{"id":"W2036216905","doi":"10.1142/s0218216515500091","title":"Alexander invariants for virtual knots","year":2015,"lang":"en","type":"article","venue":"Journal of Knot Theory and Its Ramifications","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Alexander polynomial; HOMFLY polynomial; Bracket polynomial; Knot polynomial; Quantum invariant; Jones polynomial; Skein relation; Knot theory","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":[0.001816619,0.00008227259,0.0002109104,0.0001864148,0.00009646516,0.00002188382,0.0001511396,0.00007566025,0.000106185],"category_scores_gemma":[0.004890685,0.00006223164,0.00006621986,0.0001748265,0.00006184055,0.0001608364,0.0000223897,0.0001263004,0.00001188056],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001799254,"about_ca_system_score_gemma":0.0001213363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.305528e-7,"about_ca_topic_score_gemma":5.529782e-7,"domain_scores_codex":[0.9991402,0.0001495606,0.0003739669,0.00008557939,0.000120062,0.0001306393],"domain_scores_gemma":[0.9976099,0.00146079,0.0002947059,0.0001171962,0.0003597104,0.0001577669],"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":[0.0001016014,0.0001312759,0.00002761921,0.00001123739,0.00005978301,0.000001487307,0.000821576,0.000005592535,0.0002521784,0.9876925,0.00818759,0.00270761],"study_design_scores_gemma":[0.00136587,0.0003826066,0.0006366359,0.00002263457,0.0001209977,0.0001760661,0.001986773,0.000127051,0.000430712,0.979514,0.0151268,0.0001098244],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6728654,0.002134799,0.316054,0.003321088,0.00101304,0.0004159494,0.00003356578,0.00003277692,0.004129405],"genre_scores_gemma":[0.9922537,0.00005018925,0.002424584,0.000148102,0.0002284846,0.00000539439,0.00000160015,0.00001117842,0.004876769],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3193883,"threshold_uncertainty_score":0.585496,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1168155498143271,"score_gpt":0.3544310510552978,"score_spread":0.2376155012409706,"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."}}