{"id":"W7110327960","doi":"10.4230/lipics.approx/random.2025.42","title":"On the Spectral Expansion of Monotone Subsets of the Hypercube","year":2025,"lang":"en","type":"article","venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Monotone polygon; Upper and lower bounds; Hypercube; Spectral properties; Spectral gap; Mixing (physics)","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001508175,0.0005482255,0.0006548142,0.001249372,0.0007097999,0.001187797,0.001076968,0.0008262305,0.005078454],"category_scores_gemma":[0.0106667,0.0004288067,0.0006471684,0.0008099623,0.002191451,0.003233875,0.001953707,0.001687819,0.0004287008],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001057423,"about_ca_system_score_gemma":0.000346365,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009042504,"about_ca_topic_score_gemma":0.0006813584,"domain_scores_codex":[0.9990398,0.0004530064,0.00002540763,0.0001633092,0.0001816875,0.0001367522],"domain_scores_gemma":[0.9920124,0.006329333,0.0005500242,0.0003731153,0.0003556885,0.0003793716],"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":[0.000122185,0.00003934489,0.00122637,0.000101718,0.00001847512,0.0001361757,0.00033171,0.03564504,0.005367027,0.9467452,0.001326456,0.008940286],"study_design_scores_gemma":[0.00002580858,0.00005544411,0.0007686389,0.00003906501,0.00000930368,0.0001278454,0.0001264307,0.3083591,0.00187101,0.687232,0.001369414,0.00001589087],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4427263,0.0008905871,0.5285636,0.001501754,0.00008606229,0.00008659619,0.0003583484,0.0002067062,0.02558001],"genre_scores_gemma":[0.9352582,0.0006503459,0.05821139,0.0005197158,0.0001517412,0.0002321851,0.0003834768,0.000133408,0.004459533],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005078454,"threshold_uncertainty_score":0.01698917,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03513197230663311,"score_gpt":0.3201592485512282,"score_spread":0.2850272762445951,"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."}}