{"id":"W3099993265","doi":"","title":"Alexander Invariants for Virtual Knots","year":2016,"lang":"en","type":"article","venue":"","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Alexander polynomial; Mathematics; Bracket polynomial; HOMFLY polynomial; Knot polynomial; Jones polynomial; Normalization (sociology); Combinatorics; Polynomial; Knot (papermaking); Algebra over a field; Pure mathematics; Knot invariant; Discrete mathematics; Alternating polynomial; Knot theory; Matrix polynomial; Square-free polynomial; Mathematical analysis","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000159397,0.00007154428,0.0001287849,0.00007527197,0.0000370728,0.000005820154,0.000102477,0.00006828511,0.004109718],"category_scores_gemma":[0.0009227662,0.00003827766,0.00004764964,0.00008795327,0.00003927833,0.00005277323,0.00003606645,0.0000204274,0.0002139097],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001176327,"about_ca_system_score_gemma":0.00002179974,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003415536,"about_ca_topic_score_gemma":0.000008521,"domain_scores_codex":[0.9994373,0.00001376263,0.0001404657,0.0001371145,0.00007086656,0.0002004582],"domain_scores_gemma":[0.9986901,0.001023148,0.00003694506,0.0001606623,0.000037687,0.00005145249],"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":[0.00001139178,0.00004390143,0.0002807998,0.000005882516,0.00002199019,8.848239e-7,0.00003143374,1.915316e-8,0.0005046168,0.8859518,0.0961517,0.01699553],"study_design_scores_gemma":[0.002273612,0.0002522298,0.001578781,0.00001511936,0.00002478845,0.00001453682,0.00011869,0.00001852258,0.003910659,0.9512575,0.04032703,0.00020849],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1287759,0.0000175506,0.8279058,0.00369281,0.0004691907,0.0003126075,0.00001370487,0.0001508288,0.03866169],"genre_scores_gemma":[0.8831054,0.000003453137,0.008696415,0.0003184353,0.0001123488,0.00001960058,5.567905e-7,0.0000124019,0.1077314],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8192093,"threshold_uncertainty_score":0.9968007,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08521962376862065,"score_gpt":0.3333386617931794,"score_spread":0.2481190380245588,"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."}}