pure mathematics; Coxeter group; Conductor; Geometry; Voltage graph; Line graph; Computer science","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":[0.0005431416,0.00028801,0.0006967033,0.0004188018,0.0001142138,0.00001714244,0.0001773861,0.0002179587,0.0004196031],"category_scores_gemma":[0.0004073311,0.0002406622,0.00008673524,0.0008708168,0.0004410151,0.0002142943,0.0001761428,0.0002483748,0.00001182498],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001923414,"about_ca_system_score_gemma":0.00002400889,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001567474,"about_ca_topic_score_gemma":0.0002253244,"domain_scores_codex":[0.9980343,0.0001079409,0.0006623346,0.0004608571,0.0002634081,0.0004711782],"domain_scores_gemma":[0.9982724,0.0009663687,0.0002227954,0.0003167257,0.00006059056,0.0001611617],"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":[0.0001990471,0.001107995,0.2845111,0.000600484,0.000209548,0.0002736311,0.009478692,0.000004855284,0.0112414,0.6851392,0.006051057,0.00118292],"study_design_scores_gemma":[0.006030947,0.0007269403,0.1991768,0.0001112312,0.00009931738,0.0008583108,0.002392846,0.0003317616,0.01304972,0.775606,0.0005732404,0.001042939],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9930826,0.0004659502,0.001570076,0.000458018,0.00008687547,0.0002989773,0.000006541564,0.00008780185,0.003943132],"genre_scores_gemma":[0.9914041,0.000174355,0.00686712,0.0001630431,0.00003644256,0.000006774391,0.000004111525,0.00003141553,0.0013127],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09046672,"threshold_uncertainty_score":0.981392,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02395878684525726,"score_gpt":0.2609777128763016,"score_spread":0.2370189260310443,"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."}}