{"id":"W2053044507","doi":"10.1007/s10910-008-9364-9","title":"Thoughts on lattice knot statistics","year":2008,"lang":"en","type":"article","venue":"Journal of Mathematical Chemistry","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Knot (papermaking); Lattice (music); Mathematics; Conjecture; Geometry; Combinatorics; Monte Carlo method; Physics; Statistics; Engineering","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004435008,0.0001824747,0.0005197544,0.00006727775,0.00008408559,0.00001264122,0.0003039163,0.000152422,0.001039864],"category_scores_gemma":[0.004029876,0.0001327035,0.0001528153,0.0001918276,0.0001682692,0.00005465939,0.0000438383,0.0004936376,0.0001135127],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005351123,"about_ca_system_score_gemma":0.00009392008,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":1.350834e-7,"about_ca_topic_score_gemma":3.825784e-8,"domain_scores_codex":[0.998229,0.00003836741,0.0007692591,0.0001249732,0.0005724755,0.0002659005],"domain_scores_gemma":[0.996643,0.002166894,0.0005017755,0.0002699957,0.0002087464,0.0002095696],"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":[0.0005961845,0.008451867,0.0006231686,0.004682909,0.001097178,0.006148843,0.003967123,0.00002778222,0.01139425,0.5508869,0.4080225,0.004101343],"study_design_scores_gemma":[0.001033847,0.0002106209,0.0001198984,0.0001680601,0.0001232374,0.004472116,0.0002062575,0.0000905228,0.0289095,0.9612302,0.003181708,0.0002540482],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8905257,0.000126667,0.07494731,0.0007275445,0.0002399918,0.0001051098,0.00002027525,0.00004948238,0.03325794],"genre_scores_gemma":[0.8200739,0.00005614548,0.1694362,0.0001748162,0.001391286,0.000002658714,0.00000151604,0.00004703151,0.008816395],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4103433,"threshold_uncertainty_score":0.9998733,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05798902395898645,"score_gpt":0.3134811433376261,"score_spread":0.2554921193786396,"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."}}