{"id":"W4206224552","doi":"10.46298/hrj.2022.8343","title":"A variant of the Hardy-Ramanujan theorem","year":2022,"lang":"en","type":"article","venue":"Hardy-Ramanujan Journal","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; Queen's University","funders":"","keywords":"Ramanujan's sum; Combinatorics; Conjecture; Omega; Mathematics; Order (exchange); Constant (computer programming); Prime (order theory); Function (biology); Discrete mathematics; Physics","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":[0.003309534,0.0009405508,0.0008890091,0.001696929,0.001863407,0.002488248,0.002233646,0.0008320081,0.007992341],"category_scores_gemma":[0.007901245,0.0003500336,0.001267085,0.001703823,0.004849083,0.007584028,0.00383337,0.003276988,0.002238043],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001903653,"about_ca_system_score_gemma":0.001225456,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002188693,"about_ca_topic_score_gemma":0.001611475,"domain_scores_codex":[0.9980705,0.0004323834,0.00009387652,0.0006070206,0.0005511786,0.0002449678],"domain_scores_gemma":[0.9970866,0.001283811,0.0002391343,0.0006876347,0.0004596037,0.0002431755],"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":[0.00001266813,0.000007171437,0.0002338584,0.00002297365,0.000005598698,0.00002361866,0.0001035459,0.0004997057,0.0004413343,0.9903001,0.001915839,0.006433596],"study_design_scores_gemma":[0.000008369295,0.00003268924,0.0004456176,0.00001460037,0.000009561034,0.0001886583,0.00006451443,0.008520739,0.0009505271,0.973345,0.01639974,0.00001989759],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06603458,0.002232658,0.7625034,0.004570748,0.001715055,0.0001322692,0.0006898264,0.00035133,0.1617702],"genre_scores_gemma":[0.7059562,0.002476131,0.197954,0.003204231,0.002543957,0.0004750915,0.0005587715,0.0004836004,0.086348],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007992341,"threshold_uncertainty_score":0.02673697,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05151100392345132,"score_gpt":0.3163311736209863,"score_spread":0.264820169697535,"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."}}