{"id":"W1964609447","doi":"10.4153/cmb-2009-007-7","title":"Small Zeros of Quadratic Forms Avoiding a Finite Number of Prescribed Hyperplanes","year":2009,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Hyperplane; Exponent; Combinatorics; Quadratic equation; Upper and lower bounds; Polynomial; Finite field; Zero (linguistics); Quadratic function; Discrete mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001418752,0.0007597585,0.001043055,0.001404746,0.001372837,0.002132092,0.001122167,0.0006474094,0.004722083],"category_scores_gemma":[0.00852145,0.0004251131,0.0005378341,0.0004692294,0.003560703,0.003536666,0.002405083,0.001685766,0.0004407945],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009216724,"about_ca_system_score_gemma":0.0003552834,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004909802,"about_ca_topic_score_gemma":0.0004508248,"domain_scores_codex":[0.9990906,0.0001894106,0.0000615524,0.0002059257,0.0002433818,0.0002091621],"domain_scores_gemma":[0.9914334,0.00533749,0.001064485,0.0006711652,0.0005763623,0.0009170583],"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":[0.001000389,0.0001464728,0.01022946,0.0005805056,0.00007184347,0.0007758577,0.0007614091,0.03058116,0.05874281,0.8726711,0.002141158,0.02229784],"study_design_scores_gemma":[0.0001732821,0.0005981688,0.006698759,0.000199808,0.00007486288,0.0009195348,0.0005872822,0.1583286,0.03447619,0.7924506,0.005375131,0.0001176337],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8827438,0.0009353461,0.09889257,0.0005455591,0.0001146889,0.00003940185,0.000123674,0.0001837767,0.0164211],"genre_scores_gemma":[0.9893029,0.0002115532,0.008156243,0.00003848972,0.00008223083,0.00003259746,0.00007549495,0.00003122642,0.002069424],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004722083,"threshold_uncertainty_score":0.01579696,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06025754015233173,"score_gpt":0.3069061562146916,"score_spread":0.2466486160623599,"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."}}