{"id":"W2962729862","doi":"10.1016/j.jnt.2012.05.003","title":"The generalized Erdős–Falconer distance problems in vector spaces over finite fields","year":2012,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Ministry of Education, Science and Technology","keywords":"Mathematics; Cardinality (data modeling); Finite field; Generalization; Diagonal; Exponential function; Combinatorics; Discrete mathematics; Mathematical analysis; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002242511,0.0001689696,0.0003058749,0.0000545672,0.0001792849,0.00005722588,0.0003543634,0.0001180147,0.001094592],"category_scores_gemma":[0.0008269866,0.00009207724,0.0002070126,0.0001389097,0.0001491058,0.0002595963,0.00007897426,0.0004645452,0.000007758235],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004564456,"about_ca_system_score_gemma":0.00002703114,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003499298,"about_ca_topic_score_gemma":0.00002551503,"domain_scores_codex":[0.998239,0.0004384968,0.0005548064,0.00008598126,0.0003126823,0.0003690151],"domain_scores_gemma":[0.9963829,0.002662195,0.0004772011,0.00029774,0.00007700227,0.0001029486],"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":[0.0002204144,0.0001024197,0.01630152,0.00004730367,0.0001324682,0.00001053967,0.004377306,0.00002242129,0.00006075187,0.9647394,0.01277517,0.001210241],"study_design_scores_gemma":[0.0006958917,0.00002889992,0.005210802,0.0001167793,0.00004325469,0.00007313684,0.0003161313,0.00001983855,0.0001134704,0.9419281,0.0512931,0.0001605208],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9802769,0.002686841,0.002904356,0.000409734,0.002076162,0.000199609,0.00001971413,0.00001975624,0.01140687],"genre_scores_gemma":[0.9958187,0.0001910092,0.001221458,0.0002434405,0.0006640499,0.00000654391,6.0348e-7,0.00002738676,0.001826864],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03851794,"threshold_uncertainty_score":0.9998186,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02464609370489775,"score_gpt":0.3005630614611269,"score_spread":0.2759169677562292,"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."}}