{"id":"W2759917467","doi":"10.1016/j.jnt.2018.06.018","title":"On a function introduced by Erdös and Nicolas","year":2018,"lang":"en","type":"preprint","venue":"Journal of Number Theory","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Arithmetic function; Combinatorics; Mathematics; Pythagorean triple; Function (biology); Perimeter; Polynomial; Pythagorean theorem; Discrete mathematics; Mathematical analysis; Geometry","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003476577,0.0003396139,0.0007299472,0.0001363116,0.0001271441,0.0000615428,0.0003500244,0.0003716968,0.004524637],"category_scores_gemma":[0.002109657,0.0002754104,0.0002664217,0.0000535558,0.0002236976,0.0001002905,0.0001944786,0.001161211,0.0001617699],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001498102,"about_ca_system_score_gemma":0.0001125853,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":3.112237e-7,"about_ca_topic_score_gemma":6.417101e-7,"domain_scores_codex":[0.9976736,0.0005899175,0.0008236009,0.0002553663,0.0004492793,0.000208287],"domain_scores_gemma":[0.9955348,0.002047708,0.001465238,0.0005236522,0.0002703876,0.0001582573],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001296979,0.0006125033,0.000007409533,0.0006699542,0.0006091123,0.00002631837,0.002188024,0.000002579268,0.0003086989,0.2650748,0.7270513,0.002152323],"study_design_scores_gemma":[0.0005269503,0.0003111801,0.000006541891,0.0007670292,0.0003425285,0.0001992002,0.0001693827,0.00001109073,0.000272153,0.9665816,0.03055918,0.0002531772],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9286859,0.0005091344,0.02003982,0.0003075024,0.004112017,0.0004361327,0.0001398088,0.00008306523,0.04568661],"genre_scores_gemma":[0.9294973,0.0002528862,0.02459546,0.001463926,0.007099535,0.00004449792,0.0000412807,0.0004238035,0.03658132],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7015068,"threshold_uncertainty_score":0.9999698,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02569833410895958,"score_gpt":0.2956654092227854,"score_spread":0.2699670751138258,"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."}}