{"id":"W2292684665","doi":"10.37236/1154","title":"On the Proof of a Theorem of Pálfy","year":2006,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Lethbridge","keywords":"Combinatorics; Mathematics; Isomorphism (crystallography); Order (exchange); Group (periodic table); Vertex (graph theory); Cayley graph; Automorphism; Center (category theory); Discrete mathematics; Graph; Crystallography","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005595328,0.0001475779,0.0003903836,0.0001393464,0.00008735625,0.00001370762,0.001063191,0.00006932462,0.00005663453],"category_scores_gemma":[0.001068079,0.00007286493,0.0002233907,0.0005464567,0.0002791067,0.00005562975,0.00007486775,0.0009590028,0.000002807825],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001795366,"about_ca_system_score_gemma":0.0003946682,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000560937,"about_ca_topic_score_gemma":0.00000363978,"domain_scores_codex":[0.9972522,0.0005696528,0.0007137344,0.00007837985,0.0009228248,0.0004632322],"domain_scores_gemma":[0.9941496,0.003871328,0.0009219452,0.0005321575,0.0004948116,0.00003017781],"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":[0.0002479131,0.0004649613,0.00003816493,0.00004736395,0.0001024567,0.000002555623,0.0003084477,0.00003120942,0.001164951,0.996062,0.001398054,0.0001319637],"study_design_scores_gemma":[0.0006249532,0.001248911,0.00003951552,0.00007488541,0.00005860031,0.00005215621,0.0001923014,0.00007212621,0.04373785,0.9535902,0.0002433678,0.000065092],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9840893,0.001161115,0.00309272,0.001179768,0.0001158635,0.0003353526,0.000002332531,0.000007780927,0.01001578],"genre_scores_gemma":[0.9992802,0.00005269696,0.00001605234,0.00001936263,0.00005893361,0.000003525181,2.251885e-7,0.00002901506,0.0005399852],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0425729,"threshold_uncertainty_score":0.4166443,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02264672275225795,"score_gpt":0.2867337044146727,"score_spread":0.2640869816624147,"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."}}