{"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":"codex-gemma-dda1882f352a","candidate_categories":["research_integrity"],"consensus_categories":[],"category_scores_codex":[0.002413085,0.0002572827,0.0007121966,0.0002118181,0.0003425734,0.00002328538,0.001364161,0.000167956,0.0001306465],"category_scores_gemma":[0.0005647522,0.0001793479,0.0005622382,0.0002691622,0.0001496108,0.00004553411,0.0007863372,0.002979418,3.40449e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004844669,"about_ca_system_score_gemma":0.0009322861,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008379425,"about_ca_topic_score_gemma":0.000003238786,"domain_scores_codex":[0.9972125,0.000532116,0.000883631,0.0001515851,0.0008019267,0.0004182833],"domain_scores_gemma":[0.9959699,0.000902179,0.001901906,0.0006971096,0.0004677583,0.00006118103],"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":[0.0001120205,0.0001352511,0.000132127,0.0001099399,0.0005615204,0.00001000661,0.001964412,0.0005699786,0.00003379414,0.9953047,0.0009331918,0.0001330316],"study_design_scores_gemma":[0.0005787233,0.0002577136,0.0002140614,0.00004259711,0.0004192829,0.0001501364,0.0005448685,0.00007897597,0.0003238483,0.9965453,0.0006781278,0.0001663931],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9782925,0.003983245,0.01228152,0.0005412564,0.002475118,0.0003552936,0.00001798107,0.0000244263,0.00202869],"genre_scores_gemma":[0.998437,0.0009635594,0.0001167803,0.00003531131,0.0000972333,0.000005501866,0.000002860417,0.00004205214,0.0002996476],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02014458,"threshold_uncertainty_score":0.9993207,"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."}}