{"id":"W3202874536","doi":"10.37236/10781","title":"Density Maximizers of Layered Permutations","year":2022,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"Masarykova Univerzita; Grantová Agentura České Republiky; Leverhulme Trust","keywords":"Permutation (music); Bounded function; Combinatorics; Mathematics; Infinity; Sigma; Conjecture; Order (exchange); Cyclic permutation; Random permutation; Complement (music); Discrete mathematics; Symmetric group; Physics; Mathematical analysis; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001236493,0.0006150954,0.0008790285,0.001494545,0.001176805,0.001806055,0.001123693,0.001073039,0.00422733],"category_scores_gemma":[0.01545652,0.00075435,0.0008798623,0.0008741932,0.002317581,0.003413988,0.002424198,0.001379514,0.0006969718],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001341996,"about_ca_system_score_gemma":0.0006395911,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001253031,"about_ca_topic_score_gemma":0.001247606,"domain_scores_codex":[0.9986128,0.0003927928,0.00006674028,0.0002504892,0.0003652916,0.0003118179],"domain_scores_gemma":[0.9934306,0.003936979,0.0006687368,0.0006710892,0.0005661953,0.0007264388],"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":[0.0001587553,0.00005644185,0.002686538,0.0001431649,0.00004173888,0.0003548196,0.0004648222,0.02798624,0.008411138,0.9407197,0.002050234,0.01692641],"study_design_scores_gemma":[0.00003523805,0.00008885515,0.002308078,0.00005490745,0.00002855883,0.0005004797,0.0001833931,0.1351788,0.004516812,0.8536338,0.003421295,0.00004979604],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.673963,0.0009067998,0.2788772,0.0007947387,0.00007156503,0.0001143547,0.0005358121,0.0006190677,0.04411745],"genre_scores_gemma":[0.9611045,0.0005394868,0.0300924,0.0002066498,0.00009110154,0.000233393,0.0003372203,0.0001350098,0.007260188],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00422733,"threshold_uncertainty_score":0.01414186,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02690973644774888,"score_gpt":0.3051353618479515,"score_spread":0.2782256254002027,"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."}}