{"id":"W2020750964","doi":"10.4153/cmb-2008-019-x","title":"Consecutive Large Gaps in Sequences Defined by Multiplicative Constraints","year":2008,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Multiplicative function; Multiplication (music); Class (philosophy); Complex multiplication; Pure mathematics; Arithmetic; Combinatorics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001080169,0.0002955765,0.0005714069,0.0002375262,0.0002240077,0.00003075225,0.0004690926,0.0002071996,0.02867064],"category_scores_gemma":[0.004659308,0.0002733384,0.0001106958,0.0003522481,0.001269323,0.00003886937,0.00006817356,0.0004931076,0.009524165],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004401499,"about_ca_system_score_gemma":0.0006307609,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001314439,"about_ca_topic_score_gemma":0.002992898,"domain_scores_codex":[0.9971632,0.0003004674,0.0005889285,0.0004681259,0.0004134395,0.001065808],"domain_scores_gemma":[0.9957888,0.002623972,0.0001094953,0.0004728377,0.0001443846,0.0008604937],"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":[0.00002893086,0.0004210216,0.001880652,0.000162816,0.00009400234,0.000893496,0.003511996,3.452667e-7,0.0001823281,0.8177812,0.1749152,0.0001280329],"study_design_scores_gemma":[0.002432934,0.0001062923,0.0003381762,0.0003768171,0.00004240766,0.0006177998,0.004851028,0.0005493868,0.001086942,0.951069,0.03757014,0.0009590666],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.702252,0.0002260535,0.006565019,0.01233685,0.00006069722,0.002015234,0.0008049555,0.0001890182,0.2755501],"genre_scores_gemma":[0.9867859,0.00001657945,0.005275209,0.0006784204,0.00002495172,0.0001211071,0.00002084734,0.00004931489,0.007027684],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2845339,"threshold_uncertainty_score":0.9999719,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04239424258879437,"score_gpt":0.3083432227922416,"score_spread":0.2659489802034472,"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."}}