{"id":"W2911667065","doi":"10.4171/rmi/1219","title":"A Kakeya maximal function estimate in four dimensions using planebrushes","year":2020,"lang":"en","type":"preprint","venue":"Revista Matemática Iberoamericana","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Hausdorff dimension; Dimension (graph theory); Function (biology); Plane (geometry); Point (geometry); Set (abstract data type); Combinatorics; Discrete mathematics; Geometry; Computer science","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"],"consensus_categories":[],"category_scores_codex":[0.0006730583,0.0007699826,0.001890659,0.0004950623,0.0001747085,0.0002633605,0.0007570524,0.0003250815,0.0004755416],"category_scores_gemma":[0.001481108,0.0007573893,0.0004059277,0.001016114,0.0002860763,0.0001531031,0.001528904,0.00178712,0.0002045836],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008393349,"about_ca_system_score_gemma":0.00055922,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007072664,"about_ca_topic_score_gemma":0.00005739208,"domain_scores_codex":[0.9946874,0.0005136873,0.001383442,0.001384419,0.001018028,0.001013015],"domain_scores_gemma":[0.9964041,0.0006895512,0.0008219577,0.001450831,0.0001915484,0.0004420101],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.006309224,0.004941377,0.03620146,0.06438873,0.01505958,0.01610775,0.005930135,0.1069423,0.03753892,0.5791416,0.04871368,0.07872526],"study_design_scores_gemma":[0.00224999,0.0004527083,0.005242837,0.005864191,0.003430488,0.0002311703,0.001105068,0.6028953,0.0002692232,0.3599769,0.01362747,0.004654748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5592157,0.00406062,0.4216571,0.003205677,0.0005129783,0.004439756,0.0005509132,0.001216261,0.00514106],"genre_scores_gemma":[0.8827995,0.00047957,0.1155532,0.0001771211,0.0001911015,0.0001572882,0.0001202028,0.0002538325,0.0002682078],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4959529,"threshold_uncertainty_score":0.9994877,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1422003151855036,"score_gpt":0.3892662646037301,"score_spread":0.2470659494182265,"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."}}