{"id":"W2247384693","doi":"10.4153/cmb-2015-068-0","title":"Uncertainty Principles on Weighted Spheres, Balls, and Simplexes","year":2015,"lang":"en","type":"preprint","venue":"Canadian Mathematical Bulletin","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Unit sphere; Simplex; SPHERES; Reflection group; Mathematics; Spherical harmonics; Spherical mean; Weight function; Pure mathematics; Uncertainty principle; Invariant (physics); Constructive; Harmonic function; Mathematical analysis; Laplace transform; Combinatorics; Mathematical physics; Physics; Quantum mechanics; Computer science; Coxeter group","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":["insufficient_payload"],"category_scores_codex":[0.002188857,0.0009211464,0.001818384,0.0003360944,0.0002126831,0.000318954,0.0007553867,0.00086109,0.0232149],"category_scores_gemma":[0.003097462,0.0007139925,0.0004223533,0.0002035424,0.0003470918,0.00002565529,0.0003515979,0.00129333,0.002136508],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004304031,"about_ca_system_score_gemma":0.0007173772,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001988861,"about_ca_topic_score_gemma":0.008481422,"domain_scores_codex":[0.995297,0.0004244934,0.00134497,0.001039981,0.0008400838,0.001053495],"domain_scores_gemma":[0.9938777,0.002030553,0.0003339582,0.001357515,0.0002915959,0.002108691],"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":[0.00002901224,0.0002754672,0.00001340557,0.002742358,0.0003672559,0.000114036,0.0004611379,0.00004046866,0.000002965769,0.9393169,0.05416447,0.002472551],"study_design_scores_gemma":[0.0003706723,0.00007522211,0.00000846182,0.0008951079,0.0003588557,0.00002480096,0.0002128226,0.005786853,0.00003339351,0.8695962,0.1218864,0.0007511887],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2930719,0.001667773,0.0311763,0.03126148,0.0006519259,0.006368929,0.001727707,0.00100419,0.6330698],"genre_scores_gemma":[0.4958816,0.0003490314,0.4564934,0.004326406,0.001439595,0.001097411,0.0005299617,0.0009095995,0.03897293],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5940968,"threshold_uncertainty_score":0.9995311,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1080830505259931,"score_gpt":0.3320140920255371,"score_spread":0.223931041499544,"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."}}