{"id":"W4405626107","doi":"10.48550/arxiv.2412.13392","title":"Hamiltonian decompositions of the wreath product of hamiltonian decomposable digraphs","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada","keywords":"Wreath product; Hamiltonian (control theory); Mathematics; Combinatorics; Product (mathematics); Geometry; Mathematical optimization","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004178769,0.000480316,0.0004005116,0.0008995214,0.0006814435,0.001228003,0.000895224,0.0005012543,0.007701909],"category_scores_gemma":[0.001955379,0.0005313845,0.0007107022,0.0006448753,0.00116642,0.00270717,0.001279928,0.001458664,0.0006260474],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005243199,"about_ca_system_score_gemma":0.0003091287,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006326884,"about_ca_topic_score_gemma":0.0009859899,"domain_scores_codex":[0.9995227,0.00008322708,0.0000287457,0.0001437795,0.0001178088,0.0001037145],"domain_scores_gemma":[0.9984139,0.0005969647,0.0002859517,0.0002554764,0.0001624748,0.0002851122],"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":[0.0001174889,0.00007070362,0.0008671891,0.0001679161,0.00003470912,0.0006764134,0.0007189469,0.01236863,0.00778059,0.9559727,0.002030114,0.01919469],"study_design_scores_gemma":[0.00003865364,0.00007106591,0.0006037112,0.00003180193,0.00002645085,0.0003967617,0.0002935992,0.04373884,0.004202381,0.942991,0.007585701,0.00002021989],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6711994,0.0005890513,0.2792253,0.0006300192,0.0001202862,0.0001368715,0.0007265543,0.0002602927,0.04711215],"genre_scores_gemma":[0.929782,0.0004618748,0.05450826,0.0002058751,0.0000970047,0.00008514705,0.000941511,0.0001107338,0.01380747],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007701909,"threshold_uncertainty_score":0.02576542,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02515933043456493,"score_gpt":0.1552243331772433,"score_spread":0.1300650027426784,"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."}}