{"id":"W2025385167","doi":"10.4153/cmb-2010-076-4","title":"Non-Right-Orderable 3-Manifold Groups","year":2010,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Science Foundation","keywords":"Mathematics; 3-manifold; Manifold (fluid mechanics); Pure mathematics; Combinatorics","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0005795441,0.0002762854,0.0004505604,0.0003340559,0.0002437097,0.00007840282,0.0004830278,0.000326634,0.1391421],"category_scores_gemma":[0.001580695,0.0002387961,0.0001370196,0.0003415912,0.0001475941,0.00003421317,0.00005824173,0.0006537547,0.0271104],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006454898,"about_ca_system_score_gemma":0.0002083087,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008549255,"about_ca_topic_score_gemma":0.005777919,"domain_scores_codex":[0.9980173,0.00003014352,0.0004549197,0.0003740234,0.0002520357,0.0008715763],"domain_scores_gemma":[0.9975668,0.0006573383,0.00009062603,0.0006658765,0.00008897176,0.0009304197],"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":[0.000001909335,0.0000706104,0.00007938498,0.00008064703,0.00002262224,0.0000931988,0.0001284223,8.982831e-8,0.0001103598,0.8826572,0.1164825,0.0002730363],"study_design_scores_gemma":[0.0003504794,0.00004221298,0.0001878659,0.00002468301,0.00003478938,0.0001544456,0.000114492,0.00007958217,0.0002618704,0.8018515,0.1965601,0.0003380029],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6554654,0.00002663614,0.002659321,0.01406353,0.0006244718,0.0005632588,0.00002005997,0.0001730816,0.3264042],"genre_scores_gemma":[0.9671277,0.000001999445,0.01179749,0.001239819,0.0002906232,0.00005053926,0.000006317141,0.0000616742,0.01942382],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3116623,"threshold_uncertainty_score":0.9737821,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01278774299610244,"score_gpt":0.242821347348115,"score_spread":0.2300336043520125,"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."}}