{"id":"W4386561736","doi":"10.48550/arxiv.2309.03068","title":"On the Fourier decay of multiplicative convolutions","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; European Commission","keywords":"Multiplicative function; Exponent; Convolution (computer science); Fourier transform; Physics; Combinatorics; Energy (signal processing); Constant (computer programming); Mathematics; Mathematical analysis; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0003657349,0.0002380996,0.0003162448,0.0001614395,0.0002756324,0.00001099441,0.000839872,0.0002560186,0.00011646],"category_scores_gemma":[0.0004183847,0.0001797669,0.0003125118,0.0003060308,0.0004396423,0.00002906836,0.0009997141,0.0005957542,0.00003592426],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007390705,"about_ca_system_score_gemma":0.00006378382,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003723466,"about_ca_topic_score_gemma":0.0000271396,"domain_scores_codex":[0.9988018,0.0002055598,0.0002064809,0.0004773823,0.00009769704,0.0002110905],"domain_scores_gemma":[0.9957866,0.002291226,0.0003342836,0.001360258,0.0001645442,0.00006305258],"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":[0.00004079398,0.00005060138,0.0003425292,0.00006127914,0.0002364343,0.00001522812,0.0006619022,0.003814218,0.000009815784,0.992568,0.002178836,0.00002041289],"study_design_scores_gemma":[0.0002110774,0.00002686392,0.0006959033,0.0001108968,0.0001529035,6.011102e-7,0.0004149294,0.007394177,0.0002583233,0.9903854,0.0001552916,0.0001936675],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9634839,0.00001933314,0.02283853,0.0001828251,0.0005517093,0.0006567221,0.0002099421,0.0001765617,0.01188046],"genre_scores_gemma":[0.9953665,0.00005790769,0.0003433647,0.00004400187,0.00004502121,0.000002943817,0.000007755893,0.00003355526,0.004098959],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03188257,"threshold_uncertainty_score":0.7330682,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2046580449944602,"score_gpt":0.2418625497682997,"score_spread":0.03720450477383949,"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."}}