{"id":"W4386477833","doi":"10.1017/s0305004123000427","title":"Dirichlet law for factorisation of integers, polynomials and permutations","year":2023,"lang":"en","type":"article","venue":"Mathematical Proceedings of the Cambridge Philosophical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Dirichlet distribution; Integer (computer science); Combinatorics; Factorization; Distribution (mathematics); Dirichlet series; Pure mathematics; Mathematical analysis; Algorithm; Computer science","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":[0.001506275,0.0001865939,0.0005199881,0.00004083653,0.0001894183,0.00003357953,0.0003922425,0.0001712182,0.00001747924],"category_scores_gemma":[0.002430984,0.0001274795,0.0004361544,0.0004581034,0.0008250538,0.0001323915,0.0003086163,0.0002461018,0.000006795989],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006022301,"about_ca_system_score_gemma":0.0000293597,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004442282,"about_ca_topic_score_gemma":1.510793e-7,"domain_scores_codex":[0.9982101,0.00001985955,0.0006405329,0.0002658824,0.0005536003,0.0003100047],"domain_scores_gemma":[0.9970217,0.001987946,0.000304379,0.0001840885,0.0003883535,0.000113558],"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":[0.0000272402,0.0001102516,0.000132241,0.001515706,0.0001172749,5.667696e-8,0.0008601663,5.377568e-7,0.01080701,0.980547,0.005848633,0.00003391864],"study_design_scores_gemma":[0.0004184522,0.00006249491,0.0001608174,0.0001489396,0.0001333823,0.000004419685,0.0008196974,0.003634131,0.009526139,0.9848917,0.00007081571,0.0001290169],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9624859,0.00002244414,0.003279005,0.02112944,0.00006739371,0.001630421,0.0001691667,0.0001602282,0.01105601],"genre_scores_gemma":[0.9956391,0.000006662282,0.003596399,0.00009642453,0.0001276692,0.00007402698,0.000003790172,0.00004003481,0.0004159144],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03315319,"threshold_uncertainty_score":0.5198464,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08526529668511318,"score_gpt":0.349296180816735,"score_spread":0.2640308841316218,"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."}}