{"id":"W4416935886","doi":"10.48550/arxiv.2511.21868","title":"A Combinatorial Characterization of Constant Mixing Time","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mixing (physics); Characterization (materials science); Bipartite graph; Constant (computer programming); Logarithm; Spectral radius","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":[0.002657137,0.001081523,0.0009514223,0.002219629,0.001503673,0.002638932,0.002649229,0.002199215,0.008191001],"category_scores_gemma":[0.03240477,0.000744413,0.001097137,0.001876165,0.004869679,0.0082178,0.002780918,0.003768008,0.0008216253],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00203804,"about_ca_system_score_gemma":0.0008633318,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005636364,"about_ca_topic_score_gemma":0.0004862579,"domain_scores_codex":[0.9973745,0.0008902252,0.00009177908,0.0007964349,0.0005246936,0.0003222974],"domain_scores_gemma":[0.9652102,0.02492984,0.003145231,0.003273496,0.001673149,0.001768114],"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":[0.0001473361,0.00006898391,0.00133133,0.0001371604,0.00002944391,0.0001010875,0.0002132404,0.02019655,0.006586154,0.9620806,0.001612091,0.007496103],"study_design_scores_gemma":[0.00002944454,0.00006212116,0.0005994542,0.00002811134,0.00002297107,0.0002032851,0.0000608489,0.1614693,0.003349019,0.8322757,0.001860146,0.00003960477],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.192314,0.0006076926,0.7781471,0.001712488,0.0001142393,0.0001197962,0.0005667527,0.0005753742,0.0258425],"genre_scores_gemma":[0.9368355,0.0004123019,0.05711322,0.000540403,0.0002678357,0.000261833,0.0004381102,0.0003559254,0.003774908],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008191001,"threshold_uncertainty_score":0.02740157,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05610327662950312,"score_gpt":0.3213437132052003,"score_spread":0.2652404365756972,"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."}}