{"id":"W4406485023","doi":"10.48550/arxiv.2501.08835","title":"Relative knot probabilities in confined lattice polygons","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Knot (papermaking); Lattice (music); Combinatorics; Mathematics; Geometry; Physics; Materials 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009081487,0.0003735409,0.0008817805,0.001225721,0.0009382935,0.001854759,0.001525925,0.0009180602,0.002762103],"category_scores_gemma":[0.006101713,0.0005867262,0.0006879148,0.000781136,0.002561839,0.003530459,0.001429783,0.001117082,0.0002198848],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009370307,"about_ca_system_score_gemma":0.000615894,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002481422,"about_ca_topic_score_gemma":0.001210434,"domain_scores_codex":[0.9991291,0.0002021656,0.00002909337,0.0001673836,0.000245497,0.0002268452],"domain_scores_gemma":[0.9968334,0.001693181,0.0006066684,0.0003611391,0.0001736445,0.0003320731],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002026189,0.00009828305,0.004631461,0.00009580063,0.0000419597,0.0003660214,0.0002333965,0.8669216,0.01075122,0.1126122,0.0002836793,0.003761711],"study_design_scores_gemma":[0.00002508288,0.00008762329,0.001397017,0.0000140939,0.00001481815,0.0001510283,0.0001007509,0.9467131,0.003211658,0.0478651,0.0003719221,0.00004785251],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9506044,0.000207387,0.04564003,0.0001197456,0.00001636797,0.00001575947,0.00006321118,0.0001397754,0.00319341],"genre_scores_gemma":[0.9961172,0.0001023297,0.003023813,0.00001764165,0.000008283889,0.00002259075,0.00006446435,0.00003081004,0.0006128798],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002762103,"threshold_uncertainty_score":0.00924015,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09884947354863896,"score_gpt":0.3363529626089828,"score_spread":0.2375034890603439,"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."}}