{"id":"W4416331397","doi":"10.1090/tran/9525","title":"Order-detection, representation-detection, and applications to cable knots","year":2025,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Tuple; Boundary (topology); Knot (papermaking); Torus; Manifold (fluid mechanics)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001320665,0.001003768,0.0007608453,0.003723318,0.00145111,0.003990127,0.001827712,0.001495463,0.008556942],"category_scores_gemma":[0.007802559,0.0006816189,0.001686607,0.002850726,0.003288198,0.006414397,0.003594052,0.003072747,0.002387563],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001995193,"about_ca_system_score_gemma":0.0008844955,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003531609,"about_ca_topic_score_gemma":0.003369836,"domain_scores_codex":[0.9983144,0.0002647357,0.0001393837,0.0005059268,0.0005758889,0.0001997174],"domain_scores_gemma":[0.9970443,0.0009559964,0.0003668156,0.000661393,0.0007748842,0.0001966687],"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":[0.00007191895,0.00003961245,0.001841876,0.0001576748,0.00001230567,0.000217798,0.0005902774,0.008767173,0.00295977,0.9076699,0.005423263,0.0722485],"study_design_scores_gemma":[0.00001809409,0.00006493545,0.001031483,0.000107151,0.00002544505,0.0004595279,0.0004359967,0.1001952,0.01207543,0.844745,0.04076085,0.00008096645],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02939002,0.0003680434,0.9480585,0.0004175787,0.0001807007,0.00008157697,0.0004337062,0.001866064,0.01920383],"genre_scores_gemma":[0.3964414,0.0009476807,0.5770852,0.0002694374,0.0003115996,0.0001609838,0.001615099,0.001442476,0.02172619],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008556942,"threshold_uncertainty_score":0.02862579,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01860569449402354,"score_gpt":0.3142213991993975,"score_spread":0.2956157047053739,"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."}}