{"id":"W3193537747","doi":"10.1088/1751-8121/ac1fc2","title":"Knot probabilities in equilateral random polygons","year":2021,"lang":"en","type":"article","venue":"Journal of Physics A Mathematical and Theoretical","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Leverhulme Trust","keywords":"Knot (papermaking); Unknot; Mathematics; Combinatorics; Polygon (computer graphics); Exponential function; Monte Carlo method; Scaling; Equilateral triangle; Geometry; Mathematical analysis; Statistics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0007328961,0.0001503574,0.0006449552,0.0000796969,0.00003426194,0.00004253496,0.0001243588,0.00009300726,0.0006550862],"category_scores_gemma":[0.00193263,0.0001022352,0.0001760033,0.0002522974,0.000553941,0.00009334899,0.0001090456,0.0003526163,0.000009072252],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002155355,"about_ca_system_score_gemma":0.00008549714,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.949483e-7,"about_ca_topic_score_gemma":3.252592e-7,"domain_scores_codex":[0.9984574,0.0001701997,0.0006765265,0.0001373463,0.0002793024,0.0002791697],"domain_scores_gemma":[0.9973603,0.002045157,0.0001511758,0.0001572142,0.0001426676,0.0001434981],"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":[0.0000722326,0.0005216086,0.0001168633,0.0001567267,0.00004532762,0.0001125492,0.0007163311,7.986874e-7,0.0001679143,0.9968836,0.00006216913,0.001143821],"study_design_scores_gemma":[0.001494369,0.0001352693,0.00006026856,0.0001400171,0.00006147705,0.0005674404,0.0003938947,0.0003121501,0.001346745,0.9953443,0.00003100829,0.0001130496],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9798307,0.0001818946,0.01438189,0.001909829,0.00009076277,0.00009398498,0.000002996879,0.00000988293,0.003498053],"genre_scores_gemma":[0.9878522,0.00002226975,0.01169499,0.00008166333,0.0001790135,0.000003009803,3.830292e-7,0.00001452304,0.0001519966],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008021448,"threshold_uncertainty_score":0.7172735,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02183716064805027,"score_gpt":0.2861754808709032,"score_spread":0.2643383202228529,"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."}}