{"id":"W2951028670","doi":"10.48550/arxiv.0709.3786","title":"Geometric incidence theorems via Fourier analysis","year":2007,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"3D Shape Modeling and Analysis","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Point (geometry); Incidence (geometry); Fourier transform; Pure mathematics; Fourier analysis; Discrete Fourier transform (general); Mathematical analysis; Geometry; Fractional Fourier transform","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":[0.001748354,0.001078143,0.0007330145,0.003403733,0.0009107712,0.003602059,0.001227272,0.001050657,0.007087182],"category_scores_gemma":[0.007348331,0.0004647579,0.001242878,0.001172099,0.00365594,0.00603118,0.004676566,0.004043096,0.001116218],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001032913,"about_ca_system_score_gemma":0.000314785,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003340957,"about_ca_topic_score_gemma":0.0002729948,"domain_scores_codex":[0.9985595,0.0002660746,0.00007674305,0.000316635,0.0005745671,0.0002064063],"domain_scores_gemma":[0.996509,0.001644098,0.0004438749,0.0005894442,0.0004990502,0.0003144106],"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":[0.000008487067,0.000009450669,0.0002266593,0.00001829226,0.000005536129,0.00004967339,0.00006828938,0.001601001,0.001167881,0.9923719,0.0003710407,0.00410184],"study_design_scores_gemma":[0.000005320727,0.00002186924,0.0003972116,0.00001693609,0.000009818492,0.000214372,0.0000840294,0.03688132,0.002629455,0.9575663,0.002156382,0.00001691554],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1031627,0.0005098149,0.853591,0.000655786,0.0002275574,0.00002913293,0.0001604865,0.0002359595,0.04142745],"genre_scores_gemma":[0.9060267,0.0009470474,0.07951839,0.0003150521,0.0004960514,0.00009392817,0.0002832787,0.000236809,0.01208275],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007087182,"threshold_uncertainty_score":0.02370894,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02745323942830578,"score_gpt":0.2539952594201236,"score_spread":0.2265420199918179,"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."}}