{"id":"W4392616725","doi":"10.1090/proc/17035","title":"Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs","year":2024,"lang":"lv","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Graph theory and applications","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Power (physics); Distribution (mathematics); Mathematics; Combinatorics; Physics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001567455,0.0005792318,0.001540697,0.00008330018,0.0001306167,0.0001048053,0.0008153729,0.0004044843,0.0000715716],"category_scores_gemma":[0.0006161791,0.0004255001,0.001093796,0.001108806,0.002378242,0.0000859856,0.001600084,0.001241928,0.000004476031],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009120713,"about_ca_system_score_gemma":0.00007460812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001081983,"about_ca_topic_score_gemma":0.000004635798,"domain_scores_codex":[0.996593,0.00006842524,0.001504526,0.0007151425,0.0006257465,0.0004931685],"domain_scores_gemma":[0.996847,0.0006657377,0.001577924,0.0004509087,0.0003232452,0.0001351632],"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":[0.0001147702,0.0005800935,0.00450352,0.005207626,0.0004758913,3.266749e-7,0.006644838,7.266e-7,0.00697948,0.9734173,0.001928005,0.0001474106],"study_design_scores_gemma":[0.0003167744,0.0001215668,0.01479668,0.001889324,0.0005990026,0.000007172296,0.002941278,0.0006317894,0.008015697,0.9702451,0.00003909219,0.0003965215],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9949526,0.0003359048,0.0001550498,0.001611272,0.00005067149,0.001140432,0.0002854395,0.00008232015,0.001386294],"genre_scores_gemma":[0.9865292,0.0007139966,0.01220123,0.0001020736,0.00003554262,0.0001878336,0.00001270091,0.00006888459,0.0001485263],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01204618,"threshold_uncertainty_score":0.9998197,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01558101237870558,"score_gpt":0.2875601054928759,"score_spread":0.2719790931141703,"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."}}