{"id":"W1999225375","doi":"10.1088/1742-6596/42/1/023","title":"Eulerian graph embeddings and trails confined to lattice tubes","year":2006,"lang":"en","type":"article","venue":"Journal of Physics Conference Series","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Eulerian path; Combinatorics; Embedding; Mathematics; Exponent; Crossing number (knot theory); Lattice (music); Polygon (computer graphics); Upper and lower bounds; Discrete mathematics; Graph embedding; Graph; Computer science; Pure mathematics; Physics; Mathematical analysis; Knot (papermaking)","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":[0.0002538951,0.0002239246,0.0005405846,0.00008273796,0.0000930305,0.0001436598,0.0002379714,0.00006396187,0.00003039814],"category_scores_gemma":[0.0003243913,0.0001943886,0.00009309012,0.0002105849,0.0001253246,0.0006005978,0.00006071279,0.00021283,0.000004655934],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002645369,"about_ca_system_score_gemma":0.00008889149,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007188456,"about_ca_topic_score_gemma":0.00001218343,"domain_scores_codex":[0.9986264,0.00004479559,0.0005982879,0.000140344,0.0003471635,0.0002430449],"domain_scores_gemma":[0.998432,0.0003031831,0.000355473,0.0002009018,0.000582213,0.000126237],"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":[0.00006306698,0.0001132925,0.00005979657,0.0001128833,0.00004247515,0.00001337345,0.001670386,0.000008582118,0.02211598,0.9723843,0.0004920649,0.002923779],"study_design_scores_gemma":[0.0004671765,0.0002914382,0.0001356696,0.0001758307,0.00006779039,0.00006009988,0.0006688571,0.00001514683,0.09422465,0.9028433,0.0008493073,0.0002007442],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8846914,0.0000474323,0.1109578,0.0008436644,0.0004907757,0.0002390973,0.00001147662,0.00005204563,0.002666228],"genre_scores_gemma":[0.9391245,0.00001741214,0.06009207,0.00004568914,0.0004042538,0.00000462349,7.252498e-7,0.00003152858,0.0002791462],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07210868,"threshold_uncertainty_score":0.7926937,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03138494935216664,"score_gpt":0.29118648693528,"score_spread":0.2598015375831134,"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."}}