{"id":"W3083259271","doi":"10.1002/rsa.20253","title":"Short cycle distribution in random regular graphs recursively generated by pegging","year":2008,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Markov chain; Random graph; struct; Mathematics; Poisson distribution; Limit (mathematics); Type (biology); Coupling (piping); Distribution (mathematics); Joint probability distribution; Combinatorics; Homogeneous; Discrete mathematics; Computer science; Graph; Statistics","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":[0.0002484628,0.000250215,0.0005294066,0.00005616291,0.0002562227,0.00004123859,0.0001176513,0.0001375921,0.00002489359],"category_scores_gemma":[0.0005407322,0.0002012438,0.00007505251,0.0002421374,0.0001048271,0.00008169437,0.00003989239,0.0002245876,7.517577e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000330444,"about_ca_system_score_gemma":0.00003100156,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003678721,"about_ca_topic_score_gemma":0.000005513341,"domain_scores_codex":[0.9984843,0.0000745116,0.0004133507,0.0003699937,0.0002879187,0.0003699566],"domain_scores_gemma":[0.9990981,0.0004373969,0.0000820342,0.0001585633,0.00008565785,0.0001383064],"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":[0.006415517,0.0005546125,0.0006320535,0.0007792854,0.0005514525,0.0008440833,0.00312487,0.0003015516,0.008871009,0.6990654,0.02432738,0.2545328],"study_design_scores_gemma":[0.01595442,0.0001372512,0.0007886817,0.00009533597,0.0001043305,0.0002935943,0.0001611864,0.06051792,0.003304882,0.9175164,0.0005344939,0.0005914725],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3339309,0.001443303,0.6633406,0.0000998282,0.000211057,0.0004699047,0.0003559858,0.00007189676,0.00007655223],"genre_scores_gemma":[0.9862903,0.0005538675,0.01274593,0.00004494248,0.00008468882,0.0000356206,0.000163898,0.00002789713,0.00005283786],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6523594,"threshold_uncertainty_score":0.8206483,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02014204919939748,"score_gpt":0.2733798636874811,"score_spread":0.2532378144880836,"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."}}