{"id":"W4411393991","doi":"10.1007/s00208-025-03197-4","title":"Fourier dimension of constant rank hypersurfaces","year":2025,"lang":"de","type":"article","venue":"Mathematische Annalen","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Dimension (graph theory); Constant (computer programming); Rank (graph theory); Fourier transform; Mathematical analysis; Fourier analysis; Pure mathematics; Combinatorics","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":[0.001632323,0.0005239713,0.001540501,0.0006456436,0.0001917864,0.0001095798,0.0005614739,0.0004105703,0.001770039],"category_scores_gemma":[0.001292324,0.0004264417,0.0006402282,0.001980787,0.000263205,0.0001867353,0.0003083532,0.0004384645,0.0005408164],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004251805,"about_ca_system_score_gemma":0.0001993477,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002323995,"about_ca_topic_score_gemma":0.000008822984,"domain_scores_codex":[0.9964074,0.0002300714,0.001426509,0.0005597459,0.00082318,0.0005530838],"domain_scores_gemma":[0.9962251,0.001074417,0.0008023386,0.001223398,0.0005374411,0.0001372772],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0003409458,0.003203696,0.003162856,0.009630395,0.01080782,0.00008604551,0.006680176,0.0001144823,0.006926784,0.4977808,0.4334965,0.02776952],"study_design_scores_gemma":[0.008894159,0.0008703289,0.001712306,0.01360896,0.0219973,0.00003740153,0.01240911,0.03239548,0.04970806,0.3447182,0.5099902,0.003658502],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6014046,0.1628279,0.04495753,0.006208165,0.002679414,0.002569466,0.0003630671,0.0002819845,0.1787079],"genre_scores_gemma":[0.9072783,0.002867978,0.04548928,0.0004265276,0.0002216368,0.00004284822,0.00004673519,0.00009879794,0.04352789],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3058737,"threshold_uncertainty_score":0.9998187,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02565651426240714,"score_gpt":0.2873128500653614,"score_spread":0.2616563358029543,"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."}}